diff --git a/CMakeLists.txt b/CMakeLists.txt index ad9678a5a..31454773e 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -100,6 +100,20 @@ set(kademlia_sources logging ) +# -- ed25519 -- +set(ed25519_sources + add_scalar + fe + ge + key_exchange + keypair + sc + seed + sha512 + sign + verify +) + set(includes include) option(shared "build libtorrent as a shared library" ON) @@ -148,6 +162,9 @@ if (dht) foreach(s ${kademlia_sources}) list(APPEND sources2 src/kademlia/${s}) endforeach(s) + foreach(s ${ed25519_sources}) + list(APPEND sources2 ed25519/src/${s}) + endforeach(s) else (dht) add_definitions(-DTORRENT_DISABLE_DHT) endif (dht) diff --git a/Jamfile b/Jamfile index f6ff0740d..aac373b9b 100755 --- a/Jamfile +++ b/Jamfile @@ -565,6 +565,19 @@ KADEMLIA_SOURCES = logging ; +ED25519_SOURCES = + add_scalar + fe + ge + key_exchange + keypair + sc + seed + sha512 + sign + verify + ; + local usage-requirements = ./include ./include/libtorrent @@ -621,6 +634,7 @@ lib torrent src/$(SOURCES).cpp : # requirements + ./ed25519/src multi shared:TORRENT_BUILDING_SHARED @@ -632,6 +646,10 @@ lib torrent on:src/kademlia/$(KADEMLIA_SOURCES).cpp logging:src/kademlia/$(KADEMLIA_SOURCES).cpp + + on:ed25519/src/$(ED25519_SOURCES).c + logging:ed25519/src/$(ED25519_SOURCES).c + @building system:$(CXXFLAGS) diff --git a/Makefile.am b/Makefile.am index 98eec0bed..cc4196b6f 100644 --- a/Makefile.am +++ b/Makefile.am @@ -86,8 +86,6 @@ DOCS_PAGES = \ docs/index.rst \ docs/libtorrent_plugins.html \ docs/libtorrent_plugins.rst \ - docs/make_torrent.html \ - docs/make_torrent.rst \ docs/manual.html \ docs/manual.rst \ docs/projects.html \ @@ -112,8 +110,6 @@ EXTRA_DIST = \ LICENSE \ libtorrent-rasterbar.pc \ libtorrent-rasterbar-cmake.pc \ - parse_dht_log.py \ - parse_session_stats.py \ $(DOCS_PAGES) \ $(DOCS_IMAGES) diff --git a/docs/dht_store.html b/docs/dht_store.html index a1d21e85f..45cdf7af3 100644 --- a/docs/dht_store.html +++ b/docs/dht_store.html @@ -81,7 +81,7 @@ the key is the public key of the key pair used to sign the data.

terminology

In this document, a storage node refers to the node in the DHT to which -an item is being announced and stored on. A subscribing node refers to +an item is being announced and stored on. A requesting node refers to a node which makes look-ups in the DHT to find the storage nodes, to request items from them, and possibly re-announce those items to keep them alive.

@@ -90,15 +90,17 @@ alive.

messages

The proposed new messages get and put are similar to the existing get_peers and announce_peer.

-

Responses to get should always include nodes and nodes6 has the same -semantics as in its get_peers response. It should also include a write token, -token, with the same semantics as get_peers.

+

Responses to get should always include nodes and nodes6. Those fields +have the same semantics as in its get_peers response. It should also include a write token, +token, with the same semantics as int get_peers. The write token MAY be tied +specifically to the key which get requested. i.e. the token can only be used +to store values under that one key.

The id field in these messages has the same semantics as the standard DHT messages, i.e. the node ID of the node sending the message, to maintain the structure of the DHT network.

The token field also has the same semantics as the standard DHT message get_peers and announce_peer, when requesting an item and to write an item respectively.

-

The k field is the PKCS#1 encoded 2048 bit RSA public key, which the signature +

The k field is the 32 byte ed25519 public key, which the signature can be authenticated with. When looking up a mutable item, the target field MUST be the SHA-1 hash of this key.

The distinction between storing mutable and immutable items is the inclusion @@ -113,7 +115,7 @@ its key), its flattened, bencoded, form is used. It is important to use the exac bencoded representation as it appeared in the message. decoding and then re-encoding bencoded structures is not necessarily an identity operation.

Storing nodes SHOULD reject put requests where the bencoded form of v is longer -than 767 bytes.

+than 1000 bytes.

immutable items

@@ -129,7 +131,7 @@ that its hash matches the target that was looked up.

"a": { "id": <20 byte id of sending node (string)>, - "v": <any bencoded type, whose encoded size < 768> + "v": <any bencoded type, whose encoded size <= 1000> }, "t": <transaction-id (string)>, "y": "q", @@ -189,7 +191,7 @@ and a node hosting the list node MUST not downgrade a list head from a higher se number to a lower one, only upgrade. The sequence number SHOULD not exceed MAX_INT64, (i.e. 0x7fffffffffffffff. A client MAY reject any message with a sequence number exceeding this.

-

The signature is a 2048 bit RSA signature of the SHA-1 hash of the bencoded sequence +

The signature is a 64 byte ed25519 signature of the bencoded sequence number and v key. e.g. something like this:: 3:seqi4e1:v12:Hello world!.

put message

@@ -199,19 +201,24 @@ number and v key. e.g. something like this:: < "a": { "id": <20 byte id of sending node (string)>, - "k": <RSA-2048 public key (PKCS#1 encoded)>, + "k": <ed25519 public key (32 bytes string)>, "seq": <monotonically increasing sequence number (integer)>, - "sig": <RSA-2048 signature (256 bytes string)>, + "sig": <ed25519 signature (64 bytes string)>, "token": <write-token (string)>, - "v": <any bencoded type, whose encoded size < 768> + "v": <any bencoded type, whose encoded size < 1000> }, "t": <transaction-id (string)>, "y": "q", "q": "put" } -

Storing nodes receiving a put request where seq is lower than what's already -stored on the node, MUST reject the request.

+

Storing nodes receiving a put request where seq is lower than or equal +to what's already stored on the node, MUST reject the request. If the sequence +number is equal, and the value is also the same, the node SHOULD reset its timeout +counter.

+

Note that this request does not contain a target hash. The target hash under +which this blob is stored is implied by the k argument. The key is +the SHA-1 hash of the key (k).

Response:

 {
@@ -242,13 +249,13 @@ stored on the node, MUST reject the request.

         "r":
         {
                 "id": <20 byte id of sending node (string)>,
-                "k": <RSA-2048 public key (268 bytes string)>,
+                "k": <ed25519 public key (32 bytes string)>,
                 "nodes": <IPv4 nodes close to 'target'>,
                 "nodes6": <IPv6 nodes close to 'target'>,
                 "seq": <monotonically increasing sequence number (integer)>,
-                "sig": <RSA-2048 signature (256 bytes string)>,
+                "sig": <ed25519 signature (64 bytes string)>,
                 "token": <write-token (string)>,
-                "v": <any bencoded type, whose encoded size < 768>
+                "v": <any bencoded type, whose encoded size <= 1000>
         },
         "t": <transaction-id (string)>,
         "y": "r",
@@ -267,12 +274,11 @@ sequence number 1 of value "Hello World!" would be converted to: 3:seq
 In this way it is not possible to convince a node that part of the length is actually part of the
 sequence number even if the parser contains certain bugs. Furthermore it is not possible to have a
 verification failure if a bencoding serializer alters the order of entries in the dictionary.
-
  • hash the concatenated string with SHA-1
    • 
-
  • sign or verify the hash digest.
    • 
+
  • sign or verify the concatenated string
    • 
 
 
    On the storage node, the signature MUST be verified before accepting the store command. The data
 MUST be stored under the SHA-1 hash of the public key (as it appears in the bencoded dict).
    
-
    On the subscribing nodes, the key they get back from a get request MUST be verified to hash
+
    On the requesting nodes, the key they get back from a get request MUST be verified to hash
 to the target ID the lookup was made for, as well as verifying the signature. If any of these fail,
 the response SHOULD be considered invalid.
    diff --git a/docs/dht_store.rst b/docs/dht_store.rst index 77b782c36..28cf4a48e 100644 --- a/docs/dht_store.rst +++ b/docs/dht_store.rst @@ -22,7 +22,7 @@ terminology ----------- In this document, a *storage node* refers to the node in the DHT to which -an item is being announced and stored on. A *subscribing node* refers to +an item is being announced and stored on. A *requesting node* refers to a node which makes look-ups in the DHT to find the storage nodes, to request items from them, and possibly re-announce those items to keep them alive. @@ -33,9 +33,11 @@ messages The proposed new messages ``get`` and ``put`` are similar to the existing ``get_peers`` and ``announce_peer``. -Responses to ``get`` should always include ``nodes`` and ``nodes6`` has the same -semantics as in its ``get_peers`` response. It should also include a write token, -``token``, with the same semantics as ``get_peers``. +Responses to ``get`` should always include ``nodes`` and ``nodes6``. Those fields +have the same semantics as in its ``get_peers`` response. It should also include a write token, +``token``, with the same semantics as int ``get_peers``. The write token MAY be tied +specifically to the key which ``get`` requested. i.e. the ``token`` can only be used +to store values under that one key. The ``id`` field in these messages has the same semantics as the standard DHT messages, i.e. the node ID of the node sending the message, to maintain the structure of the DHT @@ -44,7 +46,7 @@ network. The ``token`` field also has the same semantics as the standard DHT message ``get_peers`` and ``announce_peer``, when requesting an item and to write an item respectively. -The ``k`` field is the PKCS#1 encoded 2048 bit RSA public key, which the signature +The ``k`` field is the 32 byte ed25519 public key, which the signature can be authenticated with. When looking up a mutable item, the ``target`` field MUST be the SHA-1 hash of this key. @@ -63,7 +65,7 @@ bencoded representation as it appeared in the message. decoding and then re-enco bencoded structures is not necessarily an identity operation. Storing nodes SHOULD reject ``put`` requests where the bencoded form of ``v`` is longer -than 767 bytes. +than 1000 bytes. immutable items --------------- @@ -85,7 +87,7 @@ Request: "a": { "id": *<20 byte id of sending node (string)>*, - "v": ** + "v": ** }, "t": **, "y": "q", @@ -153,8 +155,8 @@ number to a lower one, only upgrade. The sequence number SHOULD not exceed ``MAX (i.e. ``0x7fffffffffffffff``. A client MAY reject any message with a sequence number exceeding this. -The signature is a 2048 bit RSA signature of the SHA-1 hash of the bencoded sequence -number and ``v`` key. e.g. something like this:: ``3:seqi4e1:v12:Hello world!``. +The signature is a 64 byte ed25519 signature of the bencoded sequence +number concatenated with the ``v`` key. e.g. something like this:: ``3:seqi4e1:v12:Hello world!``. put message ........... @@ -167,19 +169,25 @@ Request: "a": { "id": *<20 byte id of sending node (string)>*, - "k": **, + "k": **, "seq": **, - "sig": **, + "sig": **, "token": **, - "v": ** + "v": ** }, "t": **, "y": "q", "q": "put" } -Storing nodes receiving a ``put`` request where ``seq`` is lower than what's already -stored on the node, MUST reject the request. +Storing nodes receiving a ``put`` request where ``seq`` is lower than or equal +to what's already stored on the node, MUST reject the request. If the sequence +number is equal, and the value is also the same, the node SHOULD reset its timeout +counter. + +Note that this request does not contain a target hash. The target hash under +which this blob is stored is implied by the ``k`` argument. The key is +the SHA-1 hash of the key (``k``). Response: @@ -217,13 +225,13 @@ Response: "r": { "id": *<20 byte id of sending node (string)>*, - "k": **, + "k": **, "nodes": **, "nodes6": **, "seq": **, - "sig": **, + "sig": **, "token": **, - "v": ** + "v": ** }, "t": **, "y": "r", @@ -241,13 +249,12 @@ value and sequence number should be done as follows: In this way it is not possible to convince a node that part of the length is actually part of the sequence number even if the parser contains certain bugs. Furthermore it is not possible to have a verification failure if a bencoding serializer alters the order of entries in the dictionary. -3. hash the concatenated string with SHA-1 -4. sign or verify the hash digest. +3. sign or verify the concatenated string On the storage node, the signature MUST be verified before accepting the store command. The data MUST be stored under the SHA-1 hash of the public key (as it appears in the bencoded dict). -On the subscribing nodes, the key they get back from a ``get`` request MUST be verified to hash +On the requesting nodes, the key they get back from a ``get`` request MUST be verified to hash to the target ID the lookup was made for, as well as verifying the signature. If any of these fail, the response SHOULD be considered invalid. diff --git a/ed25519/readme.md b/ed25519/readme.md new file mode 100644 index 000000000..b20289277 --- /dev/null +++ b/ed25519/readme.md @@ -0,0 +1,165 @@ +Ed25519 +======= + +This is a portable implementation of [Ed25519](http://ed25519.cr.yp.to/) based +on the SUPERCOP "ref10" implementation. Additionally there is key exchanging +and scalar addition included to further aid building a PKI using Ed25519. All +code is in the public domain. + +All code is pure ANSI C without any dependencies, except for the random seed +generation which uses standard OS cryptography APIs (`CryptGenRandom` on +Windows, `/dev/urandom` on nix). If you wish to be entirely portable define +`ED25519_NO_SEED`. This disables the `ed25519_create_seed` function, so if your +application requires key generation you must supply your own seeding function +(which is simply a 256 bit (32 byte) cryptographic random number generator). + + +Performance +----------- + +On a Windows machine with an Intel Pentium B970 @ 2.3GHz I got the following +speeds (running on only one a single core): + + Seed generation: 64us (15625 per second) + Key generation: 88us (11364 per second) + Message signing (short message): 87us (11494 per second) + Message verifying (short message): 228us (4386 per second) + Scalar addition: 100us (10000 per second) + Key exchange: 220us (4545 per second) + +The speeds on other machines may vary. Sign/verify times will be higher with +longer messages. The implementation significantly benefits from 64 bit +architectures, if possible compile as 64 bit. + + +Usage +----- + +Simply add all .c and .h files in the `src/` folder to your project and include +`ed25519.h` in any file you want to use the API. If you prefer to use a shared +library, only copy `ed25519.h` and define `ED25519_DLL` before importing. A +windows DLL is pre-built. + +There are no defined types for seeds, private keys, public keys, shared secrets +or signatures. Instead simple `unsigned char` buffers are used with the +following sizes: + +```c +unsigned char seed[32]; +unsigned char signature[64]; +unsigned char public_key[32]; +unsigned char private_key[64]; +unsigned char scalar[32]; +unsigned char shared_secret[32]; +``` + +API +--- + +```c +int ed25519_create_seed(unsigned char *seed); +``` + +Creates a 32 byte random seed in `seed` for key generation. `seed` must be a +writable 32 byte buffer. Returns 0 on success, and nonzero on failure. + +```c +void ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed); +``` + +Creates a new key pair from the given seed. `public_key` must be a writable 32 +byte buffer, `private_key` must be a writable 64 byte buffer and `seed` must be +a 32 byte buffer. + +```c +void ed25519_sign(unsigned char *signature, + const unsigned char *message, size_t message_len, + const unsigned char *public_key, const unsigned char *private_key); +``` + +Creates a signature of the given message with the given key pair. `signature` +must be a writable 64 byte buffer. `message` must have at least `message_len` +bytes to be read. + +```c +int ed25519_verify(const unsigned char *signature, + const unsigned char *message, size_t message_len, + const unsigned char *public_key); +``` + +Verifies the signature on the given message using `public_key`. `signature` +must be a readable 64 byte buffer. `message` must have at least `message_len` +bytes to be read. Returns 1 if the signature matches, 0 otherwise. + +```c +void ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, + const unsigned char *scalar); +``` + +Adds `scalar` to the given key pair where scalar is a 32 byte buffer (possibly +generated with `ed25519_create_seed`), generating a new key pair. You can +calculate the public key sum without knowing the private key and vice versa by +passing in `NULL` for the key you don't know. This is useful for enforcing +randomness on a key pair by a third party while only knowing the public key, +among other things. Warning: the last bit of the scalar is ignored - if +comparing scalars make sure to clear it with `scalar[31] &= 127`. + + +```c +void ed25519_key_exchange(unsigned char *shared_secret, + const unsigned char *public_key, const unsigned char *private_key); +``` + +Performs a key exchange on the given public key and private key, producing a +shared secret. It is recommended to hash the shared secret before using it. +`shared_secret` must be a 32 byte writable buffer where the shared secret will +be stored. + +Example +------- + +```c +unsigned char seed[32], public_key[32], private_key[64], signature[64]; +unsigned char other_public_key[32], other_private_key[64], shared_secret[32]; +const unsigned char message[] = "TEST MESSAGE"; + +/* create a random seed, and a key pair out of that seed */ +if (ed25519_create_seed(seed)) { + printf("error while generating seed\n"); + exit(1); +} + +ed25519_create_keypair(public_key, private_key, seed); + +/* create signature on the message with the key pair */ +ed25519_sign(signature, message, strlen(message), public_key, private_key); + +/* verify the signature */ +if (ed25519_verify(signature, message, strlen(message), public_key)) { + printf("valid signature\n"); +} else { + printf("invalid signature\n"); +} + +/* create a dummy keypair to use for a key exchange, normally you'd only have +the public key and receive it through some communication channel */ +if (ed25519_create_seed(seed)) { + printf("error while generating seed\n"); + exit(1); +} + +ed25519_create_keypair(other_public_key, other_private_key, seed); + +/* do a key exchange with other_public_key */ +ed25519_key_exchange(shared_secret, other_public_key, private_key); + +/* + the magic here is that ed25519_key_exchange(shared_secret, public_key, + other_private_key); would result in the same shared_secret +*/ + +``` + +License +------- +All code is in the public domain. diff --git a/ed25519/src/add_scalar.c b/ed25519/src/add_scalar.c new file mode 100644 index 000000000..262ec7251 --- /dev/null +++ b/ed25519/src/add_scalar.c @@ -0,0 +1,56 @@ +#include "ed25519.h" +#include "ge.h" +#include "sc.h" + + +/* see http://crypto.stackexchange.com/a/6215/4697 */ +void ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar) { + const unsigned char SC_1[32] = {1}; /* scalar with value 1 */ + + unsigned char n[32]; + ge_p3 nB; + ge_p1p1 A_p1p1; + ge_p3 A; + ge_p3 public_key_unpacked; + ge_cached T; + + int i; + + /* copy the scalar and clear highest bit */ + for (i = 0; i < 31; ++i) { + n[i] = scalar[i]; + } + n[31] = scalar[31] & 127; + + /* private key: a = n + t */ + if (private_key) { + sc_muladd(private_key, SC_1, n, private_key); + } + + /* public key: A = nB + T */ + if (public_key) { + /* if we know the private key we don't need a point addition, which is faster */ + /* using a "timing attack" you could find out wether or not we know the private + key, but this information seems rather useless - if this is important pass + public_key and private_key seperately in 2 function calls */ + if (private_key) { + ge_scalarmult_base(&A, private_key); + } else { + /* unpack public key into T */ + ge_frombytes_negate_vartime(&public_key_unpacked, public_key); + fe_neg(public_key_unpacked.X, public_key_unpacked.X); // undo negate + fe_neg(public_key_unpacked.T, public_key_unpacked.T); // undo negate + ge_p3_to_cached(&T, &public_key_unpacked); + + /* calculate n*B */ + ge_scalarmult_base(&nB, n); + + /* A = n*B + T */ + ge_add(&A_p1p1, &nB, &T); + ge_p1p1_to_p3(&A, &A_p1p1); + } + + /* pack public key */ + ge_p3_tobytes(public_key, &A); + } +} diff --git a/ed25519/src/ed25519.h b/ed25519/src/ed25519.h new file mode 100644 index 000000000..bb34f893a --- /dev/null +++ b/ed25519/src/ed25519.h @@ -0,0 +1,38 @@ +#ifndef ED25519_H +#define ED25519_H + +#include + +#if defined(_WIN32) + #if defined(ED25519_BUILD_DLL) + #define ED25519_DECLSPEC __declspec(dllexport) + #elif defined(ED25519_DLL) + #define ED25519_DECLSPEC __declspec(dllimport) + #else + #define ED25519_DECLSPEC + #endif +#else + #define ED25519_DECLSPEC +#endif + + +#ifdef __cplusplus +extern "C" { +#endif + +#ifndef ED25519_NO_SEED +int ED25519_DECLSPEC ed25519_create_seed(unsigned char *seed); +#endif + +void ED25519_DECLSPEC ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed); +void ED25519_DECLSPEC ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key); +int ED25519_DECLSPEC ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *private_key); +void ED25519_DECLSPEC ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar); +void ED25519_DECLSPEC ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key); + + +#ifdef __cplusplus +} +#endif + +#endif diff --git a/ed25519/src/fe.c b/ed25519/src/fe.c new file mode 100644 index 000000000..448e3e920 --- /dev/null +++ b/ed25519/src/fe.c @@ -0,0 +1,1491 @@ +#include "fixedint.h" +#include "fe.h" + + +/* + helper functions +*/ +static uint64_t load_3(const unsigned char *in) { + uint64_t result; + + result = (uint64_t) in[0]; + result |= ((uint64_t) in[1]) << 8; + result |= ((uint64_t) in[2]) << 16; + + return result; +} + +static uint64_t load_4(const unsigned char *in) { + uint64_t result; + + result = (uint64_t) in[0]; + result |= ((uint64_t) in[1]) << 8; + result |= ((uint64_t) in[2]) << 16; + result |= ((uint64_t) in[3]) << 24; + + return result; +} + + + +/* + h = 0 +*/ + +void fe_0(fe h) { + h[0] = 0; + h[1] = 0; + h[2] = 0; + h[3] = 0; + h[4] = 0; + h[5] = 0; + h[6] = 0; + h[7] = 0; + h[8] = 0; + h[9] = 0; +} + + + +/* + h = 1 +*/ + +void fe_1(fe h) { + h[0] = 1; + h[1] = 0; + h[2] = 0; + h[3] = 0; + h[4] = 0; + h[5] = 0; + h[6] = 0; + h[7] = 0; + h[8] = 0; + h[9] = 0; +} + + + +/* + h = f + g + Can overlap h with f or g. + + Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + + Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +void fe_add(fe h, const fe f, const fe g) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t h0 = f0 + g0; + int32_t h1 = f1 + g1; + int32_t h2 = f2 + g2; + int32_t h3 = f3 + g3; + int32_t h4 = f4 + g4; + int32_t h5 = f5 + g5; + int32_t h6 = f6 + g6; + int32_t h7 = f7 + g7; + int32_t h8 = f8 + g8; + int32_t h9 = f9 + g9; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + + + +/* + Replace (f,g) with (g,g) if b == 1; + replace (f,g) with (f,g) if b == 0. + + Preconditions: b in {0,1}. +*/ + +void fe_cmov(fe f, const fe g, unsigned int b) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t x0 = f0 ^ g0; + int32_t x1 = f1 ^ g1; + int32_t x2 = f2 ^ g2; + int32_t x3 = f3 ^ g3; + int32_t x4 = f4 ^ g4; + int32_t x5 = f5 ^ g5; + int32_t x6 = f6 ^ g6; + int32_t x7 = f7 ^ g7; + int32_t x8 = f8 ^ g8; + int32_t x9 = f9 ^ g9; + + b = (unsigned int) (- (int) b); /* silence warning */ + x0 &= b; + x1 &= b; + x2 &= b; + x3 &= b; + x4 &= b; + x5 &= b; + x6 &= b; + x7 &= b; + x8 &= b; + x9 &= b; + + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; + f[5] = f5 ^ x5; + f[6] = f6 ^ x6; + f[7] = f7 ^ x7; + f[8] = f8 ^ x8; + f[9] = f9 ^ x9; +} + +/* + Replace (f,g) with (g,f) if b == 1; + replace (f,g) with (f,g) if b == 0. + + Preconditions: b in {0,1}. +*/ + +void fe_cswap(fe f,fe g,unsigned int b) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t x0 = f0 ^ g0; + int32_t x1 = f1 ^ g1; + int32_t x2 = f2 ^ g2; + int32_t x3 = f3 ^ g3; + int32_t x4 = f4 ^ g4; + int32_t x5 = f5 ^ g5; + int32_t x6 = f6 ^ g6; + int32_t x7 = f7 ^ g7; + int32_t x8 = f8 ^ g8; + int32_t x9 = f9 ^ g9; + b = -b; + x0 &= b; + x1 &= b; + x2 &= b; + x3 &= b; + x4 &= b; + x5 &= b; + x6 &= b; + x7 &= b; + x8 &= b; + x9 &= b; + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; + f[5] = f5 ^ x5; + f[6] = f6 ^ x6; + f[7] = f7 ^ x7; + f[8] = f8 ^ x8; + f[9] = f9 ^ x9; + g[0] = g0 ^ x0; + g[1] = g1 ^ x1; + g[2] = g2 ^ x2; + g[3] = g3 ^ x3; + g[4] = g4 ^ x4; + g[5] = g5 ^ x5; + g[6] = g6 ^ x6; + g[7] = g7 ^ x7; + g[8] = g8 ^ x8; + g[9] = g9 ^ x9; +} + + + +/* + h = f +*/ + +void fe_copy(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + h[0] = f0; + h[1] = f1; + h[2] = f2; + h[3] = f3; + h[4] = f4; + h[5] = f5; + h[6] = f6; + h[7] = f7; + h[8] = f8; + h[9] = f9; +} + + + +/* + Ignores top bit of h. +*/ + +void fe_frombytes(fe h, const unsigned char *s) { + int64_t h0 = load_4(s); + int64_t h1 = load_3(s + 4) << 6; + int64_t h2 = load_3(s + 7) << 5; + int64_t h3 = load_3(s + 10) << 3; + int64_t h4 = load_3(s + 13) << 2; + int64_t h5 = load_4(s + 16); + int64_t h6 = load_3(s + 20) << 7; + int64_t h7 = load_3(s + 23) << 5; + int64_t h8 = load_3(s + 26) << 4; + int64_t h9 = (load_3(s + 29) & 8388607) << 2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = (h9 + (int64_t) (1 << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 << 25; + carry1 = (h1 + (int64_t) (1 << 24)) >> 25; + h2 += carry1; + h1 -= carry1 << 25; + carry3 = (h3 + (int64_t) (1 << 24)) >> 25; + h4 += carry3; + h3 -= carry3 << 25; + carry5 = (h5 + (int64_t) (1 << 24)) >> 25; + h6 += carry5; + h5 -= carry5 << 25; + carry7 = (h7 + (int64_t) (1 << 24)) >> 25; + h8 += carry7; + h7 -= carry7 << 25; + carry0 = (h0 + (int64_t) (1 << 25)) >> 26; + h1 += carry0; + h0 -= carry0 << 26; + carry2 = (h2 + (int64_t) (1 << 25)) >> 26; + h3 += carry2; + h2 -= carry2 << 26; + carry4 = (h4 + (int64_t) (1 << 25)) >> 26; + h5 += carry4; + h4 -= carry4 << 26; + carry6 = (h6 + (int64_t) (1 << 25)) >> 26; + h7 += carry6; + h6 -= carry6 << 26; + carry8 = (h8 + (int64_t) (1 << 25)) >> 26; + h9 += carry8; + h8 -= carry8 << 26; + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + + + +void fe_invert(fe out, const fe z) { + fe t0; + fe t1; + fe t2; + fe t3; + int i; + + fe_sq(t0, z); + + for (i = 1; i < 1; ++i) { + fe_sq(t0, t0); + } + + fe_sq(t1, t0); + + for (i = 1; i < 2; ++i) { + fe_sq(t1, t1); + } + + fe_mul(t1, z, t1); + fe_mul(t0, t0, t1); + fe_sq(t2, t0); + + for (i = 1; i < 1; ++i) { + fe_sq(t2, t2); + } + + fe_mul(t1, t1, t2); + fe_sq(t2, t1); + + for (i = 1; i < 5; ++i) { + fe_sq(t2, t2); + } + + fe_mul(t1, t2, t1); + fe_sq(t2, t1); + + for (i = 1; i < 10; ++i) { + fe_sq(t2, t2); + } + + fe_mul(t2, t2, t1); + fe_sq(t3, t2); + + for (i = 1; i < 20; ++i) { + fe_sq(t3, t3); + } + + fe_mul(t2, t3, t2); + fe_sq(t2, t2); + + for (i = 1; i < 10; ++i) { + fe_sq(t2, t2); + } + + fe_mul(t1, t2, t1); + fe_sq(t2, t1); + + for (i = 1; i < 50; ++i) { + fe_sq(t2, t2); + } + + fe_mul(t2, t2, t1); + fe_sq(t3, t2); + + for (i = 1; i < 100; ++i) { + fe_sq(t3, t3); + } + + fe_mul(t2, t3, t2); + fe_sq(t2, t2); + + for (i = 1; i < 50; ++i) { + fe_sq(t2, t2); + } + + fe_mul(t1, t2, t1); + fe_sq(t1, t1); + + for (i = 1; i < 5; ++i) { + fe_sq(t1, t1); + } + + fe_mul(out, t1, t0); +} + + + +/* + return 1 if f is in {1,3,5,...,q-2} + return 0 if f is in {0,2,4,...,q-1} + + Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +int fe_isnegative(const fe f) { + unsigned char s[32]; + + fe_tobytes(s, f); + + return s[0] & 1; +} + + + +/* + return 1 if f == 0 + return 0 if f != 0 + + Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +int fe_isnonzero(const fe f) { + unsigned char s[32]; + unsigned char r; + + fe_tobytes(s, f); + + r = s[0]; + #define F(i) r |= s[i] + F(1); + F(2); + F(3); + F(4); + F(5); + F(6); + F(7); + F(8); + F(9); + F(10); + F(11); + F(12); + F(13); + F(14); + F(15); + F(16); + F(17); + F(18); + F(19); + F(20); + F(21); + F(22); + F(23); + F(24); + F(25); + F(26); + F(27); + F(28); + F(29); + F(30); + F(31); + #undef F + + return r != 0; +} + + + +/* + h = f * g + Can overlap h with f or g. + + Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + + Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + */ + + /* + Notes on implementation strategy: + + Using schoolbook multiplication. + Karatsuba would save a little in some cost models. + + Most multiplications by 2 and 19 are 32-bit precomputations; + cheaper than 64-bit postcomputations. + + There is one remaining multiplication by 19 in the carry chain; + one *19 precomputation can be merged into this, + but the resulting data flow is considerably less clean. + + There are 12 carries below. + 10 of them are 2-way parallelizable and vectorizable. + Can get away with 11 carries, but then data flow is much deeper. + + With tighter constraints on inputs can squeeze carries into int32. +*/ + +void fe_mul(fe h, const fe f, const fe g) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ + int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ + int32_t g3_19 = 19 * g3; + int32_t g4_19 = 19 * g4; + int32_t g5_19 = 19 * g5; + int32_t g6_19 = 19 * g6; + int32_t g7_19 = 19 * g7; + int32_t g8_19 = 19 * g8; + int32_t g9_19 = 19 * g9; + int32_t f1_2 = 2 * f1; + int32_t f3_2 = 2 * f3; + int32_t f5_2 = 2 * f5; + int32_t f7_2 = 2 * f7; + int32_t f9_2 = 2 * f9; + int64_t f0g0 = f0 * (int64_t) g0; + int64_t f0g1 = f0 * (int64_t) g1; + int64_t f0g2 = f0 * (int64_t) g2; + int64_t f0g3 = f0 * (int64_t) g3; + int64_t f0g4 = f0 * (int64_t) g4; + int64_t f0g5 = f0 * (int64_t) g5; + int64_t f0g6 = f0 * (int64_t) g6; + int64_t f0g7 = f0 * (int64_t) g7; + int64_t f0g8 = f0 * (int64_t) g8; + int64_t f0g9 = f0 * (int64_t) g9; + int64_t f1g0 = f1 * (int64_t) g0; + int64_t f1g1_2 = f1_2 * (int64_t) g1; + int64_t f1g2 = f1 * (int64_t) g2; + int64_t f1g3_2 = f1_2 * (int64_t) g3; + int64_t f1g4 = f1 * (int64_t) g4; + int64_t f1g5_2 = f1_2 * (int64_t) g5; + int64_t f1g6 = f1 * (int64_t) g6; + int64_t f1g7_2 = f1_2 * (int64_t) g7; + int64_t f1g8 = f1 * (int64_t) g8; + int64_t f1g9_38 = f1_2 * (int64_t) g9_19; + int64_t f2g0 = f2 * (int64_t) g0; + int64_t f2g1 = f2 * (int64_t) g1; + int64_t f2g2 = f2 * (int64_t) g2; + int64_t f2g3 = f2 * (int64_t) g3; + int64_t f2g4 = f2 * (int64_t) g4; + int64_t f2g5 = f2 * (int64_t) g5; + int64_t f2g6 = f2 * (int64_t) g6; + int64_t f2g7 = f2 * (int64_t) g7; + int64_t f2g8_19 = f2 * (int64_t) g8_19; + int64_t f2g9_19 = f2 * (int64_t) g9_19; + int64_t f3g0 = f3 * (int64_t) g0; + int64_t f3g1_2 = f3_2 * (int64_t) g1; + int64_t f3g2 = f3 * (int64_t) g2; + int64_t f3g3_2 = f3_2 * (int64_t) g3; + int64_t f3g4 = f3 * (int64_t) g4; + int64_t f3g5_2 = f3_2 * (int64_t) g5; + int64_t f3g6 = f3 * (int64_t) g6; + int64_t f3g7_38 = f3_2 * (int64_t) g7_19; + int64_t f3g8_19 = f3 * (int64_t) g8_19; + int64_t f3g9_38 = f3_2 * (int64_t) g9_19; + int64_t f4g0 = f4 * (int64_t) g0; + int64_t f4g1 = f4 * (int64_t) g1; + int64_t f4g2 = f4 * (int64_t) g2; + int64_t f4g3 = f4 * (int64_t) g3; + int64_t f4g4 = f4 * (int64_t) g4; + int64_t f4g5 = f4 * (int64_t) g5; + int64_t f4g6_19 = f4 * (int64_t) g6_19; + int64_t f4g7_19 = f4 * (int64_t) g7_19; + int64_t f4g8_19 = f4 * (int64_t) g8_19; + int64_t f4g9_19 = f4 * (int64_t) g9_19; + int64_t f5g0 = f5 * (int64_t) g0; + int64_t f5g1_2 = f5_2 * (int64_t) g1; + int64_t f5g2 = f5 * (int64_t) g2; + int64_t f5g3_2 = f5_2 * (int64_t) g3; + int64_t f5g4 = f5 * (int64_t) g4; + int64_t f5g5_38 = f5_2 * (int64_t) g5_19; + int64_t f5g6_19 = f5 * (int64_t) g6_19; + int64_t f5g7_38 = f5_2 * (int64_t) g7_19; + int64_t f5g8_19 = f5 * (int64_t) g8_19; + int64_t f5g9_38 = f5_2 * (int64_t) g9_19; + int64_t f6g0 = f6 * (int64_t) g0; + int64_t f6g1 = f6 * (int64_t) g1; + int64_t f6g2 = f6 * (int64_t) g2; + int64_t f6g3 = f6 * (int64_t) g3; + int64_t f6g4_19 = f6 * (int64_t) g4_19; + int64_t f6g5_19 = f6 * (int64_t) g5_19; + int64_t f6g6_19 = f6 * (int64_t) g6_19; + int64_t f6g7_19 = f6 * (int64_t) g7_19; + int64_t f6g8_19 = f6 * (int64_t) g8_19; + int64_t f6g9_19 = f6 * (int64_t) g9_19; + int64_t f7g0 = f7 * (int64_t) g0; + int64_t f7g1_2 = f7_2 * (int64_t) g1; + int64_t f7g2 = f7 * (int64_t) g2; + int64_t f7g3_38 = f7_2 * (int64_t) g3_19; + int64_t f7g4_19 = f7 * (int64_t) g4_19; + int64_t f7g5_38 = f7_2 * (int64_t) g5_19; + int64_t f7g6_19 = f7 * (int64_t) g6_19; + int64_t f7g7_38 = f7_2 * (int64_t) g7_19; + int64_t f7g8_19 = f7 * (int64_t) g8_19; + int64_t f7g9_38 = f7_2 * (int64_t) g9_19; + int64_t f8g0 = f8 * (int64_t) g0; + int64_t f8g1 = f8 * (int64_t) g1; + int64_t f8g2_19 = f8 * (int64_t) g2_19; + int64_t f8g3_19 = f8 * (int64_t) g3_19; + int64_t f8g4_19 = f8 * (int64_t) g4_19; + int64_t f8g5_19 = f8 * (int64_t) g5_19; + int64_t f8g6_19 = f8 * (int64_t) g6_19; + int64_t f8g7_19 = f8 * (int64_t) g7_19; + int64_t f8g8_19 = f8 * (int64_t) g8_19; + int64_t f8g9_19 = f8 * (int64_t) g9_19; + int64_t f9g0 = f9 * (int64_t) g0; + int64_t f9g1_38 = f9_2 * (int64_t) g1_19; + int64_t f9g2_19 = f9 * (int64_t) g2_19; + int64_t f9g3_38 = f9_2 * (int64_t) g3_19; + int64_t f9g4_19 = f9 * (int64_t) g4_19; + int64_t f9g5_38 = f9_2 * (int64_t) g5_19; + int64_t f9g6_19 = f9 * (int64_t) g6_19; + int64_t f9g7_38 = f9_2 * (int64_t) g7_19; + int64_t f9g8_19 = f9 * (int64_t) g8_19; + int64_t f9g9_38 = f9_2 * (int64_t) g9_19; + int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38; + int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19; + int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38; + int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19; + int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38; + int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19; + int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38; + int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19; + int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38; + int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry0 = (h0 + (int64_t) (1 << 25)) >> 26; + h1 += carry0; + h0 -= carry0 << 26; + carry4 = (h4 + (int64_t) (1 << 25)) >> 26; + h5 += carry4; + h4 -= carry4 << 26; + + carry1 = (h1 + (int64_t) (1 << 24)) >> 25; + h2 += carry1; + h1 -= carry1 << 25; + carry5 = (h5 + (int64_t) (1 << 24)) >> 25; + h6 += carry5; + h5 -= carry5 << 25; + + carry2 = (h2 + (int64_t) (1 << 25)) >> 26; + h3 += carry2; + h2 -= carry2 << 26; + carry6 = (h6 + (int64_t) (1 << 25)) >> 26; + h7 += carry6; + h6 -= carry6 << 26; + + carry3 = (h3 + (int64_t) (1 << 24)) >> 25; + h4 += carry3; + h3 -= carry3 << 25; + carry7 = (h7 + (int64_t) (1 << 24)) >> 25; + h8 += carry7; + h7 -= carry7 << 25; + + carry4 = (h4 + (int64_t) (1 << 25)) >> 26; + h5 += carry4; + h4 -= carry4 << 26; + carry8 = (h8 + (int64_t) (1 << 25)) >> 26; + h9 += carry8; + h8 -= carry8 << 26; + + carry9 = (h9 + (int64_t) (1 << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 << 25; + + carry0 = (h0 + (int64_t) (1 << 25)) >> 26; + h1 += carry0; + h0 -= carry0 << 26; + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + + +/* +h = f * 121666 +Can overlap h with f. + +Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + +Postconditions: + |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +*/ + +void fe_mul121666(fe h, fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int64_t h0 = f0 * (int64_t) 121666; + int64_t h1 = f1 * (int64_t) 121666; + int64_t h2 = f2 * (int64_t) 121666; + int64_t h3 = f3 * (int64_t) 121666; + int64_t h4 = f4 * (int64_t) 121666; + int64_t h5 = f5 * (int64_t) 121666; + int64_t h6 = f6 * (int64_t) 121666; + int64_t h7 = f7 * (int64_t) 121666; + int64_t h8 = f8 * (int64_t) 121666; + int64_t h9 = f9 * (int64_t) 121666; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + + +/* +h = -f + +Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Postconditions: + |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +*/ + +void fe_neg(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t h0 = -f0; + int32_t h1 = -f1; + int32_t h2 = -f2; + int32_t h3 = -f3; + int32_t h4 = -f4; + int32_t h5 = -f5; + int32_t h6 = -f6; + int32_t h7 = -f7; + int32_t h8 = -f8; + int32_t h9 = -f9; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + + +void fe_pow22523(fe out, const fe z) { + fe t0; + fe t1; + fe t2; + int i; + fe_sq(t0, z); + + for (i = 1; i < 1; ++i) { + fe_sq(t0, t0); + } + + fe_sq(t1, t0); + + for (i = 1; i < 2; ++i) { + fe_sq(t1, t1); + } + + fe_mul(t1, z, t1); + fe_mul(t0, t0, t1); + fe_sq(t0, t0); + + for (i = 1; i < 1; ++i) { + fe_sq(t0, t0); + } + + fe_mul(t0, t1, t0); + fe_sq(t1, t0); + + for (i = 1; i < 5; ++i) { + fe_sq(t1, t1); + } + + fe_mul(t0, t1, t0); + fe_sq(t1, t0); + + for (i = 1; i < 10; ++i) { + fe_sq(t1, t1); + } + + fe_mul(t1, t1, t0); + fe_sq(t2, t1); + + for (i = 1; i < 20; ++i) { + fe_sq(t2, t2); + } + + fe_mul(t1, t2, t1); + fe_sq(t1, t1); + + for (i = 1; i < 10; ++i) { + fe_sq(t1, t1); + } + + fe_mul(t0, t1, t0); + fe_sq(t1, t0); + + for (i = 1; i < 50; ++i) { + fe_sq(t1, t1); + } + + fe_mul(t1, t1, t0); + fe_sq(t2, t1); + + for (i = 1; i < 100; ++i) { + fe_sq(t2, t2); + } + + fe_mul(t1, t2, t1); + fe_sq(t1, t1); + + for (i = 1; i < 50; ++i) { + fe_sq(t1, t1); + } + + fe_mul(t0, t1, t0); + fe_sq(t0, t0); + + for (i = 1; i < 2; ++i) { + fe_sq(t0, t0); + } + + fe_mul(out, t0, z); + return; +} + + +/* +h = f * f +Can overlap h with f. + +Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + +Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. +*/ + +/* +See fe_mul.c for discussion of implementation strategy. +*/ + +void fe_sq(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; + int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; + int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; + int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; + int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; + int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; + int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; + int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; + int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; + int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + carry0 = (h0 + (int64_t) (1 << 25)) >> 26; + h1 += carry0; + h0 -= carry0 << 26; + carry4 = (h4 + (int64_t) (1 << 25)) >> 26; + h5 += carry4; + h4 -= carry4 << 26; + carry1 = (h1 + (int64_t) (1 << 24)) >> 25; + h2 += carry1; + h1 -= carry1 << 25; + carry5 = (h5 + (int64_t) (1 << 24)) >> 25; + h6 += carry5; + h5 -= carry5 << 25; + carry2 = (h2 + (int64_t) (1 << 25)) >> 26; + h3 += carry2; + h2 -= carry2 << 26; + carry6 = (h6 + (int64_t) (1 << 25)) >> 26; + h7 += carry6; + h6 -= carry6 << 26; + carry3 = (h3 + (int64_t) (1 << 24)) >> 25; + h4 += carry3; + h3 -= carry3 << 25; + carry7 = (h7 + (int64_t) (1 << 24)) >> 25; + h8 += carry7; + h7 -= carry7 << 25; + carry4 = (h4 + (int64_t) (1 << 25)) >> 26; + h5 += carry4; + h4 -= carry4 << 26; + carry8 = (h8 + (int64_t) (1 << 25)) >> 26; + h9 += carry8; + h8 -= carry8 << 26; + carry9 = (h9 + (int64_t) (1 << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 << 25; + carry0 = (h0 + (int64_t) (1 << 25)) >> 26; + h1 += carry0; + h0 -= carry0 << 26; + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + + +/* +h = 2 * f * f +Can overlap h with f. + +Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + +Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. +*/ + +/* +See fe_mul.c for discussion of implementation strategy. +*/ + +void fe_sq2(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; + int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; + int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; + int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; + int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; + int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; + int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; + int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; + int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; + int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + h0 += h0; + h1 += h1; + h2 += h2; + h3 += h3; + h4 += h4; + h5 += h5; + h6 += h6; + h7 += h7; + h8 += h8; + h9 += h9; + carry0 = (h0 + (int64_t) (1 << 25)) >> 26; + h1 += carry0; + h0 -= carry0 << 26; + carry4 = (h4 + (int64_t) (1 << 25)) >> 26; + h5 += carry4; + h4 -= carry4 << 26; + carry1 = (h1 + (int64_t) (1 << 24)) >> 25; + h2 += carry1; + h1 -= carry1 << 25; + carry5 = (h5 + (int64_t) (1 << 24)) >> 25; + h6 += carry5; + h5 -= carry5 << 25; + carry2 = (h2 + (int64_t) (1 << 25)) >> 26; + h3 += carry2; + h2 -= carry2 << 26; + carry6 = (h6 + (int64_t) (1 << 25)) >> 26; + h7 += carry6; + h6 -= carry6 << 26; + carry3 = (h3 + (int64_t) (1 << 24)) >> 25; + h4 += carry3; + h3 -= carry3 << 25; + carry7 = (h7 + (int64_t) (1 << 24)) >> 25; + h8 += carry7; + h7 -= carry7 << 25; + carry4 = (h4 + (int64_t) (1 << 25)) >> 26; + h5 += carry4; + h4 -= carry4 << 26; + carry8 = (h8 + (int64_t) (1 << 25)) >> 26; + h9 += carry8; + h8 -= carry8 << 26; + carry9 = (h9 + (int64_t) (1 << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 << 25; + carry0 = (h0 + (int64_t) (1 << 25)) >> 26; + h1 += carry0; + h0 -= carry0 << 26; + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + + +/* +h = f - g +Can overlap h with f or g. + +Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +void fe_sub(fe h, const fe f, const fe g) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t h0 = f0 - g0; + int32_t h1 = f1 - g1; + int32_t h2 = f2 - g2; + int32_t h3 = f3 - g3; + int32_t h4 = f4 - g4; + int32_t h5 = f5 - g5; + int32_t h6 = f6 - g6; + int32_t h7 = f7 - g7; + int32_t h8 = f8 - g8; + int32_t h9 = f9 - g9; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + + + +/* +Preconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + +Write p=2^255-19; q=floor(h/p). +Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). + +Proof: + Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. + Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. + + Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). + Then 0> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + carry0 = h0 >> 26; + h1 += carry0; + h0 -= carry0 << 26; + carry1 = h1 >> 25; + h2 += carry1; + h1 -= carry1 << 25; + carry2 = h2 >> 26; + h3 += carry2; + h2 -= carry2 << 26; + carry3 = h3 >> 25; + h4 += carry3; + h3 -= carry3 << 25; + carry4 = h4 >> 26; + h5 += carry4; + h4 -= carry4 << 26; + carry5 = h5 >> 25; + h6 += carry5; + h5 -= carry5 << 25; + carry6 = h6 >> 26; + h7 += carry6; + h6 -= carry6 << 26; + carry7 = h7 >> 25; + h8 += carry7; + h7 -= carry7 << 25; + carry8 = h8 >> 26; + h9 += carry8; + h8 -= carry8 << 26; + carry9 = h9 >> 25; + h9 -= carry9 << 25; + + /* h10 = carry9 */ + /* + Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + Have h0+...+2^230 h9 between 0 and 2^255-1; + evidently 2^255 h10-2^255 q = 0. + Goal: Output h0+...+2^230 h9. + */ + s[0] = (unsigned char) (h0 >> 0); + s[1] = (unsigned char) (h0 >> 8); + s[2] = (unsigned char) (h0 >> 16); + s[3] = (unsigned char) ((h0 >> 24) | (h1 << 2)); + s[4] = (unsigned char) (h1 >> 6); + s[5] = (unsigned char) (h1 >> 14); + s[6] = (unsigned char) ((h1 >> 22) | (h2 << 3)); + s[7] = (unsigned char) (h2 >> 5); + s[8] = (unsigned char) (h2 >> 13); + s[9] = (unsigned char) ((h2 >> 21) | (h3 << 5)); + s[10] = (unsigned char) (h3 >> 3); + s[11] = (unsigned char) (h3 >> 11); + s[12] = (unsigned char) ((h3 >> 19) | (h4 << 6)); + s[13] = (unsigned char) (h4 >> 2); + s[14] = (unsigned char) (h4 >> 10); + s[15] = (unsigned char) (h4 >> 18); + s[16] = (unsigned char) (h5 >> 0); + s[17] = (unsigned char) (h5 >> 8); + s[18] = (unsigned char) (h5 >> 16); + s[19] = (unsigned char) ((h5 >> 24) | (h6 << 1)); + s[20] = (unsigned char) (h6 >> 7); + s[21] = (unsigned char) (h6 >> 15); + s[22] = (unsigned char) ((h6 >> 23) | (h7 << 3)); + s[23] = (unsigned char) (h7 >> 5); + s[24] = (unsigned char) (h7 >> 13); + s[25] = (unsigned char) ((h7 >> 21) | (h8 << 4)); + s[26] = (unsigned char) (h8 >> 4); + s[27] = (unsigned char) (h8 >> 12); + s[28] = (unsigned char) ((h8 >> 20) | (h9 << 6)); + s[29] = (unsigned char) (h9 >> 2); + s[30] = (unsigned char) (h9 >> 10); + s[31] = (unsigned char) (h9 >> 18); +} diff --git a/ed25519/src/fe.h b/ed25519/src/fe.h new file mode 100644 index 000000000..b4b62d282 --- /dev/null +++ b/ed25519/src/fe.h @@ -0,0 +1,41 @@ +#ifndef FE_H +#define FE_H + +#include "fixedint.h" + + +/* + fe means field element. + Here the field is \Z/(2^255-19). + An element t, entries t[0]...t[9], represents the integer + t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9]. + Bounds on each t[i] vary depending on context. +*/ + + +typedef int32_t fe[10]; + + +void fe_0(fe h); +void fe_1(fe h); + +void fe_frombytes(fe h, const unsigned char *s); +void fe_tobytes(unsigned char *s, const fe h); + +void fe_copy(fe h, const fe f); +int fe_isnegative(const fe f); +int fe_isnonzero(const fe f); +void fe_cmov(fe f, const fe g, unsigned int b); +void fe_cswap(fe f, fe g, unsigned int b); + +void fe_neg(fe h, const fe f); +void fe_add(fe h, const fe f, const fe g); +void fe_invert(fe out, const fe z); +void fe_sq(fe h, const fe f); +void fe_sq2(fe h, const fe f); +void fe_mul(fe h, const fe f, const fe g); +void fe_mul121666(fe h, fe f); +void fe_pow22523(fe out, const fe z); +void fe_sub(fe h, const fe f, const fe g); + +#endif diff --git a/ed25519/src/fixedint.h b/ed25519/src/fixedint.h new file mode 100644 index 000000000..81bc550cb --- /dev/null +++ b/ed25519/src/fixedint.h @@ -0,0 +1,72 @@ +/* + Portable header to provide the 32 and 64 bits type. + + Not a compatible replacement for , do not blindly use it as such. +*/ + +#if ((defined(__STDC__) && __STDC__ && __STDC_VERSION__ >= 199901L) || (defined(__WATCOMC__) && (defined(_STDINT_H_INCLUDED) || __WATCOMC__ >= 1250)) || (defined(__GNUC__) && (defined(_STDINT_H) || defined(_STDINT_H_) || defined(__UINT_FAST64_TYPE__)) )) && !defined(FIXEDINT_H_INCLUDED) + #include + #define FIXEDINT_H_INCLUDED + + #if defined(__WATCOMC__) && __WATCOMC__ >= 1250 && !defined(UINT64_C) + #include + #define UINT64_C(x) (x + (UINT64_MAX - UINT64_MAX)) + #endif +#endif + + +#ifndef FIXEDINT_H_INCLUDED + #define FIXEDINT_H_INCLUDED + + #include + + /* (u)int32_t */ + #ifndef uint32_t + #if (ULONG_MAX == 0xffffffffUL) + typedef unsigned long uint32_t; + #elif (UINT_MAX == 0xffffffffUL) + typedef unsigned int uint32_t; + #elif (USHRT_MAX == 0xffffffffUL) + typedef unsigned short uint32_t; + #endif + #endif + + + #ifndef int32_t + #if (LONG_MAX == 0x7fffffffL) + typedef signed long int32_t; + #elif (INT_MAX == 0x7fffffffL) + typedef signed int int32_t; + #elif (SHRT_MAX == 0x7fffffffL) + typedef signed short int32_t; + #endif + #endif + + + /* (u)int64_t */ + #if (defined(__STDC__) && defined(__STDC_VERSION__) && __STDC__ && __STDC_VERSION__ >= 199901L) + typedef long long int64_t; + typedef unsigned long long uint64_t; + + #define UINT64_C(v) v ##ULL + #define INT64_C(v) v ##LL + #elif defined(__GNUC__) + __extension__ typedef long long int64_t; + __extension__ typedef unsigned long long uint64_t; + + #define UINT64_C(v) v ##ULL + #define INT64_C(v) v ##LL + #elif defined(__MWERKS__) || defined(__SUNPRO_C) || defined(__SUNPRO_CC) || defined(__APPLE_CC__) || defined(_LONG_LONG) || defined(_CRAYC) + typedef long long int64_t; + typedef unsigned long long uint64_t; + + #define UINT64_C(v) v ##ULL + #define INT64_C(v) v ##LL + #elif (defined(__WATCOMC__) && defined(__WATCOM_INT64__)) || (defined(_MSC_VER) && _INTEGRAL_MAX_BITS >= 64) || (defined(__BORLANDC__) && __BORLANDC__ > 0x460) || defined(__alpha) || defined(__DECC) + typedef __int64 int64_t; + typedef unsigned __int64 uint64_t; + + #define UINT64_C(v) v ##UI64 + #define INT64_C(v) v ##I64 + #endif +#endif diff --git a/ed25519/src/ge.c b/ed25519/src/ge.c new file mode 100644 index 000000000..3c342b1d2 --- /dev/null +++ b/ed25519/src/ge.c @@ -0,0 +1,467 @@ +#include "ge.h" +#include "precomp_data.h" + + +/* +r = p + q +*/ + +void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { + fe t0; + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->YplusX); + fe_mul(r->Y, r->Y, q->YminusX); + fe_mul(r->T, q->T2d, p->T); + fe_mul(r->X, p->Z, q->Z); + fe_add(t0, r->X, r->X); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_add(r->Z, t0, r->T); + fe_sub(r->T, t0, r->T); +} + + +static void slide(signed char *r, const unsigned char *a) { + int i; + int b; + int k; + + for (i = 0; i < 256; ++i) { + r[i] = 1 & (a[i >> 3] >> (i & 7)); + } + + for (i = 0; i < 256; ++i) + if (r[i]) { + for (b = 1; b <= 6 && i + b < 256; ++b) { + if (r[i + b]) { + if (r[i] + (r[i + b] << b) <= 15) { + r[i] += r[i + b] << b; + r[i + b] = 0; + } else if (r[i] - (r[i + b] << b) >= -15) { + r[i] -= r[i + b] << b; + + for (k = i + b; k < 256; ++k) { + if (!r[k]) { + r[k] = 1; + break; + } + + r[k] = 0; + } + } else { + break; + } + } + } + } +} + +/* +r = a * A + b * B +where a = a[0]+256*a[1]+...+256^31 a[31]. +and b = b[0]+256*b[1]+...+256^31 b[31]. +B is the Ed25519 base point (x,4/5) with x positive. +*/ + +void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) { + signed char aslide[256]; + signed char bslide[256]; + ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ + ge_p1p1 t; + ge_p3 u; + ge_p3 A2; + int i; + slide(aslide, a); + slide(bslide, b); + ge_p3_to_cached(&Ai[0], A); + ge_p3_dbl(&t, A); + ge_p1p1_to_p3(&A2, &t); + ge_add(&t, &A2, &Ai[0]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[1], &u); + ge_add(&t, &A2, &Ai[1]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[2], &u); + ge_add(&t, &A2, &Ai[2]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[3], &u); + ge_add(&t, &A2, &Ai[3]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[4], &u); + ge_add(&t, &A2, &Ai[4]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[5], &u); + ge_add(&t, &A2, &Ai[5]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[6], &u); + ge_add(&t, &A2, &Ai[6]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[7], &u); + ge_p2_0(r); + + for (i = 255; i >= 0; --i) { + if (aslide[i] || bslide[i]) { + break; + } + } + + for (; i >= 0; --i) { + ge_p2_dbl(&t, r); + + if (aslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Ai[aslide[i] / 2]); + } else if (aslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); + } + + if (bslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_madd(&t, &u, &Bi[bslide[i] / 2]); + } else if (bslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); + } + + ge_p1p1_to_p2(r, &t); + } +} + + +static const fe d = { + -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116 +}; + +static const fe sqrtm1 = { + -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482 +}; + +int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s) { + fe u; + fe v; + fe v3; + fe vxx; + fe check; + fe_frombytes(h->Y, s); + fe_1(h->Z); + fe_sq(u, h->Y); + fe_mul(v, u, d); + fe_sub(u, u, h->Z); /* u = y^2-1 */ + fe_add(v, v, h->Z); /* v = dy^2+1 */ + fe_sq(v3, v); + fe_mul(v3, v3, v); /* v3 = v^3 */ + fe_sq(h->X, v3); + fe_mul(h->X, h->X, v); + fe_mul(h->X, h->X, u); /* x = uv^7 */ + fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ + fe_mul(h->X, h->X, v3); + fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ + fe_sq(vxx, h->X); + fe_mul(vxx, vxx, v); + fe_sub(check, vxx, u); /* vx^2-u */ + + if (fe_isnonzero(check)) { + fe_add(check, vxx, u); /* vx^2+u */ + + if (fe_isnonzero(check)) { + return -1; + } + + fe_mul(h->X, h->X, sqrtm1); + } + + if (fe_isnegative(h->X) == (s[31] >> 7)) { + fe_neg(h->X, h->X); + } + + fe_mul(h->T, h->X, h->Y); + return 0; +} + + +/* +r = p + q +*/ + +void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { + fe t0; + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->yplusx); + fe_mul(r->Y, r->Y, q->yminusx); + fe_mul(r->T, q->xy2d, p->T); + fe_add(t0, p->Z, p->Z); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_add(r->Z, t0, r->T); + fe_sub(r->T, t0, r->T); +} + + +/* +r = p - q +*/ + +void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->yminusx); + fe_mul(r->Y, r->Y, q->yplusx); + fe_mul(r->T, q->xy2d, p->T); + fe_add(t0, p->Z, p->Z); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_sub(r->Z, t0, r->T); + fe_add(r->T, t0, r->T); +} + + +/* +r = p +*/ + +void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { + fe_mul(r->X, p->X, p->T); + fe_mul(r->Y, p->Y, p->Z); + fe_mul(r->Z, p->Z, p->T); +} + + + +/* +r = p +*/ + +void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { + fe_mul(r->X, p->X, p->T); + fe_mul(r->Y, p->Y, p->Z); + fe_mul(r->Z, p->Z, p->T); + fe_mul(r->T, p->X, p->Y); +} + + +void ge_p2_0(ge_p2 *h) { + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); +} + + + +/* +r = 2 * p +*/ + +void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { + fe t0; + + fe_sq(r->X, p->X); + fe_sq(r->Z, p->Y); + fe_sq2(r->T, p->Z); + fe_add(r->Y, p->X, p->Y); + fe_sq(t0, r->Y); + fe_add(r->Y, r->Z, r->X); + fe_sub(r->Z, r->Z, r->X); + fe_sub(r->X, t0, r->Y); + fe_sub(r->T, r->T, r->Z); +} + + +void ge_p3_0(ge_p3 *h) { + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); + fe_0(h->T); +} + + +/* +r = 2 * p +*/ + +void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { + ge_p2 q; + ge_p3_to_p2(&q, p); + ge_p2_dbl(r, &q); +} + + + +/* +r = p +*/ + +static const fe d2 = { + -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199 +}; + +void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { + fe_add(r->YplusX, p->Y, p->X); + fe_sub(r->YminusX, p->Y, p->X); + fe_copy(r->Z, p->Z); + fe_mul(r->T2d, p->T, d2); +} + + +/* +r = p +*/ + +void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { + fe_copy(r->X, p->X); + fe_copy(r->Y, p->Y); + fe_copy(r->Z, p->Z); +} + + +void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) { + fe recip; + fe x; + fe y; + fe_invert(recip, h->Z); + fe_mul(x, h->X, recip); + fe_mul(y, h->Y, recip); + fe_tobytes(s, y); + s[31] ^= fe_isnegative(x) << 7; +} + + +static unsigned char equal(signed char b, signed char c) { + unsigned char ub = b; + unsigned char uc = c; + unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ + uint64_t y = x; /* 0: yes; 1..255: no */ + y -= 1; /* large: yes; 0..254: no */ + y >>= 63; /* 1: yes; 0: no */ + return (unsigned char) y; +} + +static unsigned char negative(signed char b) { + uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ + x >>= 63; /* 1: yes; 0: no */ + return (unsigned char) x; +} + +static void cmov(ge_precomp *t, ge_precomp *u, unsigned char b) { + fe_cmov(t->yplusx, u->yplusx, b); + fe_cmov(t->yminusx, u->yminusx, b); + fe_cmov(t->xy2d, u->xy2d, b); +} + + +static void select(ge_precomp *t, int pos, signed char b) { + ge_precomp minust; + unsigned char bnegative = negative(b); + unsigned char babs = b - (((-bnegative) & b) << 1); + fe_1(t->yplusx); + fe_1(t->yminusx); + fe_0(t->xy2d); + cmov(t, &base[pos][0], equal(babs, 1)); + cmov(t, &base[pos][1], equal(babs, 2)); + cmov(t, &base[pos][2], equal(babs, 3)); + cmov(t, &base[pos][3], equal(babs, 4)); + cmov(t, &base[pos][4], equal(babs, 5)); + cmov(t, &base[pos][5], equal(babs, 6)); + cmov(t, &base[pos][6], equal(babs, 7)); + cmov(t, &base[pos][7], equal(babs, 8)); + fe_copy(minust.yplusx, t->yminusx); + fe_copy(minust.yminusx, t->yplusx); + fe_neg(minust.xy2d, t->xy2d); + cmov(t, &minust, bnegative); +} + +/* +h = a * B +where a = a[0]+256*a[1]+...+256^31 a[31] +B is the Ed25519 base point (x,4/5) with x positive. + +Preconditions: + a[31] <= 127 +*/ + +void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) { + signed char e[64]; + signed char carry; + ge_p1p1 r; + ge_p2 s; + ge_precomp t; + int i; + + for (i = 0; i < 32; ++i) { + e[2 * i + 0] = (a[i] >> 0) & 15; + e[2 * i + 1] = (a[i] >> 4) & 15; + } + + /* each e[i] is between 0 and 15 */ + /* e[63] is between 0 and 7 */ + carry = 0; + + for (i = 0; i < 63; ++i) { + e[i] += carry; + carry = e[i] + 8; + carry >>= 4; + e[i] -= carry << 4; + } + + e[63] += carry; + /* each e[i] is between -8 and 8 */ + ge_p3_0(h); + + for (i = 1; i < 64; i += 2) { + select(&t, i / 2, e[i]); + ge_madd(&r, h, &t); + ge_p1p1_to_p3(h, &r); + } + + ge_p3_dbl(&r, h); + ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + ge_p1p1_to_p3(h, &r); + + for (i = 0; i < 64; i += 2) { + select(&t, i / 2, e[i]); + ge_madd(&r, h, &t); + ge_p1p1_to_p3(h, &r); + } +} + + +/* +r = p - q +*/ + +void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->YminusX); + fe_mul(r->Y, r->Y, q->YplusX); + fe_mul(r->T, q->T2d, p->T); + fe_mul(r->X, p->Z, q->Z); + fe_add(t0, r->X, r->X); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_sub(r->Z, t0, r->T); + fe_add(r->T, t0, r->T); +} + + +void ge_tobytes(unsigned char *s, const ge_p2 *h) { + fe recip; + fe x; + fe y; + fe_invert(recip, h->Z); + fe_mul(x, h->X, recip); + fe_mul(y, h->Y, recip); + fe_tobytes(s, y); + s[31] ^= fe_isnegative(x) << 7; +} diff --git a/ed25519/src/ge.h b/ed25519/src/ge.h new file mode 100644 index 000000000..17fde2df1 --- /dev/null +++ b/ed25519/src/ge.h @@ -0,0 +1,74 @@ +#ifndef GE_H +#define GE_H + +#include "fe.h" + + +/* +ge means group element. + +Here the group is the set of pairs (x,y) of field elements (see fe.h) +satisfying -x^2 + y^2 = 1 + d x^2y^2 +where d = -121665/121666. + +Representations: + ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z + ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT + ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T + ge_precomp (Duif): (y+x,y-x,2dxy) +*/ + +typedef struct { + fe X; + fe Y; + fe Z; +} ge_p2; + +typedef struct { + fe X; + fe Y; + fe Z; + fe T; +} ge_p3; + +typedef struct { + fe X; + fe Y; + fe Z; + fe T; +} ge_p1p1; + +typedef struct { + fe yplusx; + fe yminusx; + fe xy2d; +} ge_precomp; + +typedef struct { + fe YplusX; + fe YminusX; + fe Z; + fe T2d; +} ge_cached; + +void ge_p3_tobytes(unsigned char *s, const ge_p3 *h); +void ge_tobytes(unsigned char *s, const ge_p2 *h); +int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s); + +void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q); +void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q); +void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b); +void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q); +void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q); +void ge_scalarmult_base(ge_p3 *h, const unsigned char *a); + +void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p); +void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p); +void ge_p2_0(ge_p2 *h); +void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p); +void ge_p3_0(ge_p3 *h); +void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p); +void ge_p3_to_cached(ge_cached *r, const ge_p3 *p); +void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p); + +#endif diff --git a/ed25519/src/key_exchange.c b/ed25519/src/key_exchange.c new file mode 100644 index 000000000..abd75da2c --- /dev/null +++ b/ed25519/src/key_exchange.c @@ -0,0 +1,79 @@ +#include "ed25519.h" +#include "fe.h" + +void ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key) { + unsigned char e[32]; + unsigned int i; + + fe x1; + fe x2; + fe z2; + fe x3; + fe z3; + fe tmp0; + fe tmp1; + + int pos; + unsigned int swap; + unsigned int b; + + /* copy the private key and make sure it's valid */ + for (i = 0; i < 32; ++i) { + e[i] = private_key[i]; + } + + e[0] &= 248; + e[31] &= 63; + e[31] |= 64; + + /* unpack the public key and convert edwards to montgomery */ + /* due to CodesInChaos: montgomeryX = (edwardsY + 1)*inverse(1 - edwardsY) mod p */ + fe_frombytes(x1, public_key); + fe_1(tmp1); + fe_add(tmp0, x1, tmp1); + fe_sub(tmp1, tmp1, x1); + fe_invert(tmp1, tmp1); + fe_mul(x1, tmp0, tmp1); + + fe_1(x2); + fe_0(z2); + fe_copy(x3, x1); + fe_1(z3); + + swap = 0; + for (pos = 254; pos >= 0; --pos) { + b = e[pos / 8] >> (pos & 7); + b &= 1; + swap ^= b; + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + swap = b; + + /* from montgomery.h */ + fe_sub(tmp0, x3, z3); + fe_sub(tmp1, x2, z2); + fe_add(x2, x2, z2); + fe_add(z2, x3, z3); + fe_mul(z3, tmp0, x2); + fe_mul(z2, z2, tmp1); + fe_sq(tmp0, tmp1); + fe_sq(tmp1, x2); + fe_add(x3, z3, z2); + fe_sub(z2, z3, z2); + fe_mul(x2, tmp1, tmp0); + fe_sub(tmp1, tmp1, tmp0); + fe_sq(z2, z2); + fe_mul121666(z3, tmp1); + fe_sq(x3, x3); + fe_add(tmp0, tmp0, z3); + fe_mul(z3, x1, z2); + fe_mul(z2, tmp1, tmp0); + } + + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + + fe_invert(z2, z2); + fe_mul(x2, x2, z2); + fe_tobytes(shared_secret, x2); +} diff --git a/ed25519/src/keypair.c b/ed25519/src/keypair.c new file mode 100644 index 000000000..dc1b8eccc --- /dev/null +++ b/ed25519/src/keypair.c @@ -0,0 +1,16 @@ +#include "ed25519.h" +#include "sha512.h" +#include "ge.h" + + +void ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed) { + ge_p3 A; + + sha512(seed, 32, private_key); + private_key[0] &= 248; + private_key[31] &= 63; + private_key[31] |= 64; + + ge_scalarmult_base(&A, private_key); + ge_p3_tobytes(public_key, &A); +} diff --git a/ed25519/src/precomp_data.h b/ed25519/src/precomp_data.h new file mode 100644 index 000000000..776b84f4c --- /dev/null +++ b/ed25519/src/precomp_data.h @@ -0,0 +1,1391 @@ +static ge_precomp Bi[8] = { + { + { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 }, + { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 }, + { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 }, + }, + { + { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 }, + { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 }, + { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 }, + }, + { + { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 }, + { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 }, + { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 }, + }, + { + { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 }, + { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 }, + { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 }, + }, + { + { -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877 }, + { -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951 }, + { 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784 }, + }, + { + { -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436 }, + { 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918 }, + { 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877 }, + }, + { + { -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800 }, + { -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305 }, + { -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300 }, + }, + { + { -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876 }, + { -24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619 }, + { -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683 }, + }, +}; + + +/* base[i][j] = (j+1)*256^i*B */ +static ge_precomp base[32][8] = { + { + { + { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 }, + { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 }, + { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 }, + }, + { + { -12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303 }, + { -21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081 }, + { 26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697 }, + }, + { + { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 }, + { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 }, + { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 }, + }, + { + { -17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540 }, + { 23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397 }, + { 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325 }, + }, + { + { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 }, + { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 }, + { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 }, + }, + { + { -15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777 }, + { -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737 }, + { -18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652 }, + }, + { + { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 }, + { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 }, + { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 }, + }, + { + { 14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726 }, + { -7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955 }, + { 27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425 }, + }, + }, + { + { + { -13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171 }, + { 27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510 }, + { 17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660 }, + }, + { + { -10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639 }, + { 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963 }, + { 5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950 }, + }, + { + { -27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568 }, + { 12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335 }, + { 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628 }, + }, + { + { -26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007 }, + { -2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772 }, + { -22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653 }, + }, + { + { 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567 }, + { 13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686 }, + { 21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372 }, + }, + { + { -13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887 }, + { -23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954 }, + { -29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953 }, + }, + { + { 24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833 }, + { -16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532 }, + { -22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876 }, + }, + { + { 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268 }, + { 33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214 }, + { 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038 }, + }, + }, + { + { + { 6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800 }, + { 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645 }, + { -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664 }, + }, + { + { 1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933 }, + { -25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182 }, + { -17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222 }, + }, + { + { -18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991 }, + { 20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880 }, + { 9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092 }, + }, + { + { -16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295 }, + { 19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788 }, + { 8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553 }, + }, + { + { -15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026 }, + { 11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347 }, + { -18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033 }, + }, + { + { -23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395 }, + { -27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278 }, + { 1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890 }, + }, + { + { 32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995 }, + { -30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596 }, + { -11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891 }, + }, + { + { 31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060 }, + { 11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608 }, + { -20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606 }, + }, + }, + { + { + { 7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389 }, + { -19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016 }, + { -11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341 }, + }, + { + { -22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505 }, + { 14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553 }, + { -28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655 }, + }, + { + { 15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220 }, + { 12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631 }, + { -4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099 }, + }, + { + { 26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556 }, + { 14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749 }, + { 236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930 }, + }, + { + { 1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391 }, + { 5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253 }, + { 20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066 }, + }, + { + { 24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958 }, + { -11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082 }, + { -28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383 }, + }, + { + { -30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521 }, + { -11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807 }, + { 23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948 }, + }, + { + { 9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134 }, + { -32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455 }, + { 27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629 }, + }, + }, + { + { + { -8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069 }, + { -32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746 }, + { 24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919 }, + }, + { + { 11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837 }, + { 8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906 }, + { -28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771 }, + }, + { + { -25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817 }, + { 10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098 }, + { 10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409 }, + }, + { + { -12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504 }, + { -26180358, 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11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313 }, + { -18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958 }, + { -6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577 }, + }, + { + { -22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743 }, + { 29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684 }, + { -20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476 }, + }, + }, +}; \ No newline at end of file diff --git a/ed25519/src/sc.c b/ed25519/src/sc.c new file mode 100644 index 000000000..ca5bad2ca --- /dev/null +++ b/ed25519/src/sc.c @@ -0,0 +1,809 @@ +#include "fixedint.h" +#include "sc.h" + +static uint64_t load_3(const unsigned char *in) { + uint64_t result; + + result = (uint64_t) in[0]; + result |= ((uint64_t) in[1]) << 8; + result |= ((uint64_t) in[2]) << 16; + + return result; +} + +static uint64_t load_4(const unsigned char *in) { + uint64_t result; + + result = (uint64_t) in[0]; + result |= ((uint64_t) in[1]) << 8; + result |= ((uint64_t) in[2]) << 16; + result |= ((uint64_t) in[3]) << 24; + + return result; +} + +/* +Input: + s[0]+256*s[1]+...+256^63*s[63] = s + +Output: + s[0]+256*s[1]+...+256^31*s[31] = s mod l + where l = 2^252 + 27742317777372353535851937790883648493. + Overwrites s in place. +*/ + +void sc_reduce(unsigned char *s) { + int64_t s0 = 2097151 & load_3(s); + int64_t s1 = 2097151 & (load_4(s + 2) >> 5); + int64_t s2 = 2097151 & (load_3(s + 5) >> 2); + int64_t s3 = 2097151 & (load_4(s + 7) >> 7); + int64_t s4 = 2097151 & (load_4(s + 10) >> 4); + int64_t s5 = 2097151 & (load_3(s + 13) >> 1); + int64_t s6 = 2097151 & (load_4(s + 15) >> 6); + int64_t s7 = 2097151 & (load_3(s + 18) >> 3); + int64_t s8 = 2097151 & load_3(s + 21); + int64_t s9 = 2097151 & (load_4(s + 23) >> 5); + int64_t s10 = 2097151 & (load_3(s + 26) >> 2); + int64_t s11 = 2097151 & (load_4(s + 28) >> 7); + int64_t s12 = 2097151 & (load_4(s + 31) >> 4); + int64_t s13 = 2097151 & (load_3(s + 34) >> 1); + int64_t s14 = 2097151 & (load_4(s + 36) >> 6); + int64_t s15 = 2097151 & (load_3(s + 39) >> 3); + int64_t s16 = 2097151 & load_3(s + 42); + int64_t s17 = 2097151 & (load_4(s + 44) >> 5); + int64_t s18 = 2097151 & (load_3(s + 47) >> 2); + int64_t s19 = 2097151 & (load_4(s + 49) >> 7); + int64_t s20 = 2097151 & (load_4(s + 52) >> 4); + int64_t s21 = 2097151 & (load_3(s + 55) >> 1); + int64_t s22 = 2097151 & (load_4(s + 57) >> 6); + int64_t s23 = (load_4(s + 60) >> 3); + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + s23 = 0; + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + s22 = 0; + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + s21 = 0; + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + s20 = 0; + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + s19 = 0; + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + s18 = 0; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 << 21; + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 << 21; + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 << 21; + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 << 21; + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + s17 = 0; + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + s16 = 0; + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + s15 = 0; + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + s14 = 0; + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + s13 = 0; + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 << 21; + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + + s[0] = (unsigned char) (s0 >> 0); + s[1] = (unsigned char) (s0 >> 8); + s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5)); + s[3] = (unsigned char) (s1 >> 3); + s[4] = (unsigned char) (s1 >> 11); + s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2)); + s[6] = (unsigned char) (s2 >> 6); + s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7)); + s[8] = (unsigned char) (s3 >> 1); + s[9] = (unsigned char) (s3 >> 9); + s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4)); + s[11] = (unsigned char) (s4 >> 4); + s[12] = (unsigned char) (s4 >> 12); + s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1)); + s[14] = (unsigned char) (s5 >> 7); + s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6)); + s[16] = (unsigned char) (s6 >> 2); + s[17] = (unsigned char) (s6 >> 10); + s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3)); + s[19] = (unsigned char) (s7 >> 5); + s[20] = (unsigned char) (s7 >> 13); + s[21] = (unsigned char) (s8 >> 0); + s[22] = (unsigned char) (s8 >> 8); + s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5)); + s[24] = (unsigned char) (s9 >> 3); + s[25] = (unsigned char) (s9 >> 11); + s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2)); + s[27] = (unsigned char) (s10 >> 6); + s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7)); + s[29] = (unsigned char) (s11 >> 1); + s[30] = (unsigned char) (s11 >> 9); + s[31] = (unsigned char) (s11 >> 17); +} + + + +/* +Input: + a[0]+256*a[1]+...+256^31*a[31] = a + b[0]+256*b[1]+...+256^31*b[31] = b + c[0]+256*c[1]+...+256^31*c[31] = c + +Output: + s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l + where l = 2^252 + 27742317777372353535851937790883648493. +*/ + +void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) { + int64_t a0 = 2097151 & load_3(a); + int64_t a1 = 2097151 & (load_4(a + 2) >> 5); + int64_t a2 = 2097151 & (load_3(a + 5) >> 2); + int64_t a3 = 2097151 & (load_4(a + 7) >> 7); + int64_t a4 = 2097151 & (load_4(a + 10) >> 4); + int64_t a5 = 2097151 & (load_3(a + 13) >> 1); + int64_t a6 = 2097151 & (load_4(a + 15) >> 6); + int64_t a7 = 2097151 & (load_3(a + 18) >> 3); + int64_t a8 = 2097151 & load_3(a + 21); + int64_t a9 = 2097151 & (load_4(a + 23) >> 5); + int64_t a10 = 2097151 & (load_3(a + 26) >> 2); + int64_t a11 = (load_4(a + 28) >> 7); + int64_t b0 = 2097151 & load_3(b); + int64_t b1 = 2097151 & (load_4(b + 2) >> 5); + int64_t b2 = 2097151 & (load_3(b + 5) >> 2); + int64_t b3 = 2097151 & (load_4(b + 7) >> 7); + int64_t b4 = 2097151 & (load_4(b + 10) >> 4); + int64_t b5 = 2097151 & (load_3(b + 13) >> 1); + int64_t b6 = 2097151 & (load_4(b + 15) >> 6); + int64_t b7 = 2097151 & (load_3(b + 18) >> 3); + int64_t b8 = 2097151 & load_3(b + 21); + int64_t b9 = 2097151 & (load_4(b + 23) >> 5); + int64_t b10 = 2097151 & (load_3(b + 26) >> 2); + int64_t b11 = (load_4(b + 28) >> 7); + int64_t c0 = 2097151 & load_3(c); + int64_t c1 = 2097151 & (load_4(c + 2) >> 5); + int64_t c2 = 2097151 & (load_3(c + 5) >> 2); + int64_t c3 = 2097151 & (load_4(c + 7) >> 7); + int64_t c4 = 2097151 & (load_4(c + 10) >> 4); + int64_t c5 = 2097151 & (load_3(c + 13) >> 1); + int64_t c6 = 2097151 & (load_4(c + 15) >> 6); + int64_t c7 = 2097151 & (load_3(c + 18) >> 3); + int64_t c8 = 2097151 & load_3(c + 21); + int64_t c9 = 2097151 & (load_4(c + 23) >> 5); + int64_t c10 = 2097151 & (load_3(c + 26) >> 2); + int64_t c11 = (load_4(c + 28) >> 7); + int64_t s0; + int64_t s1; + int64_t s2; + int64_t s3; + int64_t s4; + int64_t s5; + int64_t s6; + int64_t s7; + int64_t s8; + int64_t s9; + int64_t s10; + int64_t s11; + int64_t s12; + int64_t s13; + int64_t s14; + int64_t s15; + int64_t s16; + int64_t s17; + int64_t s18; + int64_t s19; + int64_t s20; + int64_t s21; + int64_t s22; + int64_t s23; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + int64_t carry17; + int64_t carry18; + int64_t carry19; + int64_t carry20; + int64_t carry21; + int64_t carry22; + + s0 = c0 + a0 * b0; + s1 = c1 + a0 * b1 + a1 * b0; + s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; + s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; + s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; + s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; + s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; + s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0; + s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0; + s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; + s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; + s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; + s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; + s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; + s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3; + s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4; + s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; + s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; + s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; + s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; + s20 = a9 * b11 + a10 * b10 + a11 * b9; + s21 = a10 * b11 + a11 * b10; + s22 = a11 * b11; + s23 = 0; + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 << 21; + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 << 21; + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 << 21; + carry18 = (s18 + (1 << 20)) >> 21; + s19 += carry18; + s18 -= carry18 << 21; + carry20 = (s20 + (1 << 20)) >> 21; + s21 += carry20; + s20 -= carry20 << 21; + carry22 = (s22 + (1 << 20)) >> 21; + s23 += carry22; + s22 -= carry22 << 21; + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 << 21; + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 << 21; + carry17 = (s17 + (1 << 20)) >> 21; + s18 += carry17; + s17 -= carry17 << 21; + carry19 = (s19 + (1 << 20)) >> 21; + s20 += carry19; + s19 -= carry19 << 21; + carry21 = (s21 + (1 << 20)) >> 21; + s22 += carry21; + s21 -= carry21 << 21; + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + s23 = 0; + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + s22 = 0; + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + s21 = 0; + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + s20 = 0; + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + s19 = 0; + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + s18 = 0; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 << 21; + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 << 21; + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 << 21; + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 << 21; + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + s17 = 0; + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + s16 = 0; + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + s15 = 0; + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + s14 = 0; + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + s13 = 0; + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 << 21; + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 << 21; + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 << 21; + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 << 21; + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 << 21; + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 << 21; + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 << 21; + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 << 21; + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 << 21; + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 << 21; + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 << 21; + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 << 21; + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 << 21; + + s[0] = (unsigned char) (s0 >> 0); + s[1] = (unsigned char) (s0 >> 8); + s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5)); + s[3] = (unsigned char) (s1 >> 3); + s[4] = (unsigned char) (s1 >> 11); + s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2)); + s[6] = (unsigned char) (s2 >> 6); + s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7)); + s[8] = (unsigned char) (s3 >> 1); + s[9] = (unsigned char) (s3 >> 9); + s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4)); + s[11] = (unsigned char) (s4 >> 4); + s[12] = (unsigned char) (s4 >> 12); + s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1)); + s[14] = (unsigned char) (s5 >> 7); + s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6)); + s[16] = (unsigned char) (s6 >> 2); + s[17] = (unsigned char) (s6 >> 10); + s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3)); + s[19] = (unsigned char) (s7 >> 5); + s[20] = (unsigned char) (s7 >> 13); + s[21] = (unsigned char) (s8 >> 0); + s[22] = (unsigned char) (s8 >> 8); + s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5)); + s[24] = (unsigned char) (s9 >> 3); + s[25] = (unsigned char) (s9 >> 11); + s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2)); + s[27] = (unsigned char) (s10 >> 6); + s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7)); + s[29] = (unsigned char) (s11 >> 1); + s[30] = (unsigned char) (s11 >> 9); + s[31] = (unsigned char) (s11 >> 17); +} diff --git a/ed25519/src/sc.h b/ed25519/src/sc.h new file mode 100644 index 000000000..8fa727ef1 --- /dev/null +++ b/ed25519/src/sc.h @@ -0,0 +1,12 @@ +#ifndef SC_H +#define SC_H + +/* +The set of scalars is \Z/l +where l = 2^252 + 27742317777372353535851937790883648493. +*/ + +void sc_reduce(unsigned char *s); +void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c); + +#endif \ No newline at end of file diff --git a/ed25519/src/seed.c b/ed25519/src/seed.c new file mode 100644 index 000000000..25e518220 --- /dev/null +++ b/ed25519/src/seed.c @@ -0,0 +1,40 @@ +#include "ed25519.h" + +#ifndef ED25519_NO_SEED + +#ifdef _WIN32 +#include +#include +#else +#include +#endif + +int ed25519_create_seed(unsigned char *seed) { +#ifdef _WIN32 + HCRYPTPROV prov; + + if (!CryptAcquireContext(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) { + return 1; + } + + if (!CryptGenRandom(prov, 32, seed)) { + CryptReleaseContext(prov, 0); + return 1; + } + + CryptReleaseContext(prov, 0); +#else + FILE *f = fopen("/dev/urandom", "rb"); + + if (f == NULL) { + return 1; + } + + fread(seed, 1, 32, f); + fclose(f); +#endif + + return 0; +} + +#endif \ No newline at end of file diff --git a/ed25519/src/sha512.c b/ed25519/src/sha512.c new file mode 100644 index 000000000..635d8ae09 --- /dev/null +++ b/ed25519/src/sha512.c @@ -0,0 +1,275 @@ +/* LibTomCrypt, modular cryptographic library -- Tom St Denis + * + * LibTomCrypt is a library that provides various cryptographic + * algorithms in a highly modular and flexible manner. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, tomstdenis@gmail.com, http://libtom.org + */ + +#include "fixedint.h" +#include "sha512.h" + +/* the K array */ +static const uint64_t K[80] = { + UINT64_C(0x428a2f98d728ae22), UINT64_C(0x7137449123ef65cd), + UINT64_C(0xb5c0fbcfec4d3b2f), UINT64_C(0xe9b5dba58189dbbc), + UINT64_C(0x3956c25bf348b538), UINT64_C(0x59f111f1b605d019), + UINT64_C(0x923f82a4af194f9b), UINT64_C(0xab1c5ed5da6d8118), + UINT64_C(0xd807aa98a3030242), UINT64_C(0x12835b0145706fbe), + UINT64_C(0x243185be4ee4b28c), UINT64_C(0x550c7dc3d5ffb4e2), + UINT64_C(0x72be5d74f27b896f), UINT64_C(0x80deb1fe3b1696b1), + UINT64_C(0x9bdc06a725c71235), UINT64_C(0xc19bf174cf692694), + UINT64_C(0xe49b69c19ef14ad2), UINT64_C(0xefbe4786384f25e3), + UINT64_C(0x0fc19dc68b8cd5b5), UINT64_C(0x240ca1cc77ac9c65), + UINT64_C(0x2de92c6f592b0275), UINT64_C(0x4a7484aa6ea6e483), + UINT64_C(0x5cb0a9dcbd41fbd4), UINT64_C(0x76f988da831153b5), + UINT64_C(0x983e5152ee66dfab), UINT64_C(0xa831c66d2db43210), + UINT64_C(0xb00327c898fb213f), UINT64_C(0xbf597fc7beef0ee4), + UINT64_C(0xc6e00bf33da88fc2), UINT64_C(0xd5a79147930aa725), + UINT64_C(0x06ca6351e003826f), UINT64_C(0x142929670a0e6e70), + UINT64_C(0x27b70a8546d22ffc), UINT64_C(0x2e1b21385c26c926), + UINT64_C(0x4d2c6dfc5ac42aed), UINT64_C(0x53380d139d95b3df), + UINT64_C(0x650a73548baf63de), UINT64_C(0x766a0abb3c77b2a8), + UINT64_C(0x81c2c92e47edaee6), UINT64_C(0x92722c851482353b), + UINT64_C(0xa2bfe8a14cf10364), UINT64_C(0xa81a664bbc423001), + UINT64_C(0xc24b8b70d0f89791), UINT64_C(0xc76c51a30654be30), + UINT64_C(0xd192e819d6ef5218), UINT64_C(0xd69906245565a910), + UINT64_C(0xf40e35855771202a), UINT64_C(0x106aa07032bbd1b8), + UINT64_C(0x19a4c116b8d2d0c8), UINT64_C(0x1e376c085141ab53), + UINT64_C(0x2748774cdf8eeb99), UINT64_C(0x34b0bcb5e19b48a8), + UINT64_C(0x391c0cb3c5c95a63), UINT64_C(0x4ed8aa4ae3418acb), + UINT64_C(0x5b9cca4f7763e373), UINT64_C(0x682e6ff3d6b2b8a3), + UINT64_C(0x748f82ee5defb2fc), UINT64_C(0x78a5636f43172f60), + UINT64_C(0x84c87814a1f0ab72), UINT64_C(0x8cc702081a6439ec), + UINT64_C(0x90befffa23631e28), UINT64_C(0xa4506cebde82bde9), + UINT64_C(0xbef9a3f7b2c67915), UINT64_C(0xc67178f2e372532b), + UINT64_C(0xca273eceea26619c), UINT64_C(0xd186b8c721c0c207), + UINT64_C(0xeada7dd6cde0eb1e), UINT64_C(0xf57d4f7fee6ed178), + UINT64_C(0x06f067aa72176fba), UINT64_C(0x0a637dc5a2c898a6), + UINT64_C(0x113f9804bef90dae), UINT64_C(0x1b710b35131c471b), + UINT64_C(0x28db77f523047d84), UINT64_C(0x32caab7b40c72493), + UINT64_C(0x3c9ebe0a15c9bebc), UINT64_C(0x431d67c49c100d4c), + UINT64_C(0x4cc5d4becb3e42b6), UINT64_C(0x597f299cfc657e2a), + UINT64_C(0x5fcb6fab3ad6faec), UINT64_C(0x6c44198c4a475817) +}; + +/* Various logical functions */ + +#define ROR64c(x, y) \ + ( ((((x)&UINT64_C(0xFFFFFFFFFFFFFFFF))>>((uint64_t)(y)&UINT64_C(63))) | \ + ((x)<<((uint64_t)(64-((y)&UINT64_C(63)))))) & UINT64_C(0xFFFFFFFFFFFFFFFF)) + +#define STORE64H(x, y) \ + { (y)[0] = (unsigned char)(((x)>>56)&255); (y)[1] = (unsigned char)(((x)>>48)&255); \ + (y)[2] = (unsigned char)(((x)>>40)&255); (y)[3] = (unsigned char)(((x)>>32)&255); \ + (y)[4] = (unsigned char)(((x)>>24)&255); (y)[5] = (unsigned char)(((x)>>16)&255); \ + (y)[6] = (unsigned char)(((x)>>8)&255); (y)[7] = (unsigned char)((x)&255); } + +#define LOAD64H(x, y) \ + { x = (((uint64_t)((y)[0] & 255))<<56)|(((uint64_t)((y)[1] & 255))<<48) | \ + (((uint64_t)((y)[2] & 255))<<40)|(((uint64_t)((y)[3] & 255))<<32) | \ + (((uint64_t)((y)[4] & 255))<<24)|(((uint64_t)((y)[5] & 255))<<16) | \ + (((uint64_t)((y)[6] & 255))<<8)|(((uint64_t)((y)[7] & 255))); } + + +#define Ch(x,y,z) (z ^ (x & (y ^ z))) +#define Maj(x,y,z) (((x | y) & z) | (x & y)) +#define S(x, n) ROR64c(x, n) +#define R(x, n) (((x) &UINT64_C(0xFFFFFFFFFFFFFFFF))>>((uint64_t)n)) +#define Sigma0(x) (S(x, 28) ^ S(x, 34) ^ S(x, 39)) +#define Sigma1(x) (S(x, 14) ^ S(x, 18) ^ S(x, 41)) +#define Gamma0(x) (S(x, 1) ^ S(x, 8) ^ R(x, 7)) +#define Gamma1(x) (S(x, 19) ^ S(x, 61) ^ R(x, 6)) +#ifndef MIN + #define MIN(x, y) ( ((x)<(y))?(x):(y) ) +#endif + +/* compress 1024-bits */ +static int sha512_compress(sha512_context *md, unsigned char *buf) +{ + uint64_t S[8], W[80], t0, t1; + int i; + + /* copy state into S */ + for (i = 0; i < 8; i++) { + S[i] = md->state[i]; + } + + /* copy the state into 1024-bits into W[0..15] */ + for (i = 0; i < 16; i++) { + LOAD64H(W[i], buf + (8*i)); + } + + /* fill W[16..79] */ + for (i = 16; i < 80; i++) { + W[i] = Gamma1(W[i - 2]) + W[i - 7] + Gamma0(W[i - 15]) + W[i - 16]; + } + +/* Compress */ + #define RND(a,b,c,d,e,f,g,h,i) \ + t0 = h + Sigma1(e) + Ch(e, f, g) + K[i] + W[i]; \ + t1 = Sigma0(a) + Maj(a, b, c);\ + d += t0; \ + h = t0 + t1; + + for (i = 0; i < 80; i += 8) { + RND(S[0],S[1],S[2],S[3],S[4],S[5],S[6],S[7],i+0); + RND(S[7],S[0],S[1],S[2],S[3],S[4],S[5],S[6],i+1); + RND(S[6],S[7],S[0],S[1],S[2],S[3],S[4],S[5],i+2); + RND(S[5],S[6],S[7],S[0],S[1],S[2],S[3],S[4],i+3); + RND(S[4],S[5],S[6],S[7],S[0],S[1],S[2],S[3],i+4); + RND(S[3],S[4],S[5],S[6],S[7],S[0],S[1],S[2],i+5); + RND(S[2],S[3],S[4],S[5],S[6],S[7],S[0],S[1],i+6); + RND(S[1],S[2],S[3],S[4],S[5],S[6],S[7],S[0],i+7); + } + + #undef RND + + + + /* feedback */ + for (i = 0; i < 8; i++) { + md->state[i] = md->state[i] + S[i]; + } + + return 0; +} + + +/** + Initialize the hash state + @param md The hash state you wish to initialize + @return 0 if successful +*/ +int sha512_init(sha512_context * md) { + if (md == NULL) return 1; + + md->curlen = 0; + md->length = 0; + md->state[0] = UINT64_C(0x6a09e667f3bcc908); + md->state[1] = UINT64_C(0xbb67ae8584caa73b); + md->state[2] = UINT64_C(0x3c6ef372fe94f82b); + md->state[3] = UINT64_C(0xa54ff53a5f1d36f1); + md->state[4] = UINT64_C(0x510e527fade682d1); + md->state[5] = UINT64_C(0x9b05688c2b3e6c1f); + md->state[6] = UINT64_C(0x1f83d9abfb41bd6b); + md->state[7] = UINT64_C(0x5be0cd19137e2179); + + return 0; +} + +/** + Process a block of memory though the hash + @param md The hash state + @param in The data to hash + @param inlen The length of the data (octets) + @return 0 if successful +*/ +int sha512_update (sha512_context * md, const unsigned char *in, size_t inlen) +{ + size_t n; + size_t i; + int err; + if (md == NULL) return 1; + if (in == NULL) return 1; + if (md->curlen > sizeof(md->buf)) { + return 1; + } + while (inlen > 0) { + if (md->curlen == 0 && inlen >= 128) { + if ((err = sha512_compress (md, (unsigned char *)in)) != 0) { + return err; + } + md->length += 128 * 8; + in += 128; + inlen -= 128; + } else { + n = MIN(inlen, (128 - md->curlen)); + + for (i = 0; i < n; i++) { + md->buf[i + md->curlen] = in[i]; + } + + + md->curlen += n; + in += n; + inlen -= n; + if (md->curlen == 128) { + if ((err = sha512_compress (md, md->buf)) != 0) { + return err; + } + md->length += 8*128; + md->curlen = 0; + } + } + } + return 0; +} + +/** + Terminate the hash to get the digest + @param md The hash state + @param out [out] The destination of the hash (64 bytes) + @return 0 if successful +*/ + int sha512_final(sha512_context * md, unsigned char *out) + { + int i; + + if (md == NULL) return 1; + if (out == NULL) return 1; + + if (md->curlen >= sizeof(md->buf)) { + return 1; + } + + /* increase the length of the message */ + md->length += md->curlen * UINT64_C(8); + + /* append the '1' bit */ + md->buf[md->curlen++] = (unsigned char)0x80; + + /* if the length is currently above 112 bytes we append zeros + * then compress. Then we can fall back to padding zeros and length + * encoding like normal. + */ + if (md->curlen > 112) { + while (md->curlen < 128) { + md->buf[md->curlen++] = (unsigned char)0; + } + sha512_compress(md, md->buf); + md->curlen = 0; + } + + /* pad upto 120 bytes of zeroes + * note: that from 112 to 120 is the 64 MSB of the length. We assume that you won't hash + * > 2^64 bits of data... :-) + */ +while (md->curlen < 120) { + md->buf[md->curlen++] = (unsigned char)0; +} + + /* store length */ +STORE64H(md->length, md->buf+120); +sha512_compress(md, md->buf); + + /* copy output */ +for (i = 0; i < 8; i++) { + STORE64H(md->state[i], out+(8*i)); +} + +return 0; +} + +int sha512(const unsigned char *message, size_t message_len, unsigned char *out) +{ + sha512_context ctx; + int ret; + if (ret = sha512_init(&ctx)) return ret; + if (ret = sha512_update(&ctx, message, message_len)) return ret; + if (ret = sha512_final(&ctx, out)) return ret; + return 0; +} \ No newline at end of file diff --git a/ed25519/src/sha512.h b/ed25519/src/sha512.h new file mode 100644 index 000000000..e56b00e84 --- /dev/null +++ b/ed25519/src/sha512.h @@ -0,0 +1,21 @@ +#ifndef SHA512_H +#define SHA512_H + +#include + +#include "fixedint.h" + +/* state */ +typedef struct sha512_context_ { + uint64_t length, state[8]; + size_t curlen; + unsigned char buf[128]; +} sha512_context; + + +int sha512_init(sha512_context * md); +int sha512_final(sha512_context * md, unsigned char *out); +int sha512_update(sha512_context * md, const unsigned char *in, size_t inlen); +int sha512(const unsigned char *message, size_t message_len, unsigned char *out); + +#endif \ No newline at end of file diff --git a/ed25519/src/sign.c b/ed25519/src/sign.c new file mode 100644 index 000000000..199a8393b --- /dev/null +++ b/ed25519/src/sign.c @@ -0,0 +1,31 @@ +#include "ed25519.h" +#include "sha512.h" +#include "ge.h" +#include "sc.h" + + +void ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key) { + sha512_context hash; + unsigned char hram[64]; + unsigned char r[64]; + ge_p3 R; + + + sha512_init(&hash); + sha512_update(&hash, private_key + 32, 32); + sha512_update(&hash, message, message_len); + sha512_final(&hash, r); + + sc_reduce(r); + ge_scalarmult_base(&R, r); + ge_p3_tobytes(signature, &R); + + sha512_init(&hash); + sha512_update(&hash, signature, 32); + sha512_update(&hash, public_key, 32); + sha512_update(&hash, message, message_len); + sha512_final(&hash, hram); + + sc_reduce(hram); + sc_muladd(signature + 32, hram, private_key, r); +} diff --git a/ed25519/src/verify.c b/ed25519/src/verify.c new file mode 100644 index 000000000..32f988edc --- /dev/null +++ b/ed25519/src/verify.c @@ -0,0 +1,77 @@ +#include "ed25519.h" +#include "sha512.h" +#include "ge.h" +#include "sc.h" + +static int consttime_equal(const unsigned char *x, const unsigned char *y) { + unsigned char r = 0; + + r = x[0] ^ y[0]; + #define F(i) r |= x[i] ^ y[i] + F(1); + F(2); + F(3); + F(4); + F(5); + F(6); + F(7); + F(8); + F(9); + F(10); + F(11); + F(12); + F(13); + F(14); + F(15); + F(16); + F(17); + F(18); + F(19); + F(20); + F(21); + F(22); + F(23); + F(24); + F(25); + F(26); + F(27); + F(28); + F(29); + F(30); + F(31); + #undef F + + return !r; +} + +int ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key) { + unsigned char h[64]; + unsigned char checker[32]; + sha512_context hash; + ge_p3 A; + ge_p2 R; + + if (signature[63] & 224) { + return 0; + } + + if (ge_frombytes_negate_vartime(&A, public_key) != 0) { + return 0; + } + + sha512_init(&hash); + sha512_update(&hash, signature, 32); + sha512_update(&hash, public_key, 32); + sha512_update(&hash, message, message_len); + sha512_final(&hash, h); + + sc_reduce(h); + ge_double_scalarmult_vartime(&R, h, &A, signature + 32); + ge_tobytes(checker, &R); + + if (!consttime_equal(checker, signature)) { + return 0; + } + + return 1; +} diff --git a/ed25519/test.c b/ed25519/test.c new file mode 100644 index 000000000..a56d20257 --- /dev/null +++ b/ed25519/test.c @@ -0,0 +1,149 @@ +#include +#include +#include +#include + +//#define ED25519_DLL +#include "src/ed25519.h" + +#include "src/ge.h" +#include "src/sc.h" + +const char message[] = "Hello, world!"; + + +int main(int argc, char *argv[]) { + unsigned char public_key[32], private_key[64], seed[32], scalar[32]; + unsigned char other_public_key[32], other_private_key[64]; + unsigned char shared_secret[32], other_shared_secret[32]; + unsigned char signature[64]; + + clock_t start; + clock_t end; + int i; + + /* create a random seed, and a keypair out of that seed */ + ed25519_create_seed(seed); + ed25519_create_keypair(public_key, private_key, seed); + + /* create signature on the message with the keypair */ + ed25519_sign(signature, message, strlen(message), public_key, private_key); + + /* verify the signature */ + if (ed25519_verify(signature, message, strlen(message), public_key)) { + printf("valid signature\n"); + } else { + printf("invalid signature\n"); + } + + /* create scalar and add it to the keypair */ + ed25519_create_seed(scalar); + ed25519_add_scalar(public_key, private_key, scalar); + + /* create signature with the new keypair */ + ed25519_sign(signature, message, strlen(message), public_key, private_key); + + /* verify the signature with the new keypair */ + if (ed25519_verify(signature, message, strlen(message), public_key)) { + printf("valid signature\n"); + } else { + printf("invalid signature\n"); + } + + /* make a slight adjustment and verify again */ + signature[44] ^= 0x10; + if (ed25519_verify(signature, message, strlen(message), public_key)) { + printf("did not detect signature change\n"); + } else { + printf("correctly detected signature change\n"); + } + + /* generate two keypairs for testing key exchange */ + ed25519_create_seed(seed); + ed25519_create_keypair(public_key, private_key, seed); + ed25519_create_seed(seed); + ed25519_create_keypair(other_public_key, other_private_key, seed); + + /* create two shared secrets - from both perspectives - and check if they're equal */ + ed25519_key_exchange(shared_secret, other_public_key, private_key); + ed25519_key_exchange(other_shared_secret, public_key, other_private_key); + + for (i = 0; i < 32; ++i) { + if (shared_secret[i] != other_shared_secret[i]) { + printf("key exchange was incorrect\n"); + break; + } + } + + if (i == 32) { + printf("key exchange was correct\n"); + } + + /* test performance */ + printf("testing seed generation performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_create_seed(seed); + } + end = clock(); + + printf("%fus per seed\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + + printf("testing key generation performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_create_keypair(public_key, private_key, seed); + } + end = clock(); + + printf("%fus per keypair\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + printf("testing sign performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_sign(signature, message, strlen(message), public_key, private_key); + } + end = clock(); + + printf("%fus per signature\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + printf("testing verify performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_verify(signature, message, strlen(message), public_key); + } + end = clock(); + + printf("%fus per signature\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + + printf("testing keypair scalar addition performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_add_scalar(public_key, private_key, scalar); + } + end = clock(); + + printf("%fus per keypair\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + printf("testing public key scalar addition performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_add_scalar(public_key, NULL, scalar); + } + end = clock(); + + printf("%fus per key\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + printf("testing key exchange performance: "); + start = clock(); + for (i = 0; i < 10000; ++i) { + ed25519_key_exchange(shared_secret, other_public_key, private_key); + } + end = clock(); + + printf("%fus per shared secret\n", ((double) ((end - start) * 1000)) / CLOCKS_PER_SEC / i * 1000); + + return 0; +} diff --git a/examples/Makefile.am b/examples/Makefile.am index 5493b287c..98bf36b3a 100644 --- a/examples/Makefile.am +++ b/examples/Makefile.am @@ -1,14 +1,11 @@ example_programs = \ client_test \ dump_torrent \ - enum_if \ fragmentation_test\ make_torrent \ simple_client \ rss_reader \ - parse_request_log \ upnp_test \ - utp_test \ connection_tester if ENABLE_EXAMPLES @@ -30,21 +27,12 @@ make_torrent_SOURCES = make_torrent.cpp simple_client_SOURCES = simple_client.cpp #simple_client_LDADD = $(top_builddir)/src/libtorrent-rasterbar.la -enum_if_SOURCES = enum_if.cpp -#enum_if_LDADD = $(top_builddir)/src/libtorrent-rasterbar.la - connection_tester_SOURCES = connection_tester.cpp #connection_tester_LDADD = $(top_builddir)/src/libtorrent-rasterbar.la rss_reader_SOURCES = rss_reader.cpp #rss_reader_LDADD = $(top_builddir)/src/libtorrent-rasterbar.la -utp_test_SOURCES = rss_reader.cpp -#utp_test_LDADD = $(top_builddir)/src/libtorrent-rasterbar.la - -parse_request_log_SOURCES = parse_request_log.cpp -#parse_request_log_LDADD = $(top_builddir)/src/libtorrent-rasterbar.la - fragmentation_test_SOURCES = fragmentation_test.cpp #fragmentation_test_LDADD = $(top_builddir)/src/libtorrent-rasterbar.la diff --git a/include/libtorrent/kademlia/node.hpp b/include/libtorrent/kademlia/node.hpp index 97b8b8904..3c5c4537b 100644 --- a/include/libtorrent/kademlia/node.hpp +++ b/include/libtorrent/kademlia/node.hpp @@ -135,7 +135,7 @@ struct rsa_key { char bytes[268]; }; struct dht_mutable_item : dht_immutable_item { - char sig[256]; + char sig[64]; int seq; rsa_key key; }; diff --git a/include/libtorrent/rsa.hpp b/include/libtorrent/rsa.hpp index 334ef36b6..1badbd0f7 100644 --- a/include/libtorrent/rsa.hpp +++ b/include/libtorrent/rsa.hpp @@ -1,6 +1,6 @@ /* -Copyright (c) 2011-2012, Arvid Norberg, Magnus Jonsson +Copyright (c) 2011-2012, Arvid Norberg All rights reserved. Redistribution and use in source and binary forms, with or without diff --git a/include/libtorrent/struct_debug.hpp b/include/libtorrent/struct_debug.hpp index 96d7fef54..e736624c7 100644 --- a/include/libtorrent/struct_debug.hpp +++ b/include/libtorrent/struct_debug.hpp @@ -1,6 +1,6 @@ /* -Copyright (c) 2011-2012, Arvid Norberg, Magnus Jonsson +Copyright (c) 2011-2012, Arvid Norberg All rights reserved. Redistribution and use in source and binary forms, with or without diff --git a/src/Makefile.am b/src/Makefile.am index 2296713e1..b0b620c10 100644 --- a/src/Makefile.am +++ b/src/Makefile.am @@ -10,7 +10,17 @@ KADEMLIA_SOURCES = \ kademlia/routing_table.cpp \ kademlia/rpc_manager.cpp \ kademlia/logging.cpp \ - kademlia/traversal_algorithm.cpp + kademlia/traversal_algorithm.cpp \ + ../ed25519/src/add_scalar.c \ + ../ed25519/src/fe.c \ + ../ed25519/src/ge.c \ + ../ed25519/src/key_exchange.c \ + ../ed25519/src/keypair.c \ + ../ed25519/src/sc.c \ + ../ed25519/src/seed.c \ + ../ed25519/src/sha512.c \ + ../ed25519/src/sign.c \ + ../ed25519/src/verify.c endif if WITH_SHIPPED_GEOIP @@ -118,7 +128,8 @@ libtorrent_rasterbar_la_LIBADD = @BOOST_SYSTEM_LIB@ @OPENSSL_LIBS@ #AM_CXXFLAGS= -ftemplate-depth-100 -I$(top_srcdir)/include @DEBUGFLAGS@ @OPENSSL_INCLUDES@ #AM_CPPFLAGS = -ftemplate-depth-100 -I$(top_srcdir)/include @DEBUGFLAGS@ @OPENSSL_INCLUDES@ -AM_CPPFLAGS = -ftemplate-depth-100 -I$(top_srcdir)/include @DEBUGFLAGS@ @OPENSSL_INCLUDES@ +AM_CPPFLAGS = -ftemplate-depth-100 -I$(top_srcdir)/include -I$(top_srcdir)/ed25519/src @DEBUGFLAGS@ @OPENSSL_INCLUDES@ +AM_CFLAGS = -I$(top_srcdir)/ed25519/src -std=c99 #AM_CFLAGS= -I$(top_srcdir)/include @DEBUGFLAGS@ #AM_LDFLAGS = $(LDFLAGS) @BOOST_SYSTEM_LIB@ @BOOST_FILESYSTEM_LIB@ @BOOST_THREAD_LIB@ @OPENSSL_LDFLAGS@ @OPENSSL_LIBS@ diff --git a/src/kademlia/node.cpp b/src/kademlia/node.cpp index 27d361d55..029708a63 100644 --- a/src/kademlia/node.cpp +++ b/src/kademlia/node.cpp @@ -51,7 +51,8 @@ POSSIBILITY OF SUCH DAMAGE. #include "libtorrent/kademlia/refresh.hpp" #include "libtorrent/kademlia/find_data.hpp" -#include "libtorrent/rsa.hpp" + +#include "ed25519.h" namespace libtorrent { namespace dht { @@ -807,8 +808,8 @@ void node_impl::incoming_request(msg const& m, entry& e) {"v", lazy_entry::none_t, 0, 0}, {"seq", lazy_entry::int_t, 0, key_desc_t::optional}, // public key - {"k", lazy_entry::string_t, 268, key_desc_t::optional}, - {"sig", lazy_entry::string_t, 256, key_desc_t::optional}, + {"k", lazy_entry::string_t, 32, key_desc_t::optional}, + {"sig", lazy_entry::string_t, 64, key_desc_t::optional}, }; // attempt to parse the message @@ -834,7 +835,7 @@ void node_impl::incoming_request(msg const& m, entry& e) if (!mutable_put) target = hasher(buf.first, buf.second).final(); else - target = sha1_hash(msg_keys[3]->string_ptr()); + target = hasher(msg_keys[3]->string_ptr(), 32).final(); // fprintf(stderr, "%s PUT target: %s\n" // , mutable_put ? "mutable":"immutable" @@ -894,17 +895,14 @@ void node_impl::incoming_request(msg const& m, entry& e) std::pair buf = msg_keys[1]->data_section(); digest.update(buf.first, buf.second); -#ifdef TORRENT_USE_OPENSSL - if (!verify_rsa(digest.final(), msg_keys[3]->string_ptr(), msg_keys[3]->string_length() - , msg_keys[4]->string_ptr(), msg_keys[4]->string_length())) + // msg_keys[4] is the signature, msg_keys[3] is the public key + if (ed25519_verify((unsigned char const*)msg_keys[4]->string_ptr() + , (unsigned char const*)buf.first, buf.second + , (unsigned char const*)msg_keys[3]->string_ptr()) != 0) { incoming_error(e, "invalid signature"); return; } -#else - incoming_error(e, "unsupported"); - return; -#endif sha1_hash target = hasher(msg_keys[3]->string_ptr(), msg_keys[3]->string_length()).final(); dht_mutable_table_t::iterator i = m_mutable_table.find(target); diff --git a/test/Makefile.am b/test/Makefile.am index 1af023af8..7cc5a58e9 100644 --- a/test/Makefile.am +++ b/test/Makefile.am @@ -29,8 +29,10 @@ test_programs = \ test_trackers_extension \ test_transfer \ test_upnp \ + enum_if \ test_utp \ test_session \ + test_ssl \ test_web_seed if ENABLE_TESTS @@ -49,7 +51,7 @@ EXTRA_DIST = Jamfile \ test_torrents/slash_path.torrent \ test_torrents/backslash_path.torrent \ test_torrents/url_list.torrent \ - test_torrents/url_list2.torrent \ + test_torrents/url_list2.torrent \ test_torrents/url_list3.torrent \ test_torrents/httpseed.torrent \ test_torrents/empty_httpseed.torrent \ @@ -92,7 +94,20 @@ EXTRA_PROGRAMS = $(test_programs) noinst_HEADERS = test.hpp setup_transfer.hpp -libtest_la_SOURCES = main.cpp setup_transfer.cpp +libtest_la_SOURCES = main.cpp \ + setup_transfer.cpp \ + dht_server.cpp \ + peer_server.cpp \ + ../ed25519/src/add_scalar.c \ + ../ed25519/src/fe.c \ + ../ed25519/src/ge.c \ + ../ed25519/src/key_exchange.c \ + ../ed25519/src/keypair.c \ + ../ed25519/src/sc.c \ + ../ed25519/src/seed.c \ + ../ed25519/src/sha512.c \ + ../ed25519/src/sign.c \ + ../ed25519/src/verify.c test_file_SOURCES = test_file.cpp test_file_storage_SOURCES = test_file_storage.cpp @@ -124,8 +139,10 @@ test_torrent_parse_SOURCES = test_torrent_parse.cpp test_trackers_extension_SOURCES = test_trackers_extension.cpp test_transfer_SOURCES = test_transfer.cpp test_upnp_SOURCES = test_upnp.cpp +enum_if_SOURCES = enum_if.cpp test_utp_SOURCES = test_utp.cpp test_session_SOURCES = test_session.cpp +test_ssl_SOURCES = test_ssl.cpp test_web_seed_SOURCES = test_web_seed.cpp LDADD = $(top_builddir)/src/libtorrent-rasterbar.la libtest.la diff --git a/test/test_dht.cpp b/test/test_dht.cpp index 72b80dbaa..5fb704a19 100644 --- a/test/test_dht.cpp +++ b/test/test_dht.cpp @@ -36,11 +36,12 @@ POSSIBILITY OF SUCH DAMAGE. #include "libtorrent/kademlia/node.hpp" // for verify_message #include "libtorrent/bencode.hpp" #include "libtorrent/socket_io.hpp" // for hash_address -#include "libtorrent/rsa.hpp" // for generate_rsa_keys and sign_rsa #include "libtorrent/broadcast_socket.hpp" // for supports_ipv6 #include "libtorrent/alert_dispatcher.hpp" #include +#include "../ed25519/src/ed25519.h" + #include "test.hpp" #include "setup_transfer.hpp" @@ -206,7 +207,7 @@ void announce_immutable_items(node_impl& node, udp::endpoint const* eps { TEST_EQUAL(parsed[4]->string_value(), "r"); token = parsed[2]->string_value(); - fprintf(stderr, "got token: %s\n", token.c_str()); +// fprintf(stderr, "got token: %s\n", token.c_str()); } else { @@ -383,7 +384,7 @@ int test_main() { TEST_CHECK(parsed[0]->string_value() == "r"); token = parsed[2]->string_value(); - fprintf(stderr, "got token: %s\n", token.c_str()); +// fprintf(stderr, "got token: %s\n", token.c_str()); } else { @@ -425,7 +426,7 @@ int test_main() { TEST_CHECK(parsed[0]->string_value() == "r"); token = parsed[2]->string_value(); - fprintf(stderr, "got token: %s\n", token.c_str()); +// fprintf(stderr, "got token: %s\n", token.c_str()); } else { @@ -540,24 +541,24 @@ int test_main() announce_immutable_items(node, eps, items, sizeof(items)/sizeof(items[0])); -#ifdef TORRENT_USE_OPENSSL - // RSA functions are only implemented with openssl for now - // ==== get / put mutable items === - char private_key[1192]; - int private_len = sizeof(private_key); - char public_key[268]; - int public_len = sizeof(public_key); + fprintf(stderr, "generating ed25519 keys\n"); + unsigned char seed[32]; + ed25519_create_seed(seed); + unsigned char private_key[64]; + unsigned char public_key[32]; - fprintf(stderr, "generating RSA keys\n"); - ret = generate_rsa_keys(public_key, &public_len, private_key, &private_len, 2048); - fprintf(stderr, "pub: %d priv:%d\n", public_len, private_len); + ed25519_create_keypair(public_key, private_key, seed); + fprintf(stderr, "pub: %s priv: %s\n" + , to_hex(std::string((char*)public_key, 32)).c_str() + , to_hex(std::string((char*)private_key, 64)).c_str()); TEST_CHECK(ret); send_dht_msg(node, "get", source, &response, "10", 0 - , 0, no, 0, public_key, 0, false, false, std::string(public_key + 20, public_len-20)); + , 0, no, 0, (char*)&hasher((char*)public_key, 32).final()[0] + , 0, false, false, std::string(), std::string(), 64); key_desc_t desc[] = { @@ -583,21 +584,18 @@ int test_main() TEST_ERROR(error_string); } - char signature[256]; - int sig_len = sizeof(signature); - char buffer[1024]; + unsigned char signature[64]; + char buffer[1200]; int seq = 4; int pos = snprintf(buffer, sizeof(buffer), "3:seqi%de1:v", seq); - hasher h(buffer, pos); - char* ptr = buffer; - int len = bencode(ptr, items[0].ent); - h.update(buffer, len); - sign_rsa(h.final(), private_key, private_len, signature, sig_len); + char* ptr = buffer + pos; + pos += bencode(ptr, items[0].ent); + ed25519_sign(signature, (unsigned char*)buffer, pos, private_key, public_key); send_dht_msg(node, "put", source, &response, "10", 0 , 0, token, 0, 0, &items[0].ent, false, false - , std::string(public_key, public_len) - , std::string(signature, sig_len), seq); + , std::string((char*)public_key, 32) + , std::string((char*)signature, 64), seq); key_desc_t desc2[] = { @@ -617,7 +615,6 @@ int test_main() , error_string, print_entry(response).c_str()); TEST_ERROR(error_string); } -#endif // TORRENT_USE_OPENSSL // test routing table diff --git a/tools/Makefile.am b/tools/Makefile.am index bb1ea8969..0e41abd05 100644 --- a/tools/Makefile.am +++ b/tools/Makefile.am @@ -1,15 +1,32 @@ tool_programs = \ - parse_hash_fails + parse_hash_fails \ + parse_request_log if ENABLE_EXAMPLES bin_PROGRAMS = $(tool_programs) endif EXTRA_PROGRAMS = $(tool_programs) -EXTRA_DIST = Jamfile +EXTRA_DIST = Jamfile \ + parse_bandwidth_log.py \ + parse_buffer_log.py \ + parse_dht_log.py \ + parse_dht_rtt.py \ + parse_dht_stats.py \ + parse_disk_access.py \ + parse_disk_buffer_log.py\ + parse_disk_log.py \ + parse_memory_log.py \ + parse_peer_log.py \ + parse_sample.py \ + parse_session_stats.py \ + parse_test_results.py \ + parse_utp_log.py \ + run_regression_tests.py\ + run_tests.py parse_hash_fails_SOURCES = parse_hash_fails.cpp -#client_test_LDADD = $(top_builddir)/src/libtorrent-rasterbar.la +parse_request_log_SOURCES = parse_request_log.cpp LDADD = $(top_builddir)/src/libtorrent-rasterbar.la