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annotate gf.c @ 16:09ab3354aa21 libtomcrypt

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propagate of e8bea23df30f9f46c647d06db3b223427b4e3604 and b0b6b4a8843b94d9f049cb5ffe0b1ae91ec1bf8b from branch 'au.asn.ucc.matt.ltc-orig' to 'au.asn.ucc.matt.ltc-db'
author Matt Johnston <matt@ucc.asn.au>
date Tue, 15 Jun 2004 14:27:14 +0000
parents d7da3b1e1540
children
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0
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1 /* LibTomCrypt, modular cryptographic library -- Tom St Denis
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2 *
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3 * LibTomCrypt is a library that provides various cryptographic
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4 * algorithms in a highly modular and flexible manner.
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5 *
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6 * The library is free for all purposes without any express
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7 * guarantee it works.
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8 *
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9 * Tom St Denis, [email protected], http://libtomcrypt.org
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10 */
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11 /* polynomial basis GF(2^w) routines */
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12 #include "mycrypt.h"
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13
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14 #ifdef GF
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15
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16 #define FORLOOP for (i = 0; i < LSIZE; i++)
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17
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18 /* c = a + b */
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19 void gf_add(gf_intp a, gf_intp b, gf_intp c)
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20 {
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21 int i;
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22 FORLOOP c[i] = a[i]^b[i];
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23 }
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24
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25 /* b = a */
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26 void gf_copy(gf_intp a, gf_intp b)
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27 {
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28 int i;
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29 FORLOOP b[i] = a[i];
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30 }
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31
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32 /* a = 0 */
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33 void gf_zero(gf_intp a)
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34 {
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35 int i;
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36 FORLOOP a[i] = 0;
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37 }
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38
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39 /* is a zero? */
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40 int gf_iszero(gf_intp a)
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41 {
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42 int i;
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43 FORLOOP if (a[i]) {
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44 return 0;
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45 }
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46 return 1;
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47 }
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48
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49 /* is a one? */
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50 int gf_isone(gf_intp a)
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51 {
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52 int i;
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53 for (i = 1; i < LSIZE; i++) {
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54 if (a[i]) {
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55 return 0;
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56 }
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57 }
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58 return a[0] == 1;
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59 }
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60
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61 /* b = a << 1*/
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62 void gf_shl(gf_intp a, gf_intp b)
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63 {
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64 int i;
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65 gf_int tmp;
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66
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67 gf_copy(a, tmp);
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68 for (i = LSIZE-1; i > 0; i--)
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69 b[i] = ((tmp[i]<<1)|((tmp[i-1]&0xFFFFFFFFUL)>>31))&0xFFFFFFFFUL;
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70 b[0] = (tmp[0] << 1)&0xFFFFFFFFUL;
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71 gf_zero(tmp);
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72 }
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73
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74 /* b = a >> 1 */
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75 void gf_shr(gf_intp a, gf_intp b)
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76 {
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77 int i;
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78 gf_int tmp;
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79
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80 gf_copy(a, tmp);
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81 for (i = 0; i < LSIZE-1; i++)
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82 b[i] = (((tmp[i]&0xFFFFFFFFUL)>>1)|(tmp[i+1]<<31))&0xFFFFFFFFUL;
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83 b[LSIZE-1] = (tmp[LSIZE-1]&0xFFFFFFFFUL)>>1;
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84 gf_zero(tmp);
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85 }
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86
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87 /* returns -1 if its zero, otherwise degree of a */
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88 int gf_deg(gf_intp a)
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89 {
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90 int i, ii;
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91 unsigned long t;
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92
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93 ii = -1;
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94 for (i = LSIZE-1; i >= 0; i--)
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95 if (a[i]) {
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96 for (t = a[i], ii = 0; t; t >>= 1, ++ii);
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97 break;
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98 }
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99 if (i == -1) i = 0;
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100 return (i<<5)+ii;
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101 }
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102
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103 /* c = ab */
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104 void gf_mul(gf_intp a, gf_intp b, gf_intp c)
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105 {
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106 gf_int ta, tb;
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107 int i, n;
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108
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109 gf_copy(a, ta);
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110 gf_copy(b, tb);
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111 gf_zero(c);
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112 n = gf_deg(ta)+1;
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113 for (i = 0; i < n; i++) {
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114 if (ta[i>>5]&(1<<(i&31)))
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115 gf_add(c, tb, c);
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116 gf_shl(tb, tb);
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117 }
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118 gf_zero(ta);
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119 gf_zero(tb);
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120 }
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121
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122 /* q = a/b, r = a%b */
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123 void gf_div(gf_intp a, gf_intp b, gf_intp q, gf_intp r)
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124 {
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125 gf_int ta, tb, shifts[LSIZE*32];
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126 int i, magb, mag;
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127
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128 mag = gf_deg(a);
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129 magb = gf_deg(b);
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130
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131 /* special cases */
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132 if (magb > mag) {
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133 gf_copy(a, r);
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134 gf_zero(q);
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135 return;
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136 }
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137 if (magb == -1) {
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138 return;
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139 }
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140
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141 /* copy locally */
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142 gf_copy(a, ta);
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143 gf_copy(b, tb);
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144 gf_zero(q);
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diff changeset
145
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146 /* make shifted versions of "b" */
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147 gf_copy(tb, shifts[0]);
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148 for (i = 1; i <= (mag-magb); i++)
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149 gf_shl(shifts[i-1], shifts[i]);
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150
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diff changeset
151 while (mag >= magb) {
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152 i = (mag - magb);
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153 q[i>>5] |= (1<<(i&31));
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154 gf_add(ta, shifts[i], ta);
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155 mag = gf_deg(ta);
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156 }
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157 gf_copy(ta, r);
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158 gf_zero(ta);
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159 gf_zero(tb);
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diff changeset
160 zeromem(shifts, sizeof(shifts));
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161 }
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162
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163 /* b = a mod m */
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164 void gf_mod(gf_intp a, gf_intp m, gf_intp b)
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165 {
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166 gf_int tmp;
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167 gf_div(a,m,tmp,b);
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168 gf_zero(tmp);
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169 }
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170
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171 /* c = ab (mod m) */
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172 void gf_mulmod(gf_intp a, gf_intp b, gf_intp m, gf_intp c)
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173 {
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174 gf_int tmp;
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175 gf_mul(a, b, tmp);
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176 gf_mod(tmp, m, c);
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177 gf_zero(tmp);
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178 }
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179
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180 /* B = 1/A mod M */
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181 void gf_invmod(gf_intp A, gf_intp M, gf_intp B)
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182 {
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183 gf_int m, n, p0, p1, p2, r, q, tmp;
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184
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185 /* put all variables in known setup state */
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diff changeset
186 gf_zero(p0);
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diff changeset
187 gf_zero(p2);
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188 gf_copy(M, m);
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diff changeset
189 gf_copy(A, n);
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190 p0[0] = 1;
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191 gf_div(m, n, p1, r);
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192 gf_copy(p1, q);
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diff changeset
193
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194 /* loop until r == 0 */
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195 while (!gf_iszero(r)) {
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196 gf_copy(n, m);
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197 gf_copy(r, n);
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198 gf_div(m, n, q, r);
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199 gf_mul(q, p1, tmp);
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200 gf_add(tmp, p0, p2);
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201 gf_copy(p1, p0);
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202 gf_copy(p2, p1);
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203 }
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diff changeset
204 gf_copy(p0, B);
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205 gf_zero(p0);
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206 }
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diff changeset
207
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208 /* find a square root modulo a prime. Note the number of
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diff changeset
209 * elements is 2^k - 1, so we must square k-2 times to get the
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diff changeset
210 * square root..
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211 */
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212 void gf_sqrt(gf_intp a, gf_intp M, gf_intp b)
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213 {
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214 int k;
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215 k = gf_deg(M)-2;
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216 gf_copy(a, b);
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diff changeset
217 while (k--)
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218 gf_mulmod(b, b, M, b);
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219 }
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220
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221 /* c = gcd(A,B) */
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diff changeset
222 void gf_gcd(gf_intp A, gf_intp B, gf_intp c)
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diff changeset
223 {
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diff changeset
224 gf_int a, b, r;
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225 int n;
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226
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227 gf_add(A, B, r);
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228 n = gf_deg(r);
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229 if (gf_deg(A) > n) {
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230 gf_copy(A, a);
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diff changeset
231 gf_copy(B, b);
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diff changeset
232 } else {
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233 gf_copy(A, b);
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234 gf_copy(B, a);
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235 }
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236
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diff changeset
237 do {
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238 gf_mod(a, b, r);
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diff changeset
239 gf_copy(b, a);
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diff changeset
240 gf_copy(r, b);
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diff changeset
241 } while (!gf_iszero(r));
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diff changeset
242 gf_copy(a, c);
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diff changeset
243 gf_zero(a);
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diff changeset
244 gf_zero(b);
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diff changeset
245 }
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diff changeset
246
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247 /* returns non-zero if 'a' is irreducible */
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diff changeset
248 int gf_is_prime(gf_intp a)
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diff changeset
249 {
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diff changeset
250 gf_int u, tmp;
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diff changeset
251 int m, n;
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diff changeset
252
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diff changeset
253 gf_zero(u);
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diff changeset
254 u[0] = 2; /* u(x) = x */
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diff changeset
255 m = gf_deg(a);
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diff changeset
256 for (n = 0; n < (m/2); n++) {
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diff changeset
257 gf_mulmod(u, u, a, u); /* u(x) = u(x)^2 mod a(x) */
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diff changeset
258 gf_copy(u, tmp);
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diff changeset
259 tmp[0] ^= 2; /* tmp(x) = u(x) - x */
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diff changeset
260 gf_gcd(tmp, a, tmp); /* tmp(x) = gcd(a(x), u(x) - x) */
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parents:
diff changeset
261 if (!gf_isone(tmp)) {
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diff changeset
262 return 0;
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diff changeset
263 }
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diff changeset
264 }
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diff changeset
265 return 1;
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parents:
diff changeset
266 }
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parents:
diff changeset
267
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diff changeset
268 /* returns bytes required to store a gf_int */
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diff changeset
269 int gf_size(gf_intp a)
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diff changeset
270 {
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diff changeset
271 int n;
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diff changeset
272
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diff changeset
273 n = gf_deg(a);
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diff changeset
274 if (n == -1) {
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diff changeset
275 return 4;
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276 }
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277 n = n + (32 - (n&31));
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278 return n/8;
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279 }
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280
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281 /* store a gf_int */
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282 void gf_toraw(gf_intp a, unsigned char *dst)
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283 {
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284 int x, n;
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285 n = gf_size(a)/4;
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286 for (x = 0; x < n; x++) {
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287 STORE32L(a[x], dst);
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288 dst += 4;
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289 }
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290 }
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291
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292 /* read a gf_int (len == in bytes) */
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293 void gf_readraw(gf_intp a, unsigned char *str, int len)
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294 {
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295 int x;
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296 gf_zero(a);
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297 for (x = 0; x < len/4; x++) {
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298 LOAD32L(a[x], str);
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299 str += 4;
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300 }
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301 }
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302
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303 #endif
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304
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305