Mercurial > dropbear

annotate libtommath/bn_mp_prime_strong_lucas_selfridge.c @ 1906:46f68ace1c3c

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Fix act matrix workaround which broke real actions
author Matt Johnston <matt@ucc.asn.au>
date Thu, 24 Mar 2022 16:50:42 +0800
parents 1051e4eea25a
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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 = P*P - 4*Q */
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_m*V_m - 2*Q^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_m*V_n + U_n*V_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_m*V_n + D*U_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_m*V_m - 2*Q^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 2*Q^(d*2^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^{d*2^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