1183840Sraj/* $NetBSD: bn_mp_exteuclid.c,v 1.2 2017/01/28 21:31:47 christos Exp $ */ 2183840Sraj 3183840Sraj#include <tommath.h> 4183840Sraj#ifdef BN_MP_EXTEUCLID_C 5183840Sraj/* LibTomMath, multiple-precision integer library -- Tom St Denis 6183840Sraj * 7183840Sraj * LibTomMath is a library that provides multiple-precision 8183840Sraj * integer arithmetic as well as number theoretic functionality. 9183840Sraj * 10183840Sraj * The library was designed directly after the MPI library by 11183840Sraj * Michael Fromberger but has been written from scratch with 12183840Sraj * additional optimizations in place. 13183840Sraj * 14183840Sraj * The library is free for all purposes without any express 15183840Sraj * guarantee it works. 16183840Sraj * 17183840Sraj * Tom St Denis, tomstdenis@gmail.com, http://libtom.org 18183840Sraj */ 19183840Sraj 20183840Sraj/* Extended euclidean algorithm of (a, b) produces 21183840Sraj a*u1 + b*u2 = u3 22183840Sraj */ 23183840Srajint mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) 24183840Sraj{ 25183840Sraj mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp; 26183840Sraj int err; 27183840Sraj 28183840Sraj if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) { 29183840Sraj return err; 30183840Sraj } 31183840Sraj 32183840Sraj /* initialize, (u1,u2,u3) = (1,0,a) */ 33183840Sraj mp_set(&u1, 1); 34183840Sraj if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto _ERR; } 35183840Sraj 36183840Sraj /* initialize, (v1,v2,v3) = (0,1,b) */ 37183840Sraj mp_set(&v2, 1); 38183840Sraj if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto _ERR; } 39183840Sraj 40209131Sraj /* loop while v3 != 0 */ 41183840Sraj while (mp_iszero(&v3) == MP_NO) { 42183840Sraj /* q = u3/v3 */ 43183840Sraj if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto _ERR; } 44194072Smarcel 45183840Sraj /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */ 46235609Sgber if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto _ERR; } 47235609Sgber if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto _ERR; } 48235609Sgber if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto _ERR; } 49235609Sgber if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto _ERR; } 50235609Sgber if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto _ERR; } 51235609Sgber if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto _ERR; } 52235609Sgber 53235609Sgber /* (u1,u2,u3) = (v1,v2,v3) */ 54235609Sgber if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto _ERR; } 55235609Sgber if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto _ERR; } 56235609Sgber if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto _ERR; } 57235609Sgber 58235609Sgber /* (v1,v2,v3) = (t1,t2,t3) */ 59235609Sgber if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto _ERR; } 60235609Sgber if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto _ERR; } 61235609Sgber if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; } 62235609Sgber } 63235609Sgber 64235609Sgber /* make sure U3 >= 0 */ 65235609Sgber if (u3.sign == MP_NEG) { 66235609Sgber mp_neg(&u1, &u1); 67235609Sgber mp_neg(&u2, &u2); 68235609Sgber mp_neg(&u3, &u3); 69235609Sgber } 70186909Sraj 71183840Sraj /* copy result out */ 72183840Sraj if (U1 != NULL) { mp_exch(U1, &u1); } 73183840Sraj if (U2 != NULL) { mp_exch(U2, &u2); } 74183840Sraj if (U3 != NULL) { mp_exch(U3, &u3); } 75183840Sraj 76183840Sraj err = MP_OKAY; 77183840Sraj_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); 78183840Sraj return err; 79183840Sraj} 80209131Sraj#endif 81183840Sraj 82183840Sraj/* Source: /cvs/libtom/libtommath/bn_mp_exteuclid.c,v */ 83209131Sraj/* Revision: 1.4 */ 84186899Sraj/* Date: 2006/12/28 01:25:13 */ 85186909Sraj