X-Git-Url: https://git.distorted.org.uk/~mdw/secnet/blobdiff_plain/1047c205103e6da9fc6a317f41583147dbc11aa3..a1a6042e24c9873aa6abf668bcb68d39d0eb4190:/ed25519.c diff --git a/ed25519.c b/ed25519.c new file mode 100644 index 0000000..0677442 --- /dev/null +++ b/ed25519.c @@ -0,0 +1,399 @@ +/* -*-c-*- + * + * The Ed25519 signature scheme + * + * (c) 2017 Straylight/Edgeware + */ + +/*----- Licensing notice --------------------------------------------------* + * + * This file is part of secnet. + * See README for full list of copyright holders. + * + * secnet is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version d of the License, or + * (at your option) any later version. + * + * secnet is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * version 3 along with secnet; if not, see + * https://www.gnu.org/licenses/gpl.html. + * + * This file was originally part of Catacomb, but has been automatically + * modified for incorporation into secnet: see `import-catacomb-crypto' + * for details. + * + * Catacomb is free software; you can redistribute it and/or modify + * it under the terms of the GNU Library General Public License as + * published by the Free Software Foundation; either version 2 of the + * License, or (at your option) any later version. + * + * Catacomb is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Library General Public License for more details. + * + * You should have received a copy of the GNU Library General Public + * License along with Catacomb; if not, write to the Free + * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, + * MA 02111-1307, USA. + */ + +/*----- Header files ------------------------------------------------------*/ + +#include + +#include "f25519.h" +#include "ed25519.h" +#include "scaf.h" +#include "scmul.h" +#include "sha512.h" + +/*----- A number of magic numbers -----------------------------------------*/ + +# define PIECEWD 24 + static const scaf_piece l[] = { + 0xf5d3ed, 0x631a5c, 0xd65812, 0xa2f79c, 0xdef9de, 0x000014, + 0x000000, 0x000000, 0x000000, 0x000000, 0x001000 + }; + static const scaf_piece mu[] = { + 0x1b3994, 0x0a2c13, 0x9ce5a3, 0x29a7ed, 0x5d0863, 0x210621, + 0xffffeb, 0xffffff, 0xffffff, 0xffffff, 0xffffff, 0x000fff + }; + +#define NPIECE SCAF_NPIECE(255, PIECEWD) + +# define P p26 + static const f25519_piece bx_pieces[] = { + -14297830, -7645148, 16144683, -16471763, 27570974, + -2696100, -26142465, 8378389, 20764389, 8758491 + }, by_pieces[] = { + -26843541, -6710886, 13421773, -13421773, 26843546, + 6710886, -13421773, 13421773, -26843546, -6710886 + }, d_pieces[] = { + -10913610, 13857413, -15372611, 6949391, 114729, + -8787816, -6275908, -3247719, -18696448, -12055116 + }; + +static const f25519_piece bz_pieces[NPIECE] = { 1, 0, /* ... */ }; +#define BX ((const f25519 *)bx_pieces) +#define BY ((const f25519 *)by_pieces) +#define BZ ((const f25519 *)bz_pieces) +#define D ((const f25519 *)d_pieces) + +/*----- Point encoding and decoding ---------------------------------------*/ + +static void ptencode(octet q[32], + const f25519 *X, const f25519 *Y, const f25519 *Z) +{ + f25519 x, y, t; + octet b[32]; + + f25519_inv(&t, Z); f25519_mul(&x, X, &t); f25519_mul(&y, Y, &t); + f25519_store(q, &y); f25519_store(b, &x); q[31] |= (b[0]&1u) << 7; +} + +static int ptdecode(f25519 *X, f25519 *Y, f25519 *Z, const octet q[32]) +{ + octet b[32]; + unsigned i, a; + f25519 t, u; + uint32 m; + int rc = 0; + + /* Load the y-coordinate. */ + memcpy(b, q, 32); b[31] &= 0x7fu; f25519_load(Y, b); + + /* Check that the coordinate was in range. If we store it, we'll get a + * canonical version which we can compare against Q; be careful not to + * check the top bit. + */ + f25519_store(b, Y); + for (i = a = 0; i < 31; i++) a |= b[i] ^ q[i]; + a |= (b[31] ^ q[31])&0x7fu; + a = ((a - 1) >> 8)&0x01u; /* 0 |-> 1, non-0 |-> 0 */ + rc |= (int)a - 1; + + /* Decompress the x-coordinate. */ + f25519_sqr(&t, Y); f25519_mul(&u, &t, D); t.P[0] -= 1; u.P[0] += 1; + rc |= f25519_quosqrt(X, &t, &u); + f25519_store(b, X); m = -(uint32)(((q[31] >> 7) ^ b[0])&0x1u); + f25519_condneg(X, X, m); + + /* Set Z. */ + f25519_set(Z, 1); + + /* And we're done. */ + return (rc); +} + +/*----- Edwards curve arithmetic ------------------------------------------*/ + +static void ptadd(f25519 *X, f25519 *Y, f25519 *Z, + const f25519 *X0, const f25519 *Y0, const f25519 *Z0, + const f25519 *X1, const f25519 *Y1, const f25519 *Z1) +{ + f25519 t0, t1, t2, t3; + + /* Bernstein, Birkner, Joye, Lange, and Peters, `Twisted Edwards Curves', + * 2008-03-13, https://cr.yp.to/newelliptic/twisted-20080313.pdf shows the + * formulae as: + * + * A = Z1 Z2; B = A^2; C = X1 X2; D = Y1 Y2; + * E = d C D; F = B - E; G = B + E; + * X3 = A F ((X1 + Y1) (X2 + Y2) - C - D); + * Y3 = A G (D - a C); Z3 = F G. + * + * Note that a = -1, which things easier. + */ + + f25519_mul(&t0, Z0, Z1); /* t0 = A = Z0 Z1 */ + f25519_add(&t1, X0, Y0); /* t1 = X0 + Y0 */ + f25519_add(&t2, X1, Y1); /* t2 = X1 + Y1 */ + f25519_mul(&t1, &t1, &t2); /* t1 = (X0 + Y0) (X1 + Y1) */ + f25519_mul(&t2, X0, X1); /* t2 = C = X0 X1 */ + f25519_mul(&t3, Y0, Y1); /* t3 = D = Y0 Y1 */ + f25519_add(Y, &t2, &t3); /* Y = C + D = D - a C */ + f25519_sub(X, &t1, Y); /* X = (X0 + Y0) (X1 + Y1) - C - D */ + f25519_mul(X, X, &t0); /* X = A ((X0 + Y0) (X1 + Y1) - C - D) */ + f25519_mul(Y, Y, &t0); /* Y = A (D - a C) */ + f25519_sqr(&t0, &t0); /* t0 = B = A^2 */ + f25519_mul(&t1, &t2, &t3); /* t1 = C D */ + f25519_mul(&t1, &t1, D); /* t1 = E = d C D */ + f25519_sub(&t2, &t0, &t1); /* t2 = F = B - E */ + f25519_add(&t1, &t0, &t1); /* t1 = G = B + E */ + f25519_mul(X, X, &t2); /* X = A F ((X0 + Y0) (X1 + Y1) - C - D) */ + f25519_mul(Y, Y, &t1); /* Y = A G (D - a C) */ + f25519_mul(Z, &t1, &t2); /* Z = F G */ +} + +static void ptdbl(f25519 *X, f25519 *Y, f25519 *Z, + const f25519 *X0, const f25519 *Y0, const f25519 *Z0) +{ + f25519 t0, t1, t2; + + /* Bernstein, Birkner, Joye, Lange, and Peters, `Twisted Edwards Curves', + * 2008-03-13, https://cr.yp.to/newelliptic/twisted-20080313.pdf shows the + * formulae as: + * + * B = (X1 + Y1)^2; C = X1^2; D = Y1^2; E = a C; + * F = E + D; H = Z1^2; J = F - 2 H; + * X3 = (B - C - D) J; Y3 = F (E - D); Z3 = F J. + * + * Note that a = -1, which things easier. + */ + + f25519_add(&t0, X0, Y0); /* t0 = X0 + Y0 */ + f25519_sqr(&t0, &t0); /* t0 = B = (X0 + Y0)^2 */ + f25519_sqr(&t1, X0); /* t1 = C = X0^2 */ + f25519_sqr(&t2, Y0); /* t2 = D = Y0^2 */ + f25519_add(Y, &t1, &t2); /* Y = C + D = -(E - D) */ + f25519_sub(X, &t0, Y); /* X = B - C - D */ + /* (E = a C = -C) */ + f25519_sub(&t0, &t2, &t1); /* t0 = F = D - C = E + D */ + f25519_sqr(&t1, Z0); /* t1 = H = Z0^2 */ + f25519_add(&t1, &t1, &t1); /* t1 = 2 H */ + f25519_sub(&t1, &t0, &t1); /* t1 = J = F - 2 H */ + f25519_mul(X, X, &t1); /* X = (B - C - D) J */ + f25519_mul(Y, Y, &t0); /* Y = -F (E - D) */ + f25519_neg(Y, Y); /* Y = F (E - D) */ + f25519_mul(Z, &t0, &t1); /* Z = F J */ +} + +static DEFINE_SCMUL(ptmul, f25519, 4, PIECEWD, NPIECE, ptadd, ptdbl) +static DEFINE_SCSIMMUL(ptsimmul, f25519, 2, PIECEWD, NPIECE, ptadd, ptdbl) + +/*----- Key derivation utilities ------------------------------------------*/ + +static void unpack_key(scaf_piece a[NPIECE], octet h1[32], + const octet *k, size_t ksz) +{ + struct sha512_ctx h; + octet b[SHA512_DIGEST_SIZE]; + + sha512_init_ctx(&h); sha512_process_bytes(k, ksz, &h); sha512_finish_ctx(&h, b); + b[0] &= 0xf8u; b[31] = (b[31]&0x3f) | 0x40; + scaf_load(a, b, 32, NPIECE, PIECEWD); + if (h1) memcpy(h1, b + 32, 32); +} + +#define PREFIX_BUFSZ 290 +static size_t prefix(octet b[PREFIX_BUFSZ], + int phflag, const octet *p, size_t psz) +{ + if (phflag < 0) return (0); + memcpy(b, "SigEd25519 no Ed25519 collisions", 32); + b[32] = phflag; + assert(psz < ED25519_MAXPERSOSZ); b[33] = psz; memcpy(b + 34, p, psz); + return (psz + 34); +} + +/*----- Main code ---------------------------------------------------------*/ + +/* --- @ed25519_pubkey@ --- * + * + * Arguments: @octet K[ED25519_PUBSZ]@ = where to put the public key + * @const void *k@ = private key + * @size_t ksz@ = length of private key + * + * Returns: --- + * + * Use: Derives the public key from a private key. + */ + +void ed25519_pubkey(octet K[ED25519_PUBSZ], const void *k, size_t ksz) +{ + scaf_piece a[NPIECE]; + f25519 AX, AY, AZ; + + unpack_key(a, 0, k, ksz); + ptmul(&AX, &AY, &AZ, a, BX, BY, BZ); + ptencode(K, &AX, &AY, &AZ); +} + +/* --- @ed25519_sign@, @ed25519ctx_sign@ --- * + * + * Arguments: @octet sig[ED25519_SIGSZ]@ = where to put the signature + * @const void *k@ = private key + * @size_t ksz@ = length of private key + * @const octet K[ED25519_PUBSZ]@ = public key + * @int phflag@ = whether the `message' has been hashed already + * @const void *p@ = personalization string + * @size_t psz@ = length of personalization string + * @const void *m@ = message to sign + * @size_t msz@ = length of message + * + * Returns: --- + * + * Use: Signs a message. + * + * In @ed25519ctx_sign@, if @phflag@ is @-1@ then you get plain + * old Ed25519: the personalization string pointer @p@ will be + * ignored. If @phflag > 0@ then the `message' @m@ should be a + * SHA512 hash of the actual message. + */ + +void ed25519ctx_sign(octet sig[ED25519_SIGSZ], + const void *k, size_t ksz, const octet K[ED25519_PUBSZ], + int phflag, const void *p, size_t psz, + const void *m, size_t msz) +{ + struct sha512_ctx h; + scaf_piece a[NPIECE], r[NPIECE], t[NPIECE], scratch[3*NPIECE]; + scaf_dblpiece tt[2*NPIECE]; + f25519 RX, RY, RZ; + octet h1[32], pb[PREFIX_BUFSZ], rb[SHA512_DIGEST_SIZE]; + unsigned i; + + /* Get my private key. */ + unpack_key(a, h1, k, ksz); + + /* Determine the prefix string. */ + psz = prefix(pb, phflag, p, psz); + + /* Select the nonce and the vector part. */ + sha512_init_ctx(&h); + sha512_process_bytes(pb, psz, &h); + sha512_process_bytes(h1, 32, &h); + sha512_process_bytes(m, msz, &h); + sha512_finish_ctx(&h, rb); + scaf_loaddbl(tt, rb, 64, 2*NPIECE, PIECEWD); + scaf_reduce(r, tt, l, mu, NPIECE, PIECEWD, scratch); + ptmul(&RX, &RY, &RZ, r, BX, BY, BZ); + ptencode(sig, &RX, &RY, &RZ); + + /* Calculate the scalar part. */ + sha512_init_ctx(&h); + sha512_process_bytes(pb, psz, &h); + sha512_process_bytes(sig, 32, &h); + sha512_process_bytes(K, 32, &h); + sha512_process_bytes(m, msz, &h); + sha512_finish_ctx(&h, rb); + scaf_loaddbl(tt, rb, 64, 2*NPIECE, PIECEWD); + scaf_reduce(t, tt, l, mu, NPIECE, PIECEWD, scratch); + scaf_mul(tt, t, a, NPIECE); + for (i = 0; i < NPIECE; i++) tt[i] += r[i]; + scaf_reduce(t, tt, l, mu, NPIECE, PIECEWD, scratch); + scaf_store(sig + 32, 32, t, NPIECE, PIECEWD); +} + +void ed25519_sign(octet sig[ED25519_SIGSZ], + const void *k, size_t ksz, const octet K[ED25519_PUBSZ], + const void *m, size_t msz) + { ed25519ctx_sign(sig, k, ksz, K, -1, 0, 0, m, msz); } + +/* --- @ed25519_verify@, @ed25519ctx_verify@ --- * + * + * Arguments: @const octet K[ED25519_PUBSZ]@ = public key + * @int phflag@ = whether the `message' has been hashed already + * @const void *p@ = personalization string + * @size_t psz@ = length of personalization string + * @const void *m@ = message to sign + * @size_t msz@ = length of message + * @const octet sig[ED25519_SIGSZ]@ = signature + * + * Returns: Zero if OK, negative on failure. + * + * Use: Verify a signature. + * + * In @ed25519ctx_verify@, if @phflag@ is @-1@ then you get + * plain old Ed25519: the personalization string pointer @p@ + * will be ignored. If @phflag > 0@ then the `message' @m@ + * should be a SHA512 hash of the actual message. + */ + +int ed25519ctx_verify(const octet K[ED25519_PUBSZ], + int phflag, const void *p, size_t psz, + const void *m, size_t msz, + const octet sig[ED25519_SIGSZ]) +{ + struct sha512_ctx h; + scaf_piece s[NPIECE], t[NPIECE], scratch[3*NPIECE]; + scaf_dblpiece tt[2*NPIECE]; + f25519 AX, AY, AZ, RX, RY, RZ; + octet b[PREFIX_BUFSZ]; + + /* Unpack the public key. Negate it: we're meant to subtract the term + * involving the public key point, and this is easier than negating the + * scalar. + */ + if (ptdecode(&AX, &AY, &AZ, K)) return (-1); + f25519_neg(&AX, &AX); + + /* Load the scalar and check that it's in range. The easy way is to store + * it again and see if the two match. + */ + scaf_loaddbl(tt, sig + 32, 32, 2*NPIECE, PIECEWD); + scaf_reduce(s, tt, l, mu, NPIECE, PIECEWD, scratch); + scaf_store(b, 32, s, NPIECE, PIECEWD); + if (memcmp(b, sig + 32, 32) != 0) return (-1); + + /* Check the signature. */ + psz = prefix(b, phflag, p, psz); + sha512_init_ctx(&h); + sha512_process_bytes(b, psz, &h); + sha512_process_bytes(sig, 32, &h); + sha512_process_bytes(K, 32, &h); + sha512_process_bytes(m, msz, &h); + sha512_finish_ctx(&h, b); + scaf_loaddbl(tt, b, 64, 2*NPIECE, PIECEWD); + scaf_reduce(t, tt, l, mu, NPIECE, PIECEWD, scratch); + ptsimmul(&RX, &RY, &RZ, s, BX, BY, BZ, t, &AX, &AY, &AZ); + ptencode(b, &RX, &RY, &RZ); + if (memcmp(b, sig, 32) != 0) return (-1); + + /* All is good. */ + return (0); +} + +int ed25519_verify(const octet K[ED25519_PUBSZ], + const void *m, size_t msz, + const octet sig[ED25519_SIGSZ]) + { return (ed25519ctx_verify(K, -1, 0, 0, m, msz, sig)); } + +/*----- That's all, folks -------------------------------------------------*/