| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: rsa-priv.c,v 1.4 2004/04/08 01:36:15 mdw Exp $ |
| 4 | * |
| 5 | * RSA private-key operations |
| 6 | * |
| 7 | * (c) 1999 Straylight/Edgeware |
| 8 | */ |
| 9 | |
| 10 | /*----- Licensing notice --------------------------------------------------* |
| 11 | * |
| 12 | * This file is part of Catacomb. |
| 13 | * |
| 14 | * Catacomb is free software; you can redistribute it and/or modify |
| 15 | * it under the terms of the GNU Library General Public License as |
| 16 | * published by the Free Software Foundation; either version 2 of the |
| 17 | * License, or (at your option) any later version. |
| 18 | * |
| 19 | * Catacomb is distributed in the hope that it will be useful, |
| 20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 22 | * GNU Library General Public License for more details. |
| 23 | * |
| 24 | * You should have received a copy of the GNU Library General Public |
| 25 | * License along with Catacomb; if not, write to the Free |
| 26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 27 | * MA 02111-1307, USA. |
| 28 | */ |
| 29 | |
| 30 | /*----- Header files ------------------------------------------------------*/ |
| 31 | |
| 32 | #include <mLib/alloc.h> |
| 33 | #include <mLib/bits.h> |
| 34 | #include <mLib/dstr.h> |
| 35 | |
| 36 | #include "mp.h" |
| 37 | #include "mpmont.h" |
| 38 | #include "mprand.h" |
| 39 | #include "rsa.h" |
| 40 | |
| 41 | /*----- Public key operations ---------------------------------------------*/ |
| 42 | |
| 43 | /* --- @rsa_privcreate@ --- * |
| 44 | * |
| 45 | * Arguments: @rsa_privctx *rd@ = pointer to an RSA private key context |
| 46 | * @rsa_priv *rp@ = pointer to RSA private key |
| 47 | * @grand *r@ = pointer to random number source for blinding |
| 48 | * |
| 49 | * Returns: --- |
| 50 | * |
| 51 | * Use: Initializes an RSA private-key context. Keeping a context |
| 52 | * for several decryption or signing operations provides a minor |
| 53 | * performance benefit. |
| 54 | * |
| 55 | * The random number source may be null if blinding is not |
| 56 | * desired. This improves decryption speed, at the risk of |
| 57 | * permitting timing attacks. |
| 58 | */ |
| 59 | |
| 60 | void rsa_privcreate(rsa_privctx *rd, rsa_priv *rp, grand *r) |
| 61 | { |
| 62 | rd->rp = rp; |
| 63 | rd->r = r; |
| 64 | if (r) |
| 65 | mpmont_create(&rd->nm, rp->n); |
| 66 | mpmont_create(&rd->pm, rp->p); |
| 67 | mpmont_create(&rd->qm, rp->q); |
| 68 | } |
| 69 | |
| 70 | /* --- @rsa_privdestroy@ --- * |
| 71 | * |
| 72 | * Arguments: @rsa_privctx *rd@ = pointer to an RSA decryption context |
| 73 | * |
| 74 | * Returns: --- |
| 75 | * |
| 76 | * Use: Destroys an RSA decryption context. |
| 77 | */ |
| 78 | |
| 79 | void rsa_privdestroy(rsa_privctx *rd) |
| 80 | { |
| 81 | if (rd->r) |
| 82 | mpmont_destroy(&rd->nm); |
| 83 | mpmont_destroy(&rd->pm); |
| 84 | mpmont_destroy(&rd->qm); |
| 85 | } |
| 86 | |
| 87 | /* --- @rsa_privop@ --- * |
| 88 | * |
| 89 | * Arguments: @rsa_privctx *rd@ = pointer to RSA private key context |
| 90 | * @mp *d@ = destination |
| 91 | * @mp *c@ = input message |
| 92 | * |
| 93 | * Returns: The transformed output message. |
| 94 | * |
| 95 | * Use: Performs an RSA private key operation. This function takes |
| 96 | * advantage of knowledge of the key factors in order to speed |
| 97 | * up decryption. It also blinds the ciphertext prior to |
| 98 | * decryption and unblinds it afterwards to thwart timing |
| 99 | * attacks. |
| 100 | */ |
| 101 | |
| 102 | mp *rsa_privop(rsa_privctx *rd, mp *d, mp *c) |
| 103 | { |
| 104 | mp *ki = MP_NEW; |
| 105 | rsa_priv *rp = rd->rp; |
| 106 | |
| 107 | /* --- If so desired, set up a blinding constant --- * |
| 108 | * |
| 109 | * Choose a constant %$k$% relatively prime to the modulus %$m$%. Compute |
| 110 | * %$c' = c k^e \bmod n$%, and %$k^{-1} \bmod n$%. Don't bother with the |
| 111 | * CRT stuff here because %$e$% is chosen to be small. |
| 112 | */ |
| 113 | |
| 114 | c = MP_COPY(c); |
| 115 | if (rd->r) { |
| 116 | mp *k = MP_NEWSEC, *g = MP_NEW; |
| 117 | |
| 118 | do { |
| 119 | k = mprand_range(k, rp->n, rd->r, 0); |
| 120 | mp_gcd(&g, 0, &ki, rp->n, k); |
| 121 | } while (!MP_EQ(g, MP_ONE)); |
| 122 | k = mpmont_mul(&rd->nm, k, k, rd->nm.r2); |
| 123 | k = mpmont_expr(&rd->nm, k, k, rp->e); |
| 124 | c = mpmont_mul(&rd->nm, c, c, k); |
| 125 | mp_drop(k); |
| 126 | mp_drop(g); |
| 127 | } |
| 128 | |
| 129 | /* --- Do the actual modular exponentiation --- * |
| 130 | * |
| 131 | * Use a slightly hacked version of the Chinese Remainder Theorem stuff. |
| 132 | * |
| 133 | * Let %$q' = q^{-1} \bmod p$%. Then note that |
| 134 | * %$c^d \equiv q (q'(c_p^{d_p} - c_q^{d_q}) \bmod p) + c_q^{d_q} \pmod n$% |
| 135 | */ |
| 136 | |
| 137 | { |
| 138 | mp *cp = MP_NEW, *cq = MP_NEW; |
| 139 | |
| 140 | /* --- Work out the two halves of the result --- */ |
| 141 | |
| 142 | mp_div(0, &cp, c, rp->p); |
| 143 | cp = mpmont_exp(&rd->pm, cp, cp, rp->dp); |
| 144 | |
| 145 | mp_div(0, &cq, c, rp->q); |
| 146 | cq = mpmont_exp(&rd->qm, cq, cq, rp->dq); |
| 147 | |
| 148 | /* --- Combine the halves using the result above --- */ |
| 149 | |
| 150 | d = mp_sub(d, cp, cq); |
| 151 | mp_div(0, &d, d, rp->p); |
| 152 | d = mpmont_mul(&rd->pm, d, d, rp->q_inv); |
| 153 | d = mpmont_mul(&rd->pm, d, d, rd->pm.r2); |
| 154 | |
| 155 | d = mp_mul(d, d, rp->q); |
| 156 | d = mp_add(d, d, cq); |
| 157 | if (MP_CMP(d, >=, rp->n)) |
| 158 | d = mp_sub(d, d, rp->n); |
| 159 | |
| 160 | /* --- Tidy away temporary variables --- */ |
| 161 | |
| 162 | mp_drop(cp); |
| 163 | mp_drop(cq); |
| 164 | } |
| 165 | |
| 166 | /* --- Finally, possibly remove the blinding factor --- */ |
| 167 | |
| 168 | if (ki) { |
| 169 | d = mpmont_mul(&rd->nm, d, d, ki); |
| 170 | d = mpmont_mul(&rd->nm, d, d, rd->nm.r2); |
| 171 | mp_drop(ki); |
| 172 | } |
| 173 | |
| 174 | /* --- Done --- */ |
| 175 | |
| 176 | mp_drop(c); |
| 177 | return (d); |
| 178 | } |
| 179 | |
| 180 | /* --- @rsa_qprivop@ --- * |
| 181 | * |
| 182 | * Arguments: @rsa_priv *rp@ = pointer to RSA parameters |
| 183 | * @mp *d@ = destination |
| 184 | * @mp *c@ = input message |
| 185 | * @grand *r@ = pointer to random number source for blinding |
| 186 | * |
| 187 | * Returns: Correctly transformed output message |
| 188 | * |
| 189 | * Use: Performs an RSA private key operation, very carefully. |
| 190 | */ |
| 191 | |
| 192 | mp *rsa_qprivop(rsa_priv *rp, mp *d, mp *c, grand *r) |
| 193 | { |
| 194 | rsa_privctx rd; |
| 195 | rsa_privcreate(&rd, rp, r); |
| 196 | d = rsa_privop(&rd, d, c); |
| 197 | rsa_privdestroy(&rd); |
| 198 | return (d); |
| 199 | } |
| 200 | |
| 201 | /*----- Operations with padding -------------------------------------------*/ |
| 202 | |
| 203 | /* --- @rsa_sign@ --- * |
| 204 | * |
| 205 | * Arguments: @rsa_privctx *rp@ = pointer to an RSA private key context |
| 206 | * @mp *d@ = where to put the result |
| 207 | * @const void *m@ = pointer to input message |
| 208 | * @size_t msz@ = size of input message |
| 209 | * @rsa_pad *e@ = encoding procedure |
| 210 | * @void *earg@ = argument pointer for encoding procedure |
| 211 | * |
| 212 | * Returns: The signature, as a multiprecision integer, or null on |
| 213 | * failure. |
| 214 | * |
| 215 | * Use: Computes an RSA digital signature. |
| 216 | */ |
| 217 | |
| 218 | mp *rsa_sign(rsa_privctx *rp, mp *d, const void *m, size_t msz, |
| 219 | rsa_pad *e, void *earg) |
| 220 | { |
| 221 | octet *p; |
| 222 | unsigned long nb = mp_bits(rp->rp->n); |
| 223 | size_t n = (nb + 7)/8; |
| 224 | arena *a = d && d->a ? d->a->a : arena_global; |
| 225 | |
| 226 | p = x_alloc(a, n); |
| 227 | d = e(d, m, msz, p, n, nb, earg); |
| 228 | x_free(a, p); |
| 229 | return (d ? rsa_privop(rp, d, d) : 0); |
| 230 | } |
| 231 | |
| 232 | /* --- @rsa_decrypt@ --- * |
| 233 | * |
| 234 | * Arguments: @rsa_privctx *rp@ = pointer to an RSA private key context |
| 235 | * @mp *m@ = encrypted message, as a multiprecision integer |
| 236 | * @dstr *d@ = pointer to output string |
| 237 | * @rsa_decunpad *e@ = decoding procedure |
| 238 | * @void *earg@ = argument pointer for decoding procedure |
| 239 | * |
| 240 | * Returns: The length of the output string if successful, negative on |
| 241 | * failure. |
| 242 | * |
| 243 | * Use: Does RSA decryption. |
| 244 | */ |
| 245 | |
| 246 | int rsa_decrypt(rsa_privctx *rp, mp *m, dstr *d, |
| 247 | rsa_decunpad *e, void *earg) |
| 248 | { |
| 249 | mp *p = rsa_privop(rp, MP_NEW, m); |
| 250 | unsigned long nb = mp_bits(rp->rp->n); |
| 251 | size_t n = (nb + 7)/8; |
| 252 | int rc; |
| 253 | |
| 254 | dstr_ensure(d, n); |
| 255 | rc = e(p, (octet *)d->buf + d->len, n, nb, earg); |
| 256 | if (rc >= 0) |
| 257 | d->len += rc; |
| 258 | mp_drop(p); |
| 259 | return (rc); |
| 260 | } |
| 261 | |
| 262 | /*----- That's all, folks -------------------------------------------------*/ |