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annotate tomsfastmath/src/exptmod/fp_exptmod.c @ 643:a362b62d38b2 dropbear-tfm

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Add tomsfastmath from git rev bfa4582842bc3bab42e4be4aed5703437049502a with Makefile.in renamed
author Matt Johnston <matt@ucc.asn.au>
date Wed, 23 Nov 2011 18:10:20 +0700
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a362b62d38b2 Add tomsfastmath from git rev bfa4582842bc3bab42e4be4aed5703437049502a
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1 /* TomsFastMath, a fast ISO C bignum library.
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2 *
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3 * This project is meant to fill in where LibTomMath
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4 * falls short. That is speed ;-)
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5 *
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6 * This project is public domain and free for all purposes.
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7 *
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8 * Tom St Denis, [email protected]
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9 */
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10 #include <tfm.h>
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11
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12 #ifdef TFM_TIMING_RESISTANT
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14 /* timing resistant montgomery ladder based exptmod
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16 Based on work by Marc Joye, Sung-Ming Yen, "The Montgomery Powering Ladder", Cryptographic Hardware and Embedded Systems, CHES 2002
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17 */
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18 static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
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19 {
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20 fp_int R[2];
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21 fp_digit buf, mp;
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22 int err, bitcnt, digidx, y;
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23
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24 /* now setup montgomery */
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25 if ((err = fp_montgomery_setup (P, &mp)) != FP_OKAY) {
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26 return err;
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27 }
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29 fp_init(&R[0]);
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30 fp_init(&R[1]);
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31
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32 /* now we need R mod m */
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33 fp_montgomery_calc_normalization (&R[0], P);
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34
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35 /* now set R[0][1] to G * R mod m */
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36 if (fp_cmp_mag(P, G) != FP_GT) {
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37 /* G > P so we reduce it first */
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38 fp_mod(G, P, &R[1]);
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39 } else {
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40 fp_copy(G, &R[1]);
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41 }
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42 fp_mulmod (&R[1], &R[0], P, &R[1]);
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43
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44 /* for j = t-1 downto 0 do
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45 r_!k = R0*R1; r_k = r_k^2
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46 */
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47
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48 /* set initial mode and bit cnt */
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49 bitcnt = 1;
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50 buf = 0;
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51 digidx = X->used - 1;
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52
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53 for (;;) {
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54 /* grab next digit as required */
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55 if (--bitcnt == 0) {
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56 /* if digidx == -1 we are out of digits so break */
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57 if (digidx == -1) {
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58 break;
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59 }
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60 /* read next digit and reset bitcnt */
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61 buf = X->dp[digidx--];
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62 bitcnt = (int)DIGIT_BIT;
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63 }
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64
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65 /* grab the next msb from the exponent */
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66 y = (fp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
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67 buf <<= (fp_digit)1;
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68
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69 /* do ops */
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70 fp_mul(&R[0], &R[1], &R[y^1]); fp_montgomery_reduce(&R[y^1], P, mp);
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71 fp_sqr(&R[y], &R[y]); fp_montgomery_reduce(&R[y], P, mp);
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72 }
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73
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74 fp_montgomery_reduce(&R[0], P, mp);
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75 fp_copy(&R[0], Y);
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76 return FP_OKAY;
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77 }
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78
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79 #else
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80
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81 /* y = g**x (mod b)
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82 * Some restrictions... x must be positive and < b
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83 */
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84 static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
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85 {
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86 fp_int M[64], res;
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87 fp_digit buf, mp;
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88 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
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89
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90 /* find window size */
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91 x = fp_count_bits (X);
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92 if (x <= 21) {
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93 winsize = 1;
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94 } else if (x <= 36) {
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95 winsize = 3;
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96 } else if (x <= 140) {
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97 winsize = 4;
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98 } else if (x <= 450) {
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99 winsize = 5;
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100 } else {
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101 winsize = 6;
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102 }
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103
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104 /* init M array */
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105 memset(M, 0, sizeof(M));
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106
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107 /* now setup montgomery */
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108 if ((err = fp_montgomery_setup (P, &mp)) != FP_OKAY) {
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parents:
diff changeset
109 return err;
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parents:
diff changeset
110 }
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parents:
diff changeset
111
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
112 /* setup result */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
113 fp_init(&res);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
114
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
115 /* create M table
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
116 *
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
117 * The M table contains powers of the input base, e.g. M[x] = G^x mod P
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
118 *
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
119 * The first half of the table is not computed though accept for M[0] and M[1]
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
120 */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
121
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
122 /* now we need R mod m */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
123 fp_montgomery_calc_normalization (&res, P);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
124
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
125 /* now set M[1] to G * R mod m */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
126 if (fp_cmp_mag(P, G) != FP_GT) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
127 /* G > P so we reduce it first */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
128 fp_mod(G, P, &M[1]);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
129 } else {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
130 fp_copy(G, &M[1]);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
131 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
132 fp_mulmod (&M[1], &res, P, &M[1]);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
133
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parents:
diff changeset
134 /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
135 fp_copy (&M[1], &M[1 << (winsize - 1)]);
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parents:
diff changeset
136 for (x = 0; x < (winsize - 1); x++) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
137 fp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)]);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
138 fp_montgomery_reduce (&M[1 << (winsize - 1)], P, mp);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
139 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
140
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
141 /* create upper table */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
142 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
143 fp_mul(&M[x - 1], &M[1], &M[x]);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
144 fp_montgomery_reduce(&M[x], P, mp);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
145 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
146
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
147 /* set initial mode and bit cnt */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
148 mode = 0;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
149 bitcnt = 1;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
150 buf = 0;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
151 digidx = X->used - 1;
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parents:
diff changeset
152 bitcpy = 0;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
153 bitbuf = 0;
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parents:
diff changeset
154
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
155 for (;;) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
156 /* grab next digit as required */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
157 if (--bitcnt == 0) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
158 /* if digidx == -1 we are out of digits so break */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
159 if (digidx == -1) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
160 break;
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parents:
diff changeset
161 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
162 /* read next digit and reset bitcnt */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
163 buf = X->dp[digidx--];
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
164 bitcnt = (int)DIGIT_BIT;
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parents:
diff changeset
165 }
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parents:
diff changeset
166
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parents:
diff changeset
167 /* grab the next msb from the exponent */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
168 y = (fp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
169 buf <<= (fp_digit)1;
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parents:
diff changeset
170
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parents:
diff changeset
171 /* if the bit is zero and mode == 0 then we ignore it
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
172 * These represent the leading zero bits before the first 1 bit
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parents:
diff changeset
173 * in the exponent. Technically this opt is not required but it
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
174 * does lower the # of trivial squaring/reductions used
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
175 */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
176 if (mode == 0 && y == 0) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
177 continue;
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parents:
diff changeset
178 }
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parents:
diff changeset
179
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parents:
diff changeset
180 /* if the bit is zero and mode == 1 then we square */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
181 if (mode == 1 && y == 0) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
182 fp_sqr(&res, &res);
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parents:
diff changeset
183 fp_montgomery_reduce(&res, P, mp);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
184 continue;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
185 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
186
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
187 /* else we add it to the window */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
188 bitbuf |= (y << (winsize - ++bitcpy));
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
189 mode = 2;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
190
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
191 if (bitcpy == winsize) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
192 /* ok window is filled so square as required and multiply */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
193 /* square first */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
194 for (x = 0; x < winsize; x++) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
195 fp_sqr(&res, &res);
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parents:
diff changeset
196 fp_montgomery_reduce(&res, P, mp);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
197 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
198
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
199 /* then multiply */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
200 fp_mul(&res, &M[bitbuf], &res);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
201 fp_montgomery_reduce(&res, P, mp);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
202
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
203 /* empty window and reset */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
204 bitcpy = 0;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
205 bitbuf = 0;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
206 mode = 1;
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
207 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
208 }
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
209
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
210 /* if bits remain then square/multiply */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
211 if (mode == 2 && bitcpy > 0) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
212 /* square then multiply if the bit is set */
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
213 for (x = 0; x < bitcpy; x++) {
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
214 fp_sqr(&res, &res);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
215 fp_montgomery_reduce(&res, P, mp);
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
216
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Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
217 /* get next bit of the window */
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Matt Johnston <matt@ucc.asn.au>
parents:
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218 bitbuf <<= 1;
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219 if ((bitbuf & (1 << winsize)) != 0) {
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220 /* then multiply */
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221 fp_mul(&res, &M[1], &res);
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222 fp_montgomery_reduce(&res, P, mp);
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223 }
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224 }
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225 }
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226
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227 /* fixup result if Montgomery reduction is used
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228 * recall that any value in a Montgomery system is
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229 * actually multiplied by R mod n. So we have
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230 * to reduce one more time to cancel out the factor
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231 * of R.
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232 */
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233 fp_montgomery_reduce(&res, P, mp);
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234
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235 /* swap res with Y */
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236 fp_copy (&res, Y);
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237 return FP_OKAY;
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238 }
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239
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240 #endif
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241
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242
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243 int fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
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244 {
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245 fp_int tmp;
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246 int err;
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247
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248 #ifdef TFM_CHECK
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249 /* prevent overflows */
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250 if (P->used > (FP_SIZE/2)) {
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251 return FP_VAL;
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252 }
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253 #endif
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254
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255 /* is X negative? */
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256 if (X->sign == FP_NEG) {
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257 /* yes, copy G and invmod it */
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258 fp_copy(G, &tmp);
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259 if ((err = fp_invmod(&tmp, P, &tmp)) != FP_OKAY) {
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260 return err;
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261 }
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262 X->sign = FP_ZPOS;
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263 err = _fp_exptmod(&tmp, X, P, Y);
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264 if (X != Y) {
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265 X->sign = FP_NEG;
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266 }
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267 return err;
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268 } else {
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269 /* Positive exponent so just exptmod */
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270 return _fp_exptmod(G, X, P, Y);
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271 }
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272 }
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273
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274 /* $Source$ */
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275 /* $Revision$ */
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276 /* $Date$ */