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comparison libtommath/bn_mp_karatsuba_mul.c @ 1655:f52919ffd3b1

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update ltm to 1.1.0 and enable FIPS 186.4 compliant key-generation (#79) * make key-generation compliant to FIPS 186.4 * fix includes in tommath_class.h * update fuzzcorpus instead of error-out * fixup fuzzing make-targets * update Makefile.in * apply necessary patches to ltm sources * clean-up not required ltm files * update to vanilla ltm 1.1.0 this already only contains the required files * remove set/get double
author Steffen Jaeckel <s_jaeckel@gmx.de>
date Mon, 16 Sep 2019 15:50:38 +0200
parents 8bba51a55704
children
comparison
equal deleted inserted replaced
1654:cc0fc5131c5c 1655:f52919ffd3b1
1 #include <tommath_private.h> 1 #include "tommath_private.h"
2 #ifdef BN_MP_KARATSUBA_MUL_C 2 #ifdef BN_MP_KARATSUBA_MUL_C
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis 3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
4 * 4 *
5 * LibTomMath is a library that provides multiple-precision 5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality. 6 * integer arithmetic as well as number theoretic functionality.
7 * 7 *
8 * The library was designed directly after the MPI library by 8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with 9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place. 10 * additional optimizations in place.
11 * 11 *
12 * The library is free for all purposes without any express 12 * SPDX-License-Identifier: Unlicense
13 * guarantee it works.
14 *
15 * Tom St Denis, [email protected], http://libtom.org
16 */ 13 */
17 14
18 /* c = |a| * |b| using Karatsuba Multiplication using 15 /* c = |a| * |b| using Karatsuba Multiplication using
19 * three half size multiplications 16 * three half size multiplications
20 * 17 *
21 * Let B represent the radix [e.g. 2**DIGIT_BIT] and 18 * Let B represent the radix [e.g. 2**DIGIT_BIT] and
22 * let n represent half of the number of digits in 19 * let n represent half of the number of digits in
23 * the min(a,b) 20 * the min(a,b)
24 * 21 *
25 * a = a1 * B**n + a0 22 * a = a1 * B**n + a0
26 * b = b1 * B**n + b0 23 * b = b1 * B**n + b0
27 * 24 *
28 * Then, a * b => 25 * Then, a * b =>
29 a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 26 a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
30 * 27 *
31 * Note that a1b1 and a0b0 are used twice and only need to be 28 * Note that a1b1 and a0b0 are used twice and only need to be
32 * computed once. So in total three half size (half # of 29 * computed once. So in total three half size (half # of
33 * digit) multiplications are performed, a0b0, a1b1 and 30 * digit) multiplications are performed, a0b0, a1b1 and
34 * (a1+b1)(a0+b0) 31 * (a1+b1)(a0+b0)
35 * 32 *
36 * Note that a multiplication of half the digits requires 33 * Note that a multiplication of half the digits requires
37 * 1/4th the number of single precision multiplications so in 34 * 1/4th the number of single precision multiplications so in
38 * total after one call 25% of the single precision multiplications 35 * total after one call 25% of the single precision multiplications
39 * are saved. Note also that the call to mp_mul can end up back 36 * are saved. Note also that the call to mp_mul can end up back
40 * in this function if the a0, a1, b0, or b1 are above the threshold. 37 * in this function if the a0, a1, b0, or b1 are above the threshold.
41 * This is known as divide-and-conquer and leads to the famous 38 * This is known as divide-and-conquer and leads to the famous
42 * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than 39 * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
43 * the standard O(N**2) that the baseline/comba methods use. 40 * the standard O(N**2) that the baseline/comba methods use.
44 * Generally though the overhead of this method doesn't pay off 41 * Generally though the overhead of this method doesn't pay off
45 * until a certain size (N ~ 80) is reached. 42 * until a certain size (N ~ 80) is reached.
46 */ 43 */
47 int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c) 44 int mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
48 { 45 {
49 mp_int x0, x1, y0, y1, t1, x0y0, x1y1; 46 mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
50 int B, err; 47 int B, err;
51 48
52 /* default the return code to an error */ 49 /* default the return code to an error */
53 err = MP_MEM; 50 err = MP_MEM;
54 51
55 /* min # of digits */ 52 /* min # of digits */
56 B = MIN (a->used, b->used); 53 B = MIN(a->used, b->used);
57 54
58 /* now divide in two */ 55 /* now divide in two */
59 B = B >> 1; 56 B = B >> 1;
60 57
61 /* init copy all the temps */ 58 /* init copy all the temps */
62 if (mp_init_size (&x0, B) != MP_OKAY) 59 if (mp_init_size(&x0, B) != MP_OKAY)
63 goto ERR; 60 goto LBL_ERR;
64 if (mp_init_size (&x1, a->used - B) != MP_OKAY) 61 if (mp_init_size(&x1, a->used - B) != MP_OKAY)
65 goto X0; 62 goto X0;
66 if (mp_init_size (&y0, B) != MP_OKAY) 63 if (mp_init_size(&y0, B) != MP_OKAY)
67 goto X1; 64 goto X1;
68 if (mp_init_size (&y1, b->used - B) != MP_OKAY) 65 if (mp_init_size(&y1, b->used - B) != MP_OKAY)
69 goto Y0; 66 goto Y0;
70 67
71 /* init temps */ 68 /* init temps */
72 if (mp_init_size (&t1, B * 2) != MP_OKAY) 69 if (mp_init_size(&t1, B * 2) != MP_OKAY)
73 goto Y1; 70 goto Y1;
74 if (mp_init_size (&x0y0, B * 2) != MP_OKAY) 71 if (mp_init_size(&x0y0, B * 2) != MP_OKAY)
75 goto T1; 72 goto T1;
76 if (mp_init_size (&x1y1, B * 2) != MP_OKAY) 73 if (mp_init_size(&x1y1, B * 2) != MP_OKAY)
77 goto X0Y0; 74 goto X0Y0;
78 75
79 /* now shift the digits */ 76 /* now shift the digits */
80 x0.used = y0.used = B; 77 x0.used = y0.used = B;
81 x1.used = a->used - B; 78 x1.used = a->used - B;
82 y1.used = b->used - B; 79 y1.used = b->used - B;
83 80
84 { 81 {
85 int x; 82 int x;
86 mp_digit *tmpa, *tmpb, *tmpx, *tmpy; 83 mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
87 84
88 /* we copy the digits directly instead of using higher level functions 85 /* we copy the digits directly instead of using higher level functions
89 * since we also need to shift the digits 86 * since we also need to shift the digits
90 */ 87 */
91 tmpa = a->dp; 88 tmpa = a->dp;
92 tmpb = b->dp; 89 tmpb = b->dp;
93 90
94 tmpx = x0.dp; 91 tmpx = x0.dp;
95 tmpy = y0.dp; 92 tmpy = y0.dp;
96 for (x = 0; x < B; x++) { 93 for (x = 0; x < B; x++) {
97 *tmpx++ = *tmpa++; 94 *tmpx++ = *tmpa++;
98 *tmpy++ = *tmpb++; 95 *tmpy++ = *tmpb++;
99 } 96 }
100 97
101 tmpx = x1.dp; 98 tmpx = x1.dp;
102 for (x = B; x < a->used; x++) { 99 for (x = B; x < a->used; x++) {
103 *tmpx++ = *tmpa++; 100 *tmpx++ = *tmpa++;
104 } 101 }
105 102
106 tmpy = y1.dp; 103 tmpy = y1.dp;
107 for (x = B; x < b->used; x++) { 104 for (x = B; x < b->used; x++) {
108 *tmpy++ = *tmpb++; 105 *tmpy++ = *tmpb++;
109 } 106 }
110 } 107 }
111 108
112 /* only need to clamp the lower words since by definition the 109 /* only need to clamp the lower words since by definition the
113 * upper words x1/y1 must have a known number of digits 110 * upper words x1/y1 must have a known number of digits
114 */ 111 */
115 mp_clamp (&x0); 112 mp_clamp(&x0);
116 mp_clamp (&y0); 113 mp_clamp(&y0);
117 114
118 /* now calc the products x0y0 and x1y1 */ 115 /* now calc the products x0y0 and x1y1 */
119 /* after this x0 is no longer required, free temp [x0==t2]! */ 116 /* after this x0 is no longer required, free temp [x0==t2]! */
120 if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY) 117 if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY)
121 goto X1Y1; /* x0y0 = x0*y0 */ 118 goto X1Y1; /* x0y0 = x0*y0 */
122 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) 119 if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY)
123 goto X1Y1; /* x1y1 = x1*y1 */ 120 goto X1Y1; /* x1y1 = x1*y1 */
124 121
125 /* now calc x1+x0 and y1+y0 */ 122 /* now calc x1+x0 and y1+y0 */
126 if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) 123 if (s_mp_add(&x1, &x0, &t1) != MP_OKAY)
127 goto X1Y1; /* t1 = x1 - x0 */ 124 goto X1Y1; /* t1 = x1 - x0 */
128 if (s_mp_add (&y1, &y0, &x0) != MP_OKAY) 125 if (s_mp_add(&y1, &y0, &x0) != MP_OKAY)
129 goto X1Y1; /* t2 = y1 - y0 */ 126 goto X1Y1; /* t2 = y1 - y0 */
130 if (mp_mul (&t1, &x0, &t1) != MP_OKAY) 127 if (mp_mul(&t1, &x0, &t1) != MP_OKAY)
131 goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ 128 goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
132 129
133 /* add x0y0 */ 130 /* add x0y0 */
134 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) 131 if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY)
135 goto X1Y1; /* t2 = x0y0 + x1y1 */ 132 goto X1Y1; /* t2 = x0y0 + x1y1 */
136 if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY) 133 if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY)
137 goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ 134 goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
138 135
139 /* shift by B */ 136 /* shift by B */
140 if (mp_lshd (&t1, B) != MP_OKAY) 137 if (mp_lshd(&t1, B) != MP_OKAY)
141 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */ 138 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
142 if (mp_lshd (&x1y1, B * 2) != MP_OKAY) 139 if (mp_lshd(&x1y1, B * 2) != MP_OKAY)
143 goto X1Y1; /* x1y1 = x1y1 << 2*B */ 140 goto X1Y1; /* x1y1 = x1y1 << 2*B */
144 141
145 if (mp_add (&x0y0, &t1, &t1) != MP_OKAY) 142 if (mp_add(&x0y0, &t1, &t1) != MP_OKAY)
146 goto X1Y1; /* t1 = x0y0 + t1 */ 143 goto X1Y1; /* t1 = x0y0 + t1 */
147 if (mp_add (&t1, &x1y1, c) != MP_OKAY) 144 if (mp_add(&t1, &x1y1, c) != MP_OKAY)
148 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */ 145 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
149 146
150 /* Algorithm succeeded set the return code to MP_OKAY */ 147 /* Algorithm succeeded set the return code to MP_OKAY */
151 err = MP_OKAY; 148 err = MP_OKAY;
152 149
153 X1Y1:mp_clear (&x1y1); 150 X1Y1:
154 X0Y0:mp_clear (&x0y0); 151 mp_clear(&x1y1);
155 T1:mp_clear (&t1); 152 X0Y0:
156 Y1:mp_clear (&y1); 153 mp_clear(&x0y0);
157 Y0:mp_clear (&y0); 154 T1:
158 X1:mp_clear (&x1); 155 mp_clear(&t1);
159 X0:mp_clear (&x0); 156 Y1:
160 ERR: 157 mp_clear(&y1);
161 return err; 158 Y0:
159 mp_clear(&y0);
160 X1:
161 mp_clear(&x1);
162 X0:
163 mp_clear(&x0);
164 LBL_ERR:
165 return err;
162 } 166 }
163 #endif 167 #endif
164 168
165 /* ref: $Format:%D$ */ 169 /* ref: HEAD -> master, tag: v1.1.0 */
166 /* git commit: $Format:%H$ */ 170 /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
167 /* commit time: $Format:%ai$ */ 171 /* commit time: 2019-01-28 20:32:32 +0100 */