--- /dev/null
+/* -*-c-*-
+ *
+ * The Ed448 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 <string.h>
+
+#include "fgoldi.h"
+#include "ed448.h"
+#include "scaf.h"
+#include "scmul.h"
+#include "sha3.h"
+
+/*----- A number of magic numbers -----------------------------------------*/
+
+# define PIECEWD 24
+ static const scaf_piece l[] = {
+ 0x5844f3, 0xc292ab, 0x552378, 0x8dc58f, 0x6cc272,
+ 0x369021, 0x49aed6, 0xc44edb, 0xca23e9, 0xffff7c,
+ 0xffffff, 0xffffff, 0xffffff, 0xffffff, 0xffffff,
+ 0xffffff, 0xffffff, 0xffffff, 0x003fff
+ };
+ static const scaf_piece mu[] = {
+ 0xe0d00a, 0x4a7bb0, 0x73d6d5, 0x0aadc8, 0xd723a7,
+ 0xe933d8, 0x9c96fd, 0x4b6512, 0x63bb12, 0x335dc1,
+ 0x000008, 0x000000, 0x000000, 0x000000, 0x000000,
+ 0x000000, 0x000000, 0x000000, 0x000000, 0x000400
+ };
+
+#define NPIECE SCAF_NPIECE(448, PIECEWD)
+
+# define P p28
+ static const fgoldi_piece bx_pieces[] = {
+ 118276190, 40534716, 9670182, -133293904,
+ 85017404, -9262234, 68333083, -96650682,
+ -93461723, 15824511, 73756743, 57518561,
+ 94773951, -19783215, 107736334, 82941708
+ }, by_pieces[] = {
+ 36764180, 8885695, 130592152, 20104429,
+ -104530499, 30304196, 121295871, 5901357,
+ 125344798, -96893944, -93097107, -59366209,
+ 3626698, 38307682, 24032956, 110359655
+ };
+
+static const fgoldi_piece bz_pieces[NPIECE] = { 1, 0, /* ... */ };
+#define BX ((const fgoldi *)bx_pieces)
+#define BY ((const fgoldi *)by_pieces)
+#define BZ ((const fgoldi *)bz_pieces)
+#define D (-39081)
+
+/*----- Point encoding and decoding ---------------------------------------*/
+
+static void ptencode(octet q[57],
+ const fgoldi *X, const fgoldi *Y, const fgoldi *Z)
+{
+ fgoldi x, y, t;
+ octet b[56];
+
+ fgoldi_inv(&t, Z); fgoldi_mul(&x, X, &t); fgoldi_mul(&y, Y, &t);
+ fgoldi_store(q, &y); fgoldi_store(b, &x); q[56] = (b[0]&1u) << 7;
+}
+
+static int ptdecode(fgoldi *X, fgoldi *Y, fgoldi *Z, const octet q[57])
+{
+ octet b[56];
+ unsigned i, a;
+ fgoldi t, u;
+ uint32 m;
+ int rc = 0;
+
+ /* Load the y-coordinate. */
+ fgoldi_load(Y, q);
+
+ /* Check that the coordinate was in range. If we store it, we'll get a
+ * canonical version which we can compare against Q. Also, check that the
+ * extra bits in the top byte are zero.
+ */
+ fgoldi_store(b, Y);
+ for (i = a = 0; i < 56; i++) a |= b[i] ^ q[i];
+ a |= q[56]&0x7fu;
+ a = ((a - 1) >> 8)&0x01u; /* 0 |-> 1, non-0 |-> 0 */
+ rc |= (int)a - 1;
+
+ /* Decompress the x-coordinate. */
+ fgoldi_sqr(&t, Y); fgoldi_mulconst(&u, &t, D); t.P[0] -= 1; u.P[0] -= 1;
+ rc |= fgoldi_quosqrt(X, &t, &u);
+ fgoldi_store(b, X); m = -(uint32)(((q[56] >> 7) ^ b[0])&0x1u);
+ fgoldi_condneg(X, X, m);
+
+ /* Set Z. */
+ fgoldi_set(Z, 1);
+
+ /* And we're done. */
+ return (rc);
+}
+
+/*----- Edwards curve arithmetic ------------------------------------------*/
+
+static void ptadd(fgoldi *X, fgoldi *Y, fgoldi *Z,
+ const fgoldi *X0, const fgoldi *Y0, const fgoldi *Z0,
+ const fgoldi *X1, const fgoldi *Y1, const fgoldi *Z1)
+{
+ fgoldi t0, t1, t2, t3;
+
+ /* Bernstein and Lange, `Faster addition and doubling on elliptic curves',
+ * 2007-09-06, https://cr.yp.to/newelliptic/newelliptic-20070906.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 - C); Z3 = c F G.
+ *
+ * But c = 1 here.
+ */
+
+ fgoldi_mul(&t0, Z0, Z1); /* t0 = A = Z0 Z1 */
+ fgoldi_add(&t1, X0, Y0); /* t1 = X0 + Y0 */
+ fgoldi_add(&t2, X1, Y1); /* t2 = X1 + Y1 */
+ fgoldi_mul(&t1, &t1, &t2); /* t1 = (X0 + Y0) (X1 + Y1) */
+ fgoldi_mul(&t2, X0, X1); /* t2 = C = X0 X1 */
+ fgoldi_mul(&t3, Y0, Y1); /* t3 = D = Y0 Y1 */
+ fgoldi_sub(X, &t1, &t2); /* X = (X0 + Y0) (X1 + Y1) - C */
+ fgoldi_sub(X, X, &t3); /* X = (X0 + Y0) (X1 + Y1) - C - D */
+ fgoldi_sub(Y, &t3, &t2); /* Y = D - C */
+ fgoldi_mul(X, X, &t0); /* X = A ((X0 + Y0) (X1 + Y1) - C - D) */
+ fgoldi_mul(Y, Y, &t0); /* Y = A (D - C) */
+ fgoldi_sqr(&t0, &t0); /* t0 = B = A^2 */
+ fgoldi_mul(&t1, &t2, &t3); /* t1 = C D */
+ fgoldi_mulconst(&t1, &t1, D); /* t1 = E = d C D */
+ fgoldi_sub(&t2, &t0, &t1); /* t2 = F = B - E */
+ fgoldi_add(&t1, &t0, &t1); /* t1 = G = B + E */
+ fgoldi_mul(X, X, &t2); /* X = A F ((X0 + Y0) (X1 + Y1) - C - D) */
+ fgoldi_mul(Y, Y, &t1); /* Y = A G (D - C) */
+ fgoldi_mul(Z, &t1, &t2); /* Z = c F G */
+}
+
+static void ptdbl(fgoldi *X, fgoldi *Y, fgoldi *Z,
+ const fgoldi *X0, const fgoldi *Y0, const fgoldi *Z0)
+{
+ fgoldi t0, t1, t2;
+
+ /* Bernstein and Lange, `Faster addition and doubling on elliptic curves',
+ * 2007-09-06, https://cr.yp.to/newelliptic/newelliptic-20070906.pdf shows
+ * the formulae as:
+ *
+ * B = (X1 + Y1)^2; C = X1^2; D = Y1^2;
+ * E = C + D; H = (c Z1)^2; J = E - 2 H;
+ * X3 = c (B - E) J; Y3 = c E (C - D); Z3 = E J
+ *
+ * But c = 1 here.
+ */
+
+ fgoldi_add(&t0, X0, Y0); /* t0 = X0 + Y0 */
+ fgoldi_sqr(&t0, &t0); /* t0 = B = (X0 + Y0)^2 */
+ fgoldi_sqr(&t1, X0); /* t1 = C = X0^2 */
+ fgoldi_sqr(&t2, Y0); /* t2 = D = Y0^2 */
+ fgoldi_add(Y, &t1, &t2); /* Y = E = C + D */
+ fgoldi_sub(&t1, &t1, &t2); /* t1 = C - D */
+ fgoldi_sub(X, &t0, Y); /* X = c (B - E) */
+ fgoldi_sqr(&t0, Z0); /* t0 = H = (c Z0)^2 */
+ fgoldi_add(&t0, &t0, &t0); /* t0 = 2 H */
+ fgoldi_sub(&t0, Y, &t0); /* t0 = J = E - 2 H */
+ fgoldi_mul(X, X, &t0); /* X = c (B - E) J */
+ fgoldi_mul(Z, Y, &t0); /* Z = E J */
+ fgoldi_mul(Y, Y, &t1); /* Y = c E (C - D) */
+}
+
+static DEFINE_SCMUL(ptmul, fgoldi, 4, PIECEWD, NPIECE, ptadd, ptdbl)
+static DEFINE_SCSIMMUL(ptsimmul, fgoldi, 2, PIECEWD, NPIECE, ptadd, ptdbl)
+
+/*----- Key derivation utilities ------------------------------------------*/
+
+static void unpack_key(scaf_piece a[NPIECE], octet h1[57],
+ const octet *k, size_t ksz)
+{
+ shake_ctx h;
+ octet b[57];
+
+ shake256_init(&h); shake_hash(&h, k, ksz);
+ shake_xof(&h); shake_get(&h, b, sizeof(b));
+ b[0] &= 0xfcu; b[55] |= 0x80u; scaf_load(a, b, 56, NPIECE, PIECEWD);
+ if (h1) shake_get(&h, h1, 57);
+}
+
+#define PREFIX_BUFSZ 266
+static size_t prefix(octet b[PREFIX_BUFSZ],
+ int phflag, const octet *p, size_t psz)
+{
+ memcpy(b, "SigEd448", 8);
+ b[8] = phflag;
+ assert(psz <= ED448_MAXPERSOSZ); b[9] = psz; memcpy(b + 10, p, psz);
+ return (psz + 10);
+}
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @ed448_pubkey@ --- *
+ *
+ * Arguments: @octet K[ED448_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 ed448_pubkey(octet K[ED448_PUBSZ], const void *k, size_t ksz)
+{
+ scaf_piece a[NPIECE];
+ fgoldi AX, AY, AZ;
+
+ unpack_key(a, 0, k, ksz);
+ ptmul(&AX, &AY, &AZ, a, BX, BY, BZ);
+ ptencode(K, &AX, &AY, &AZ);
+}
+
+/* --- @ed448_sign@ --- *
+ *
+ * Arguments: @octet sig[ED448_SIGSZ]@ = where to put the signature
+ * @const void *k@ = private key
+ * @size_t ksz@ = length of private key
+ * @const octet K[ED448_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.
+ */
+
+void ed448_sign(octet sig[ED448_SIGSZ],
+ const void *k, size_t ksz, const octet K[ED448_PUBSZ],
+ int phflag, const void *p, size_t psz,
+ const void *m, size_t msz)
+{
+ shake_ctx h;
+ scaf_piece a[NPIECE], r[NPIECE], t[NPIECE], scratch[3*NPIECE];
+ scaf_dblpiece tt[2*NPIECE];
+ fgoldi RX, RY, RZ;
+ octet h1[57], pb[PREFIX_BUFSZ], rb[114];
+ 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. */
+ shake256_init(&h);
+ shake_hash(&h, pb, psz);
+ shake_hash(&h, h1, sizeof(h1));
+ shake_hash(&h, m, msz);
+ shake_done(&h, rb, 114);
+ scaf_loaddbl(tt, rb, 114, 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. */
+ shake256_init(&h);
+ shake_hash(&h, pb, psz);
+ shake_hash(&h, sig, 57);
+ shake_hash(&h, K, 57);
+ shake_hash(&h, m, msz);
+ shake_done(&h, rb, 114);
+ scaf_loaddbl(tt, rb, 114, 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 + 57, 57, t, NPIECE, PIECEWD);
+}
+
+/* --- @ed448_verify@ --- *
+ *
+ * Arguments: @const octet K[ED448_PUBSZ]@ = public key
+ * @const void *m@ = message to sign
+ * @int phflag@ = whether the `message' has been hashed already
+ * @const void *p@ = personalization string
+ * @size_t psz@ = length of personalization string
+ * @size_t msz@ = length of message
+ * @const octet sig[ED448_SIGSZ]@ = signature
+ *
+ * Returns: Zero if OK, negative on failure.
+ *
+ * Use: Verify a signature.
+ */
+
+int ed448_verify(const octet K[ED448_PUBSZ],
+ int phflag, const void *p, size_t psz,
+ const void *m, size_t msz,
+ const octet sig[ED448_SIGSZ])
+{
+ shake_ctx h;
+ scaf_piece s[NPIECE], t[NPIECE], scratch[3*NPIECE];
+ scaf_dblpiece tt[2*NPIECE];
+ fgoldi 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);
+ fgoldi_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 + 57, 57, 2*NPIECE, PIECEWD);
+ scaf_reduce(s, tt, l, mu, NPIECE, PIECEWD, scratch);
+ scaf_store(b, 57, s, NPIECE, PIECEWD);
+ if (memcmp(b, sig + 57, 57) != 0) return (-1);
+
+ /* Check the signature. */
+ psz = prefix(b, phflag, p, psz);
+ shake256_init(&h);
+ shake_hash(&h, b, psz);
+ shake_hash(&h, sig, 57);
+ shake_hash(&h, K, ED448_PUBSZ);
+ shake_hash(&h, m, msz);
+ shake_done(&h, b, 114);
+ scaf_loaddbl(tt, b, 114, 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, 57) != 0) return (-1);
+
+ /* All is good. */
+ return (0);
+}
+
+/*----- That's all, folks -------------------------------------------------*/
~mdw / secnet / blobdiff