| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: rsa-gen.c,v 1.4 2000/10/08 12:11:22 mdw Exp $ |
| 4 | * |
| 5 | * RSA parameter generation |
| 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-gen.c,v $ |
| 33 | * Revision 1.4 2000/10/08 12:11:22 mdw |
| 34 | * Use @MP_EQ@ instead of @MP_CMP@. |
| 35 | * |
| 36 | * Revision 1.3 2000/07/01 11:22:22 mdw |
| 37 | * Remove bad type name `rsa_param'. |
| 38 | * |
| 39 | * Revision 1.2 2000/06/17 12:05:15 mdw |
| 40 | * Lots of changes: |
| 41 | * |
| 42 | * * Apply limits on %$\gcd(p - 1, q - 1)$% to reduce the space of |
| 43 | * equivalent decryption exponents. |
| 44 | * |
| 45 | * * Force %$e = F_4 = 2^{16} + 1$% to avoid small-encryption-exponent |
| 46 | * attacks. |
| 47 | * |
| 48 | * * Ensure that %$p > q$% and that %$p - q$% is large to deter |
| 49 | * square-root-based factoring methods. |
| 50 | * |
| 51 | * * Use %$e d \equiv 1 \pmod{\lambda(n)}$%, where %$\lambda(n)$% is |
| 52 | * %$\lcm(p - 1, q - 1)$%, as recommended in PKCS#1, rather than the |
| 53 | * more usual %$\varphi(n) = (p - 1)(q - 1)$%. |
| 54 | * |
| 55 | * * Handle aborts from pgen_jump. |
| 56 | * |
| 57 | * Revision 1.1 1999/12/22 15:50:45 mdw |
| 58 | * Initial RSA support. |
| 59 | * |
| 60 | */ |
| 61 | |
| 62 | /*----- Header files ------------------------------------------------------*/ |
| 63 | |
| 64 | #include <mLib/dstr.h> |
| 65 | |
| 66 | #include "grand.h" |
| 67 | #include "mp.h" |
| 68 | #include "mpint.h" |
| 69 | #include "pgen.h" |
| 70 | #include "rsa.h" |
| 71 | #include "strongprime.h" |
| 72 | |
| 73 | /*----- Main code ---------------------------------------------------------*/ |
| 74 | |
| 75 | /* --- @rsa_gen@ --- * |
| 76 | * |
| 77 | * Arguments: @rsa_priv *rp@ = pointer to block to be filled in |
| 78 | * @unsigned nbits@ = required modulus size in bits |
| 79 | * @grand *r@ = random number source |
| 80 | * @unsigned n@ = number of attempts to make |
| 81 | * @pgen_proc *event@ = event handler function |
| 82 | * @void *ectx@ = argument for the event handler |
| 83 | * |
| 84 | * Returns: Zero if all went well, nonzero otherwise. |
| 85 | * |
| 86 | * Use: Constructs a pair of strong RSA primes and other useful RSA |
| 87 | * parameters. A small encryption exponent is chosen if |
| 88 | * possible. |
| 89 | */ |
| 90 | |
| 91 | int rsa_gen(rsa_priv *rp, unsigned nbits, grand *r, unsigned n, |
| 92 | pgen_proc *event, void *ectx) |
| 93 | { |
| 94 | pgen_gcdstepctx g; |
| 95 | mp *phi = MP_NEW; |
| 96 | |
| 97 | /* --- Bits of initialization --- */ |
| 98 | |
| 99 | rp->e = mp_fromulong(MP_NEW, 0x10001); |
| 100 | rp->d = MP_NEW; |
| 101 | |
| 102 | /* --- Generate strong primes %$p$% and %$q$% --- * |
| 103 | * |
| 104 | * Constrain the GCD of @q@ to ensure that overly small private exponents |
| 105 | * are impossible. Current results suggest that if %$d < n^{0.29}$% then |
| 106 | * it can be guessed fairly easily. This implementation is rather more |
| 107 | * conservative about that sort of thing. |
| 108 | */ |
| 109 | |
| 110 | again: |
| 111 | if ((rp->p = strongprime("p", MP_NEWSEC, nbits/2, r, n, event, ectx)) == 0) |
| 112 | goto fail_p; |
| 113 | |
| 114 | /* --- Do painful fiddling with GCD steppers --- */ |
| 115 | |
| 116 | { |
| 117 | mp *q; |
| 118 | rabin rb; |
| 119 | |
| 120 | if ((q = strongprime_setup("q", MP_NEWSEC, &g.jp, nbits / 2, |
| 121 | r, n, event, ectx)) == 0) |
| 122 | goto fail_q; |
| 123 | g.r = mp_lsr(MP_NEW, rp->p, 1); |
| 124 | g.g = MP_NEW; |
| 125 | g.max = MP_256; |
| 126 | q = pgen("q", q, q, event, ectx, n, pgen_gcdstep, &g, |
| 127 | rabin_iters(nbits/2), pgen_test, &rb); |
| 128 | pfilt_destroy(&g.jp); |
| 129 | mp_drop(g.r); |
| 130 | if (!q) { |
| 131 | mp_drop(g.g); |
| 132 | if (n) |
| 133 | goto fail_q; |
| 134 | mp_drop(rp->p); |
| 135 | goto again; |
| 136 | } |
| 137 | rp->q = q; |
| 138 | } |
| 139 | |
| 140 | /* --- Ensure that %$p > q$% --- * |
| 141 | * |
| 142 | * Also ensure that %$p$% and %$q$% are sufficiently different to deter |
| 143 | * square-root-based factoring methods. |
| 144 | */ |
| 145 | |
| 146 | phi = mp_sub(phi, rp->p, rp->q); |
| 147 | if (MP_LEN(phi) * 4 < MP_LEN(rp->p) * 3 || |
| 148 | MP_LEN(phi) * 4 < MP_LEN(rp->q) * 3) { |
| 149 | mp_drop(rp->p); |
| 150 | mp_drop(g.g); |
| 151 | if (n) |
| 152 | goto fail_q; |
| 153 | mp_drop(rp->q); |
| 154 | goto again; |
| 155 | } |
| 156 | |
| 157 | if (phi->f & MP_NEG) { |
| 158 | mp *z = rp->p; |
| 159 | rp->p = rp->q; |
| 160 | rp->q = z; |
| 161 | } |
| 162 | |
| 163 | /* --- Work out the modulus and the CRT coefficient --- */ |
| 164 | |
| 165 | rp->n = mp_mul(MP_NEW, rp->p, rp->q); |
| 166 | rp->q_inv = MP_NEW; mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q); |
| 167 | |
| 168 | /* --- Work out %$\varphi(n) = (p - 1)(q - 1)$% --- * |
| 169 | * |
| 170 | * Save on further multiplications by noting that %$n = pq$% is known and |
| 171 | * that %$(p - 1)(q - 1) = pq - p - q + 1$%. To minimize the size of @d@ |
| 172 | * (useful for performance reasons, although not very because an overly |
| 173 | * small @d@ will be rejected for security reasons) this is then divided by |
| 174 | * %$\gcd(p - 1, q - 1)$%. |
| 175 | */ |
| 176 | |
| 177 | phi = mp_sub(phi, rp->n, rp->p); |
| 178 | phi = mp_sub(phi, phi, rp->q); |
| 179 | phi = mp_add(phi, phi, MP_ONE); |
| 180 | phi = mp_lsr(phi, phi, 1); |
| 181 | mp_div(&phi, 0, phi, g.g); |
| 182 | |
| 183 | /* --- Decide on a public exponent --- * |
| 184 | * |
| 185 | * Simultaneously compute the private exponent. |
| 186 | */ |
| 187 | |
| 188 | mp_gcd(&g.g, 0, &rp->d, phi, rp->e); |
| 189 | if (!MP_EQ(g.g, MP_ONE) && MP_LEN(rp->d) * 4 > MP_LEN(rp->n) * 3) |
| 190 | goto fail_e; |
| 191 | |
| 192 | /* --- Work out exponent residues --- */ |
| 193 | |
| 194 | rp->dp = MP_NEW; phi = mp_sub(phi, rp->p, MP_ONE); |
| 195 | mp_div(0, &rp->dp, rp->d, phi); |
| 196 | |
| 197 | rp->dq = MP_NEW; phi = mp_sub(phi, rp->q, MP_ONE); |
| 198 | mp_div(0, &rp->dq, rp->d, phi); |
| 199 | |
| 200 | /* --- Done --- */ |
| 201 | |
| 202 | mp_drop(phi); |
| 203 | mp_drop(g.g); |
| 204 | return (0); |
| 205 | |
| 206 | /* --- Tidy up when something goes wrong --- */ |
| 207 | |
| 208 | fail_e: |
| 209 | mp_drop(g.g); |
| 210 | mp_drop(phi); |
| 211 | mp_drop(rp->n); |
| 212 | mp_drop(rp->q_inv); |
| 213 | mp_drop(rp->q); |
| 214 | fail_q: |
| 215 | mp_drop(rp->p); |
| 216 | fail_p: |
| 217 | mp_drop(rp->e); |
| 218 | if (rp->d) |
| 219 | mp_drop(rp->d); |
| 220 | return (-1); |
| 221 | } |
| 222 | |
| 223 | /*----- That's all, folks -------------------------------------------------*/ |