/* $OpenBSD: math_group.c,v 1.3 1998/11/17 11:10:17 niklas Exp $ */ /* $EOM: math_group.c,v 1.9 1998/08/09 19:03:47 niklas Exp $ */ /* * Copyright (c) 1998 Niels Provos. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgement: * This product includes software developed by Ericsson Radio Systems. * 4. The name of the author may not be used to endorse or promote products * derived from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* * This code was written under funding by Ericsson Radio Systems. */ #include #include #include #include #include "gmp_util.h" #include "math_2n.h" #include "math_ec2n.h" #include "math_group.h" #include "log.h" #include "sysdep.h" /* We do not want to export these definitions */ int modp_getlen (struct group *); void modp_getraw (struct group *, mpz_ptr, u_int8_t *); void modp_setraw (struct group *, mpz_ptr, u_int8_t *, int); void modp_setrandom (struct group *, mpz_ptr); void modp_operation (struct group *, mpz_ptr, mpz_ptr, mpz_ptr); int ec2n_getlen (struct group *); void ec2n_getraw (struct group *, ec2np_ptr, u_int8_t *); void ec2n_setraw (struct group *, ec2np_ptr, u_int8_t *, int); void ec2n_setrandom (struct group *, ec2np_ptr); void ec2n_operation (struct group *, ec2np_ptr, ec2np_ptr, ec2np_ptr); struct ec2n_group { ec2np_t gen; /* Generator */ ec2ng_t grp; ec2np_t a, b, c, d; }; struct modp_group { mpz_t gen; /* Generator */ mpz_t p; /* Prime */ mpz_t a, b, c, d; }; /* * This module provides access to the operations on the specified group * and is absolutly free of any cryptographic devices. This is math :-). */ #define OAKLEY_GRP_1 1 #define OAKLEY_GRP_2 2 #define OAKLEY_GRP_3 3 #define OAKLEY_GRP_4 4 /* Describe preconfigured MODP groups */ /* * The Generalized Number Field Sieve has an asymptotic running time * of: O(exp(1.9223 * (ln q)^(1/3) (ln ln q)^(2/3))), where q is the * group order, e.g. q = 2**768. */ struct modp_dscr oakley_modp[] = { { OAKLEY_GRP_1, 72, /* This group is insecure, only sufficient for DES */ "0xFFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1" "29024E088A67CC74020BBEA63B139B22514A08798E3404DD" "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245" "E485B576625E7EC6F44C42E9A63A3620FFFFFFFFFFFFFFFF", "0x02" }, { OAKLEY_GRP_2, 82, /* This group is a bit better */ "0xFFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1" "29024E088A67CC74020BBEA63B139B22514A08798E3404DD" "EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245" "E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED" "EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE65381" "FFFFFFFFFFFFFFFF", "0x02" } }; /* Describe preconfigured EC2N groups */ /* * Related collision-search methods can compute discrete logarithmns * in O(sqrt(r)), r being the subgroup order. */ struct ec2n_dscr oakley_ec2n[] = { { OAKLEY_GRP_3, 76, /* This group is also considered insecure (P1363) */ "0x0800000000000000000000004000000000000001", "0x7b", "0x00", "0x7338f" }, { OAKLEY_GRP_4, 91, "0x020000000000000000000000000000200000000000000001", "0x18", "0x00", "0x1ee9" }, }; struct group groups[] = { { MODP, OAKLEY_GRP_1, 0, &oakley_modp[0], NULL, NULL, NULL, NULL, NULL, (int (*) (struct group *))modp_getlen, (void (*) (struct group *, void *, u_int8_t *))modp_getraw, (void (*) (struct group *, void *, u_int8_t *, int))modp_setraw, (void (*) (struct group *, void *))modp_setrandom, (void (*) (struct group *, void *, void *, void *))modp_operation }, { MODP, OAKLEY_GRP_2, 0, &oakley_modp[1], NULL, NULL, NULL, NULL, NULL, (int (*) (struct group *))modp_getlen, (void (*) (struct group *, void *, u_int8_t *))modp_getraw, (void (*) (struct group *, void *, u_int8_t *, int))modp_setraw, (void (*) (struct group *, void *))modp_setrandom, (void (*) (struct group *, void *, void *, void *))modp_operation }, { EC2N, OAKLEY_GRP_3, 0, &oakley_ec2n[0], NULL, NULL, NULL, NULL, NULL, (int (*) (struct group *))ec2n_getlen, (void (*) (struct group *, void *, u_int8_t *))ec2n_getraw, (void (*) (struct group *, void *, u_int8_t *, int))ec2n_setraw, (void (*) (struct group *, void *))ec2n_setrandom, (void (*) (struct group *, void *, void *, void *))ec2n_operation }, { EC2N, OAKLEY_GRP_4, 0, &oakley_ec2n[1], NULL, NULL, NULL, NULL, NULL, (int (*) (struct group *))ec2n_getlen, (void (*) (struct group *, void *, u_int8_t *))ec2n_getraw, (void (*) (struct group *, void *, u_int8_t *, int))ec2n_setraw, (void (*) (struct group *, void *))ec2n_setrandom, (void (*) (struct group *, void *, void *, void *))ec2n_operation } }; /* * Initalize the group structure for later use, * this is done by converting the values given in the describtion * and converting them to their native representation. */ void group_init (void) { int i; for (i = sizeof (groups)/sizeof (groups[0]) -1; i >= 0; i--) switch (groups[i].type) { case EC2N: /* Initalize an Elliptic Curve over GF(2**n) */ ec2n_init (&groups[i]); break; case MODP: /* Initalize an over GF(p) */ modp_init (&groups[i]); break; default: log_print ("Unknown group type %d at index %d in group_init().", groups[i].type, i); break; } } struct group * group_get (int id) { struct group *new, *clone; if (id < 1 || id > (sizeof (groups)/sizeof (groups[0]))) return NULL; clone = &groups[id-1]; if ((new = malloc (sizeof (struct group))) == NULL) { log_print ("group_get: Out of memory"); return (NULL); } switch (clone->type) { case EC2N: new = ec2n_clone (new, clone); break; case MODP: new = modp_clone (new, clone); break; default: log_print ("group_get: Unknown group type %d", clone->type); free (new); return (NULL); } return (new); } void group_free (struct group *grp) { switch (grp->type) { case EC2N: ec2n_free (grp); break; case MODP: modp_free (grp); default: log_print ("group_free: Unknown group type %d", grp->type); break; } free (grp); } struct group * modp_clone (struct group *new, struct group *clone) { struct modp_group *new_grp, *clone_grp = clone->group; if ((new_grp = malloc (sizeof (struct modp_group))) == NULL) { log_print ("modp_clone: Out of memory"); free (new); return (NULL); } memcpy (new, clone, sizeof (struct group)); new->group = new_grp; mpz_init_set (new_grp->p, clone_grp->p); mpz_init_set (new_grp->gen, clone_grp->gen); mpz_init (new_grp->a); mpz_init (new_grp->b); mpz_init (new_grp->c); new->gen = new_grp->gen; new->a = new_grp->a; new->b = new_grp->b; new->c = new_grp->c; return (new); } void modp_free (struct group *old) { struct modp_group *grp = old->group; mpz_clear (grp->p); mpz_clear (grp->gen); mpz_clear (grp->a); mpz_clear (grp->b); mpz_clear (grp->c); free (grp); } void modp_init (struct group *group) { struct modp_dscr *dscr = (struct modp_dscr *)group->group; struct modp_group *grp; if ((grp = malloc (sizeof (struct modp_group))) == NULL) log_fatal ("modp_init: Out of memory"); group->bits = dscr->bits; mpz_init_set_str (grp->p, dscr->prime, 0); mpz_init_set_str (grp->gen, dscr->gen, 0); mpz_init (grp->a); mpz_init (grp->b); mpz_init (grp->c); group->gen = grp->gen; group->a = grp->a; group->b = grp->b; group->c = grp->c; group->group = grp; } struct group * ec2n_clone (struct group *new, struct group *clone) { struct ec2n_group *new_grp, *clone_grp = clone->group; if ((new_grp = malloc (sizeof (struct ec2n_group))) == NULL) { log_print ("ec2n_clone: Out of memory"); free (new); return (NULL); } memcpy (new, clone, sizeof (struct group)); new->group = new_grp; ec2ng_init (new_grp->grp); ec2ng_set (new_grp->grp, clone_grp->grp); ec2np_init (new_grp->gen); ec2np_set (new_grp->gen, clone_grp->gen); ec2np_init (new_grp->a); ec2np_init (new_grp->b); ec2np_init (new_grp->c); new->gen = new_grp->gen; new->a = new_grp->a; new->b = new_grp->b; new->c = new_grp->c; new->d = ((ec2np_ptr)new->a)->x; return (new); } void ec2n_free (struct group *old) { struct ec2n_group *grp = old->group; ec2ng_clear (grp->grp); ec2np_clear (grp->gen); ec2np_clear (grp->a); ec2np_clear (grp->b); ec2np_clear (grp->c); free (grp); } void ec2n_init (struct group *group) { struct ec2n_dscr *dscr = (struct ec2n_dscr *)group->group; struct ec2n_group *grp; if ((grp = malloc (sizeof (struct ec2n_group))) == NULL) log_fatal ("ec2n_init: Out of memory"); group->bits = dscr->bits; ec2ng_init (grp->grp); ec2ng_set_p_str (grp->grp, dscr->polynomial); grp->grp->p->bits = b2n_sigbit (grp->grp->p); ec2ng_set_a_str (grp->grp, dscr->a); ec2ng_set_b_str (grp->grp, dscr->b); ec2np_init (grp->gen); ec2np_set_x_str (grp->gen, dscr->gen_x); ec2np_find_y (grp->gen, grp->grp); /* Sanity check */ if (!ec2np_ison (grp->gen, grp->grp)) log_fatal ("ec2n_init: Generator is not on curve"); ec2np_init (grp->a); ec2np_init (grp->b); ec2np_init (grp->c); group->gen = grp->gen; group->a = grp->a; group->b = grp->b; group->c = grp->c; group->d = ((ec2np_ptr)group->a)->x; group->group = grp; } int modp_getlen (struct group *group) { struct modp_group *grp = (struct modp_group *)group->group; return mpz_sizeinoctets (grp->p); } void modp_getraw (struct group *grp, mpz_ptr v, u_int8_t *d) { mpz_getraw (d, v, grp->getlen (grp)); } void modp_setraw (struct group *grp, mpz_ptr d, u_int8_t *s, int l) { mpz_setraw (d, s, l); } void modp_setrandom (struct group *grp, mpz_ptr d) { int i, l = grp->getlen (grp); u_int32_t tmp = 0; mpz_set_ui (d, 0); for (i = 0; i < l; i++) { if (i % 4) tmp = sysdep_random(); mpz_mul_2exp (d, d, 8); mpz_add_ui (d, d, tmp & 0xFF); tmp >>= 8; } } void modp_operation (struct group *group, mpz_ptr d, mpz_ptr a, mpz_ptr e) { struct modp_group *grp = (struct modp_group *)group->group; mpz_powm (d, a, e, grp->p); } int ec2n_getlen (struct group *group) { struct ec2n_group *grp = (struct ec2n_group *)group->group; int bits = b2n_sigbit (grp->grp->p) - 1; return (7 + bits) >> 3; } void ec2n_getraw (struct group *group, ec2np_ptr xo, u_int8_t *e) { struct ec2n_group *grp = (struct ec2n_group *)group->group; int chunks, bytes, i, j; b2n_ptr x = xo->x; CHUNK_TYPE tmp; bytes = b2n_sigbit (grp->grp->p) - 1; chunks = (CHUNK_MASK + bytes) >> CHUNK_SHIFTS; bytes = ((7 + (bytes & CHUNK_MASK)) >> 3); for (i = chunks-1; i >= 0; i--) { tmp = (i >= x->chunks ? 0 : x->limp[i]); for (j = (i == chunks - 1 ? bytes : CHUNK_BYTES) - 1; j >= 0; j--) { e[j] = tmp & 0xFF; tmp >>= 8; } e += (i == chunks - 1 ? bytes : CHUNK_BYTES); } } void ec2n_setraw (struct group *grp, ec2np_ptr out, u_int8_t *s, int l) { int len, bytes, i, j; b2n_ptr outx = out->x; CHUNK_TYPE tmp; len = (CHUNK_BYTES - 1 + l)/CHUNK_BYTES; b2n_resize (outx, len); bytes = ((l - 1) % CHUNK_BYTES) + 1; for (i = len - 1; i >= 0; i--) { tmp = 0; for (j = (i == len - 1 ? bytes : CHUNK_BYTES); j > 0; j--) { tmp <<= 8; tmp |= *s++; } outx->limp[i] = tmp; } } void ec2n_setrandom (struct group *group, ec2np_ptr x) { b2n_ptr d = x->x; struct ec2n_group *grp = (struct ec2n_group *)group->group; b2n_random (d, b2n_sigbit (grp->grp->p) - 1); } /* * This is an attempt at operation abstraction. It can happen * that we need to initalize the y variable for the operation * to proceed correctly. When this is the case operation has * to supply the variable 'a' with the chunks of the Y cooridnate * set to zero. */ void ec2n_operation (struct group *grp, ec2np_ptr d, ec2np_ptr a, ec2np_ptr e) { b2n_ptr ex = e->x; struct ec2n_group *group = (struct ec2n_group *)grp->group; if (a->y->chunks == 0) ec2np_find_y (a, group->grp); ec2np_mul (d, a, ex, group->grp); }