| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: rsa-decrypt.c,v 1.2 2000/06/17 11:57:56 mdw Exp $ |
| 4 | * |
| 5 | * RSA decryption |
| 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 | /*----- Revision history --------------------------------------------------* |
| 31 | * |
| 32 | * $Log: rsa-decrypt.c,v $ |
| 33 | * Revision 1.2 2000/06/17 11:57:56 mdw |
| 34 | * Improve bulk performance by making better use of Montgomery |
| 35 | * multiplication and separating out initialization and finalization from |
| 36 | * the main code. |
| 37 | * |
| 38 | * Revision 1.1 1999/12/22 15:50:45 mdw |
| 39 | * Initial RSA support. |
| 40 | * |
| 41 | */ |
| 42 | |
| 43 | /*----- Header files ------------------------------------------------------*/ |
| 44 | |
| 45 | #include "mp.h" |
| 46 | #include "mpmont.h" |
| 47 | #include "mprand.h" |
| 48 | #include "rsa.h" |
| 49 | |
| 50 | /*----- Main code ---------------------------------------------------------*/ |
| 51 | |
| 52 | /* --- @rsa_deccreate@ --- * |
| 53 | * |
| 54 | * Arguments: @rsa_decctx *rd@ = pointer to an RSA decryption context |
| 55 | * @rsa_priv *rp@ = pointer to RSA private key |
| 56 | * @grand *r@ = pointer to random number source for blinding |
| 57 | * |
| 58 | * Returns: --- |
| 59 | * |
| 60 | * Use: Initializes an RSA decryption context. Keeping a context |
| 61 | * for several decryption or signing operations provides a minor |
| 62 | * performance benefit. |
| 63 | * |
| 64 | * The random number source may be null if blinding is not |
| 65 | * desired. This improves decryption speed, at the risk of |
| 66 | * permitting timing attacks. |
| 67 | */ |
| 68 | |
| 69 | void rsa_deccreate(rsa_decctx *rd, rsa_param *rp, grand *r) |
| 70 | { |
| 71 | rd->rp = rp; |
| 72 | rd->r = r; |
| 73 | if (r) |
| 74 | mpmont_create(&rd->nm, rp->n); |
| 75 | mpmont_create(&rd->pm, rp->p); |
| 76 | mpmont_create(&rd->qm, rp->q); |
| 77 | } |
| 78 | |
| 79 | /* --- @rsa_decdestroy@ --- * |
| 80 | * |
| 81 | * Arguments: @rsa_decctx *rd@ = pointer to an RSA decryption context |
| 82 | * |
| 83 | * Returns: --- |
| 84 | * |
| 85 | * Use: Destroys an RSA decryption context. |
| 86 | */ |
| 87 | |
| 88 | void rsa_decdestroy(rsa_decctx *rd) |
| 89 | { |
| 90 | if (rd->r) |
| 91 | mpmont_destroy(&rd->nm); |
| 92 | mpmont_destroy(&rd->pm); |
| 93 | mpmont_destroy(&rd->qm); |
| 94 | } |
| 95 | |
| 96 | /* --- @rsa_dec@ --- * |
| 97 | * |
| 98 | * Arguments: @rsa_decctx *rd@ = pointer to RSA decryption context |
| 99 | * @mp *d@ = destination |
| 100 | * @mp *c@ = ciphertext message |
| 101 | * |
| 102 | * Returns: The recovered plaintext message. |
| 103 | * |
| 104 | * Use: Performs RSA decryption. This function takes advantage of |
| 105 | * knowledge of the key factors in order to speed up |
| 106 | * decryption. It also blinds the ciphertext prior to |
| 107 | * decryption and unblinds it afterwards to thwart timing |
| 108 | * attacks. |
| 109 | */ |
| 110 | |
| 111 | mp *rsa_dec(rsa_decctx *rd, mp *d, mp *c) |
| 112 | { |
| 113 | mp *ki = MP_NEW; |
| 114 | rsa_param *rp = rd->rp; |
| 115 | |
| 116 | /* --- If so desired, set up a blinding constant --- * |
| 117 | * |
| 118 | * Choose a constant %$k$% relatively prime to the modulus %$m$%. Compute |
| 119 | * %$c' = c k^e \bmod n$%, and %$k^{-1} \bmod n$%. Don't bother with the |
| 120 | * CRT stuff here because %$e$% is chosen to be small. |
| 121 | */ |
| 122 | |
| 123 | c = MP_COPY(c); |
| 124 | if (rd->r) { |
| 125 | mp *k = MP_NEWSEC, *g = MP_NEW; |
| 126 | |
| 127 | do { |
| 128 | k = mprand_range(k, rp->n, rd->r, 0); |
| 129 | mp_gcd(&g, 0, &ki, rp->n, k); |
| 130 | } while (MP_CMP(g, !=, MP_ONE)); |
| 131 | k = mpmont_expr(&rd->nm, k, k, rp->e); |
| 132 | c = mpmont_mul(&rd->nm, c, c, k); |
| 133 | mp_drop(k); |
| 134 | mp_drop(g); |
| 135 | } |
| 136 | |
| 137 | /* --- Do the actual modular exponentiation --- * |
| 138 | * |
| 139 | * Use a slightly hacked version of the Chinese Remainder Theorem stuff. |
| 140 | * |
| 141 | * Let %$q' = q^{-1} \bmod p$%. Then note that |
| 142 | * %$c^d \equiv q (q'(c_p^{d_p} - c_q^{d_q}) \bmod p) + c_q^{d_q} \pmod n$% |
| 143 | */ |
| 144 | |
| 145 | { |
| 146 | mp *cp = MP_NEW, *cq = MP_NEW; |
| 147 | |
| 148 | /* --- Work out the two halves of the result --- */ |
| 149 | |
| 150 | mp_div(0, &cp, c, rp->p); |
| 151 | cp = mpmont_exp(&rd->pm, cp, cp, rp->dp); |
| 152 | |
| 153 | mp_div(0, &cq, c, rp->q); |
| 154 | cq = mpmont_exp(&rd->qm, cq, cq, rp->dq); |
| 155 | |
| 156 | /* --- Combine the halves using the result above --- */ |
| 157 | |
| 158 | d = mp_sub(d, cp, cq); |
| 159 | mp_div(0, &d, d, rp->p); |
| 160 | d = mpmont_mul(&rd->pm, d, d, rp->q_inv); |
| 161 | d = mpmont_mul(&rd->pm, d, d, rd->pm.r2); |
| 162 | |
| 163 | d = mp_mul(d, d, rp->q); |
| 164 | d = mp_add(d, d, cq); |
| 165 | if (MP_CMP(d, >=, rp->n)) |
| 166 | d = mp_sub(d, d, rp->n); |
| 167 | |
| 168 | /* --- Tidy away temporary variables --- */ |
| 169 | |
| 170 | mp_drop(cp); |
| 171 | mp_drop(cq); |
| 172 | } |
| 173 | |
| 174 | /* --- Finally, possibly remove the blinding factor --- */ |
| 175 | |
| 176 | if (ki) { |
| 177 | d = mpmont_mul(&rd->nm, d, d, ki); |
| 178 | d = mpmont_mul(&rd->nm, d, d, rd->nm.r2); |
| 179 | mp_drop(ki); |
| 180 | } |
| 181 | |
| 182 | /* --- Done --- */ |
| 183 | |
| 184 | mp_drop(c); |
| 185 | return (d); |
| 186 | } |
| 187 | |
| 188 | /* --- @rsa_decrypt@ --- * |
| 189 | * |
| 190 | * Arguments: @rsa_param *rp@ = pointer to RSA parameters |
| 191 | * @mp *d@ = destination |
| 192 | * @mp *c@ = ciphertext message |
| 193 | * @grand *r@ = pointer to random number source for blinding |
| 194 | * |
| 195 | * Returns: Correctly decrypted message. |
| 196 | * |
| 197 | * Use: Performs RSA decryption, very carefully. |
| 198 | */ |
| 199 | |
| 200 | mp *rsa_decrypt(rsa_param *rp, mp *d, mp *c, grand *r) |
| 201 | { |
| 202 | rsa_decctx rd; |
| 203 | rsa_deccreate(&rd, rp, r); |
| 204 | d = rsa_dec(&rd, d, c); |
| 205 | rsa_decdestroy(&rd); |
| 206 | return (d); |
| 207 | } |
| 208 | |
| 209 | /*----- That's all, folks -------------------------------------------------*/ |