dropbear: libtommath/bn_mp_prime_strong_lucas

annotate libtommath/bn_mp_prime_strong_lucas_selfridge.c @ 1692:1051e4eea25a

Update LibTomMath to 1.2.0 (#84) * update C files * update other files * update headers * update makefiles * remove mp_set/get_double() * use ltm 1.2.0 API * update ltm_desc * use bundled tommath if system-tommath is too old * XMALLOC etc. were changed to MP_MALLOC etc.

author	Steffen Jaeckel <s@jaeckel.eu>
date	Tue, 26 May 2020 17:36:47 +0200
parents	f52919ffd3b1
children

rev	line source
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	1 #include "tommath_private.h"
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	2 #ifdef BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	3
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	4 /* LibTomMath, multiple-precision integer library -- Tom St Denis */
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	5 /* SPDX-License-Identifier: Unlicense */
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	6
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	7 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	8 * See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	9 */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	10 #ifndef LTM_USE_ONLY_MR
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	11
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	12 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	13 * 8-bit is just too small. You can try the Frobenius test
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	14 * but that frobenius test can fail, too, for the same reason.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	15 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	16 #ifndef MP_8BIT
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	17
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	18 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	19 * multiply bigint a with int d and put the result in c
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	20 * Like mp_mul_d() but with a signed long as the small input
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	21 */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	22 static mp_err s_mp_mul_si(const mp_int a, int32_t d, mp_int c)
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	23 {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	24 mp_int t;
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	25 mp_err err;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	26
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	27 if ((err = mp_init(&t)) != MP_OKAY) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	28 return err;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	29 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	30
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	31 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	32 * mp_digit might be smaller than a long, which excludes
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	33 * the use of mp_mul_d() here.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	34 */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	35 mp_set_i32(&t, d);
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	36 err = mp_mul(a, &t, c);
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	37 mp_clear(&t);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	38 return err;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	39 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	40 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	41 Strong Lucas-Selfridge test.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	42 returns MP_YES if it is a strong L-S prime, MP_NO if it is composite
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	43
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	44 Code ported from Thomas Ray Nicely's implementation of the BPSW test
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	45 at http://www.trnicely.net/misc/bpsw.html
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	46
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	47 Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	48 Released into the public domain by the author, who disclaims any legal
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	49 liability arising from its use
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	50
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	51 The multi-line comments are made by Thomas R. Nicely and are copied verbatim.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	52 Additional comments marked "CZ" (without the quotes) are by the code-portist.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	53
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	54 (If that name sounds familiar, he is the guy who found the fdiv bug in the
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	55 Pentium (P5x, I think) Intel processor)
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	56 */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	57 mp_err mp_prime_strong_lucas_selfridge(const mp_int a, mp_bool result)
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	58 {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	59 /* CZ TODO: choose better variable names! */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	60 mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	61 /* CZ TODO: Some of them need the full 32 bit, hence the (temporary) exclusion of MP_8BIT */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	62 int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits;
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	63 mp_err err;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	64 mp_bool oddness;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	65
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	66 *result = MP_NO;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	67 /*
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	68 Find the first element D in the sequence {5, -7, 9, -11, 13, ...}
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	69 such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	70 indicates that, if N is not a perfect square, D will "nearly
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	71 always" be "small." Just in case, an overflow trap for D is
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	72 included.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	73 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	74
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	75 if ((err = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz,
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	76 NULL)) != MP_OKAY) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	77 return err;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	78 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	79
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	80 D = 5;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	81 sign = 1;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	82
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	83 for (;;) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	84 Ds = sign * D;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	85 sign = -sign;
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	86 mp_set_u32(&Dz, (uint32_t)D);
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	87 if ((err = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	88
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	89 /* if 1 < GCD < N then N is composite with factor "D", and
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	90 Jacobi(D,N) is technically undefined (but often returned
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	91 as zero). */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	92 if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	93 goto LBL_LS_ERR;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	94 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	95 if (Ds < 0) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	96 Dz.sign = MP_NEG;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	97 }
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	98 if ((err = mp_kronecker(&Dz, a, &J)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	99
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	100 if (J == -1) {
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	101 break;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	102 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	103 D += 2;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	104
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	105 if (D > (INT_MAX - 2)) {
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	106 err = MP_VAL;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	107 goto LBL_LS_ERR;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	108 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	109 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	110
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	111
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	112
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	113 P = 1; /* Selfridge's choice */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	114 Q = (1 - Ds) / 4; /* Required so D = PP - 4Q */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	115
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	116 /* NOTE: The conditions (a) N does not divide Q, and
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	117 (b) D is square-free or not a perfect square, are included by
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	118 some authors; e.g., "Prime numbers and computer methods for
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	119 factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston),
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	120 p. 130. For this particular application of Lucas sequences,
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	121 these conditions were found to be immaterial. */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	122
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	123 /* Now calculate N - Jacobi(D,N) = N + 1 (even), and calculate the
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	124 odd positive integer d and positive integer s for which
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	125 N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test).
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	126 The strong Lucas-Selfridge test then returns N as a strong
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	127 Lucas probable prime (slprp) if any of the following
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	128 conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0,
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	129 V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	130 (all equalities mod N). Thus d is the highest index of U that
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	131 must be computed (since V_2m is independent of U), compared
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	132 to U_{N+1} for the standard Lucas-Selfridge test; and no
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	133 index of V beyond (N+1)/2 is required, just as in the
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	134 standard Lucas-Selfridge test. However, the quantity Q^d must
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	135 be computed for use (if necessary) in the latter stages of
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	136 the test. The result is that the strong Lucas-Selfridge test
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	137 has a running time only slightly greater (order of 10 %) than
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	138 that of the standard Lucas-Selfridge test, while producing
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	139 only (roughly) 30 % as many pseudoprimes (and every strong
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	140 Lucas pseudoprime is also a standard Lucas pseudoprime). Thus
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	141 the evidence indicates that the strong Lucas-Selfridge test is
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	142 more effective than the standard Lucas-Selfridge test, and a
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	143 Baillie-PSW test based on the strong Lucas-Selfridge test
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	144 should be more reliable. */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	145
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	146 if ((err = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	147 s = mp_cnt_lsb(&Np1);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	148
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	149 /* CZ
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	150 * This should round towards zero because
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	151 * Thomas R. Nicely used GMP's mpz_tdiv_q_2exp()
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	152 * and mp_div_2d() is equivalent. Additionally:
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	153 * dividing an even number by two does not produce
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	154 * any leftovers.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	155 */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	156 if ((err = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	157 /* We must now compute U_d and V_d. Since d is odd, the accumulated
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	158 values U and V are initialized to U_1 and V_1 (if the target
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	159 index were even, U and V would be initialized instead to U_0=0
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	160 and V_0=2). The values of U_2m and V_2m are also initialized to
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	161 U_1 and V_1; the FOR loop calculates in succession U_2 and V_2,
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	162 U_4 and V_4, U_8 and V_8, etc. If the corresponding bits
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	163 (1, 2, 3, ...) of t are on (the zero bit having been accounted
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	164 for in the initialization of U and V), these values are then
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	165 combined with the previous totals for U and V, using the
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	166 composition formulas for addition of indices. */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	167
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	168 mp_set(&Uz, 1uL); /* U=U_1 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	169 mp_set(&Vz, (mp_digit)P); /* V=V_1 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	170 mp_set(&U2mz, 1uL); /* U_1 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	171 mp_set(&V2mz, (mp_digit)P); /* V_1 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	172
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	173 mp_set_i32(&Qmz, Q);
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	174 if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	175 /* Initializes calculation of Q^d */
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	176 mp_set_i32(&Qkdz, Q);
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	177
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	178 Nbits = mp_count_bits(&Dz);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	179
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	180 for (u = 1; u < Nbits; u++) { /* zero bit off, already accounted for */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	181 /* Formulas for doubling of indices (carried out mod N). Note that
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	182 * the indices denoted as "2m" are actually powers of 2, specifically
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	183 * 2^(ul-1) beginning each loop and 2^ul ending each loop.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	184 *
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	185 * U_2m = U_m*V_m
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	186 * V_2m = V_mV_m - 2Q^m
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	187 */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	188
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	189 if ((err = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	190 if ((err = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	191 if ((err = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	192 if ((err = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	193 if ((err = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	194
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	195 /* Must calculate powers of Q for use in V_2m, also for Q^d later */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	196 if ((err = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	197
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	198 /* prevents overflow / / CZ still necessary without a fixed prealloc'd mem.? */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	199 if ((err = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	200 if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	201
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	202 if (s_mp_get_bit(&Dz, (unsigned int)u) == MP_YES) {
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	203 /* Formulas for addition of indices (carried out mod N);
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	204 *
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	205 * U_(m+n) = (U_mV_n + U_nV_m)/2
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	206 * V_(m+n) = (V_mV_n + DU_m*U_n)/2
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	207 *
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	208 * Be careful with division by 2 (mod N)!
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	209 */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	210 if ((err = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	211 if ((err = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	212 if ((err = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	213 if ((err = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	214 if ((err = s_mp_mul_si(&T4z, Ds, &T4z)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	215 if ((err = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	216 if (MP_IS_ODD(&Uz)) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	217 if ((err = mp_add(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	218 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	219 /* CZ
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	220 * This should round towards negative infinity because
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	221 * Thomas R. Nicely used GMP's mpz_fdiv_q_2exp().
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	222 * But mp_div_2() does not do so, it is truncating instead.
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	223 */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	224 oddness = MP_IS_ODD(&Uz) ? MP_YES : MP_NO;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	225 if ((err = mp_div_2(&Uz, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	226 if ((Uz.sign == MP_NEG) && (oddness != MP_NO)) {
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	227 if ((err = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	228 }
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	229 if ((err = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	230 if (MP_IS_ODD(&Vz)) {
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	231 if ((err = mp_add(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	232 }
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	233 oddness = MP_IS_ODD(&Vz) ? MP_YES : MP_NO;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	234 if ((err = mp_div_2(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	235 if ((Vz.sign == MP_NEG) && (oddness != MP_NO)) {
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	236 if ((err = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	237 }
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	238 if ((err = mp_mod(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	239 if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	240
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	241 /* Calculating Q^d for later use */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	242 if ((err = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	243 if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	244 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	245 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	246
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	247 /* If U_d or V_d is congruent to 0 mod N, then N is a prime or a
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	248 strong Lucas pseudoprime. */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	249 if (MP_IS_ZERO(&Uz) \|\| MP_IS_ZERO(&Vz)) {
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	250 *result = MP_YES;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	251 goto LBL_LS_ERR;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	252 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	253
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	254 /* NOTE: Ribenboim ("The new book of prime number records," 3rd ed.,
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	255 1995/6) omits the condition V0 on p.142, but includes it on
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	256 p. 130. The condition is NECESSARY; otherwise the test will
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	257 return false negatives---e.g., the primes 29 and 2000029 will be
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	258 returned as composite. */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	259
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	260 /* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d}
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	261 by repeated use of the formula V_2m = V_mV_m - 2Q^m. If any of
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	262 these are congruent to 0 mod N, then N is a prime or a strong
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	263 Lucas pseudoprime. */
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	264
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	265 /* Initialize 2Q^(d2^r) for V_2m */
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	266 if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	267
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	268 for (r = 1; r < s; r++) {
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	269 if ((err = mp_sqr(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	270 if ((err = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	271 if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	272 if (MP_IS_ZERO(&Vz)) {
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	273 *result = MP_YES;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	274 goto LBL_LS_ERR;
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	275 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	276 /* Calculate Q^{d2^r} for next r (final iteration irrelevant). /
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	277 if (r < (s - 1)) {
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	278 if ((err = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	279 if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	280 if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	281 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	282 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	283 LBL_LS_ERR:
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	284 mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL);
1692 1051e4eea25a Update LibTomMath to 1.2.0 (#84) Steffen Jaeckel <s@jaeckel.eu> parents: 1655 diff changeset	285 return err;
1655 f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	286 }
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	287 #endif
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	288 #endif
f52919ffd3b1 update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) Steffen Jaeckel <s_jaeckel@gmx.de> parents: diff changeset	289 #endif

Mercurial > dropbear

annotate libtommath/bn_mp_prime_strong_lucas_selfridge.c @ 1692:1051e4eea25a