X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/dfdacfdcd7e3376072506d6bdf69271a0e6bd2e0..01898d8eb947e922eb289589cd7b1f016e2ada06:/rsa-recover.c diff --git a/rsa-recover.c b/rsa-recover.c new file mode 100644 index 0000000..c125aef --- /dev/null +++ b/rsa-recover.c @@ -0,0 +1,243 @@ +/* -*-c-*- + * + * $Id: rsa-recover.c,v 1.1 1999/12/22 15:50:45 mdw Exp $ + * + * Recover RSA parameters + * + * (c) 1999 Straylight/Edgeware + */ + +/*----- Licensing notice --------------------------------------------------* + * + * This file is part of Catacomb. + * + * 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. + */ + +/*----- Revision history --------------------------------------------------* + * + * $Log: rsa-recover.c,v $ + * Revision 1.1 1999/12/22 15:50:45 mdw + * Initial RSA support. + * + */ + +/*----- Header files ------------------------------------------------------*/ + +#include "mp.h" +#include "mpmont.h" +#include "rsa.h" + +/*----- Main code ---------------------------------------------------------*/ + +/* --- @rsa_recover@ --- * + * + * Arguments: @rsa_param *rp@ = pointer to parameter block + * + * Returns: Zero if all went well, nonzero if the parameters make no + * sense. + * + * Use: Derives the full set of RSA parameters given a minimal set. + */ + +int rsa_recover(rsa_param *rp) +{ + /* --- If there is no modulus, calculate it --- */ + + if (!rp->n) { + if (!rp->p || !rp->q) + return (-1); + rp->n = mp_mul(MP_NEW, rp->p, rp->q); + } + + /* --- If there are no factors, compute them --- */ + + else if (!rp->p || !rp->q) { + + /* --- If one is missing, use simple division to recover the other --- */ + + if (rp->p || rp->q) { + mp *r = MP_NEW; + if (rp->p) + mp_div(&rp->q, &r, rp->n, rp->p); + else + mp_div(&rp->p, &r, rp->n, rp->q); + if (MP_CMP(r, !=, MP_ZERO)) { + mp_drop(r); + return (-1); + } + mp_drop(r); + } + + /* --- Otherwise use the public and private moduli --- */ + + else if (rp->e && rp->d) { + mp *t; + unsigned s; + mpscan ms; + mp a; mpw aw; + mp *m1; + mpmont mm; + int i; + mp *z = MP_NEW; + + /* --- Work out the appropriate exponent --- * + * + * I need to compute %$s$% and %$t$% such that %$2^s t = e d - 1$%, and + * %$t$% is odd. + */ + + t = mp_mul(MP_NEW, rp->e, rp->d); + t = mp_sub(t, t, MP_ONE); + s = 0; + mp_scan(&ms, t); + for (;;) { + MP_STEP(&ms); + if (MP_BIT(&ms)) + break; + s++; + } + t = mp_lsr(t, t, s); + + /* --- Set up for the exponentiation --- */ + + mpmont_create(&mm, rp->n); + m1 = mp_sub(MP_NEW, rp->n, mm.r); + + /* --- Now for the main loop --- * + * + * Choose candidate integers and attempt to factor the modulus. + */ + + mp_build(&a, &aw, &aw + 1); + i = 0; + for (;;) { + again: + + /* --- Choose a random %$a$% and calculate %$z = a^t \bmod n$% --- * + * + * If %$z \equiv 1$% or %$z \equiv -1 \pmod n$% then this iteration + * is a failure. + */ + + aw = primetab[i++]; + z = mpmont_expr(&mm, z, &a, t); + if (MP_CMP(z, ==, mm.r) || MP_CMP(z, ==, m1)) + continue; + + /* --- Now square until something interesting happens --- * + * + * Compute %$z^{2i} \bmod n$%. Eventually, I'll either get %$-1$% or + * %$1$%. If the former, the number is uninteresting, and I need to + * restart. If the latter, the previous number minus 1 has a common + * factor with %$n$%. + */ + + for (;;) { + mp *zz = mp_sqr(MP_NEW, z); + zz = mpmont_reduce(&mm, zz, zz); + if (MP_CMP(zz, ==, mm.r)) { + mp_drop(zz); + goto done; + } else if (MP_CMP(zz, ==, m1)) { + mp_drop(zz); + goto again; + } + mp_drop(z); + z = zz; + } + } + + /* --- Do the factoring --- * + * + * Here's how it actually works. I've found an interesting square + * root of %$1 \pmod n$%. Any square root of 1 must be congruent to + * %$\pm 1$% modulo both %$p$% and %$q$%. Both congruent to %$1$% is + * boring, as is both congruent to %$-1$%. Subtracting one from the + * result makes it congruent to %$0$% modulo %$p$% or %$q$% (and + * nobody cares which), and hence can be extracted by a GCD + * operation. + */ + + done: + z = mpmont_reduce(&mm, z, z); + z = mp_sub(z, z, MP_ONE); + rp->p = MP_NEW; + mp_gcd(&rp->p, 0, 0, rp->n, z); + rp->q = MP_NEW; + mp_div(&rp->q, 0, rp->n, rp->p); + mp_drop(z); + mp_drop(t); + mp_drop(m1); + mpmont_destroy(&mm); + } + } + + /* --- If %$e$% or %$d$% is missing, recalculate it --- */ + + if (!rp->e || !rp->d) { + mp *phi; + mp *g = MP_NEW; + + /* --- Compute %$\varphi(n)$% --- */ + + phi = mp_sub(MP_NEW, rp->n, rp->p); + phi = mp_sub(phi, phi, rp->q); + phi = mp_add(phi, phi, MP_ONE); + + /* --- Recover the other exponent --- */ + + if (rp->e) + mp_gcd(&g, 0, &rp->d, phi, rp->e); + else if (rp->d) + mp_gcd(&g, 0, &rp->e, phi, rp->d); + else { + mp_drop(phi); + return (-1); + } + + mp_drop(phi); + if (MP_CMP(g, !=, MP_ONE)) { + mp_drop(g); + return (-1); + } + mp_drop(g); + } + + /* --- Compute %$q^{-1} \bmod p$% --- */ + + if (!rp->q_inv) + mp_gcd(0, 0, &rp->q_inv, rp->p, rp->q); + + /* --- Compute %$d \bmod (p - 1)$% and %$d \bmod (q - 1)$% --- */ + + if (!rp->dp) { + mp *p1 = mp_sub(MP_NEW, rp->p, MP_ONE); + mp_div(0, &rp->dp, rp->d, p1); + mp_drop(p1); + } + if (!rp->dq) { + mp *q1 = mp_sub(MP_NEW, rp->q, MP_ONE); + mp_div(0, &rp->dq, rp->d, q1); + mp_drop(q1); + } + + /* --- Done --- */ + + return (0); +} + +/*----- That's all, folks -------------------------------------------------*/