Mercurial > dropbear
annotate curve25519-donna.c @ 1060:4c733310c21d nocircbuffer
reword comment for clarity
| author | Matt Johnston <matt@ucc.asn.au> |
|---|---|
| date | Sun, 01 Mar 2015 23:26:42 +0800 |
| parents | d3925ed45a85 |
| children | 27b9ddb06b09 |
| rev | line source |
|---|---|
| 848 | 1 /* Copyright 2008, Google Inc. |
| 2 * All rights reserved. | |
| 3 * | |
| 4 * Redistribution and use in source and binary forms, with or without | |
| 5 * modification, are permitted provided that the following conditions are | |
| 6 * met: | |
| 7 * | |
| 8 * * Redistributions of source code must retain the above copyright | |
| 9 * notice, this list of conditions and the following disclaimer. | |
| 10 * * Redistributions in binary form must reproduce the above | |
| 11 * copyright notice, this list of conditions and the following disclaimer | |
| 12 * in the documentation and/or other materials provided with the | |
| 13 * distribution. | |
| 14 * * Neither the name of Google Inc. nor the names of its | |
| 15 * contributors may be used to endorse or promote products derived from | |
| 16 * this software without specific prior written permission. | |
| 17 * | |
| 18 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
| 19 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
| 20 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | |
| 21 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT | |
| 22 * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
| 23 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT | |
| 24 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, | |
| 25 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY | |
| 26 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT | |
| 27 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | |
| 28 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
| 29 * | |
| 30 * curve25519-donna: Curve25519 elliptic curve, public key function | |
| 31 * | |
| 32 * http://code.google.com/p/curve25519-donna/ | |
| 33 * | |
| 34 * Adam Langley <[email protected]> | |
| 35 * | |
| 36 * Derived from public domain C code by Daniel J. Bernstein <[email protected]> | |
| 37 * | |
| 38 * More information about curve25519 can be found here | |
| 39 * http://cr.yp.to/ecdh.html | |
| 40 * | |
| 41 * djb's sample implementation of curve25519 is written in a special assembly | |
| 42 * language called qhasm and uses the floating point registers. | |
| 43 * | |
| 44 * This is, almost, a clean room reimplementation from the curve25519 paper. It | |
| 45 * uses many of the tricks described therein. Only the crecip function is taken | |
| 46 * from the sample implementation. | |
| 47 */ | |
| 48 | |
| 49 #include <string.h> | |
| 50 #include <stdint.h> | |
| 51 | |
| 52 #ifdef _MSC_VER | |
| 53 #define inline __inline | |
| 54 #endif | |
| 55 | |
| 56 typedef uint8_t u8; | |
| 57 typedef int32_t s32; | |
| 58 typedef int64_t limb; | |
| 59 | |
| 60 /* Field element representation: | |
| 61 * | |
| 62 * Field elements are written as an array of signed, 64-bit limbs, least | |
| 63 * significant first. The value of the field element is: | |
| 64 * x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ... | |
| 65 * | |
| 66 * i.e. the limbs are 26, 25, 26, 25, ... bits wide. | |
| 67 */ | |
| 68 | |
| 69 /* Sum two numbers: output += in */ | |
| 70 static void fsum(limb *output, const limb *in) { | |
| 71 unsigned i; | |
| 72 for (i = 0; i < 10; i += 2) { | |
| 73 output[0+i] = (output[0+i] + in[0+i]); | |
| 74 output[1+i] = (output[1+i] + in[1+i]); | |
| 75 } | |
| 76 } | |
| 77 | |
| 78 /* Find the difference of two numbers: output = in - output | |
| 79 * (note the order of the arguments!) | |
| 80 */ | |
| 81 static void fdifference(limb *output, const limb *in) { | |
| 82 unsigned i; | |
| 83 for (i = 0; i < 10; ++i) { | |
| 84 output[i] = (in[i] - output[i]); | |
| 85 } | |
| 86 } | |
| 87 | |
| 88 /* Multiply a number by a scalar: output = in * scalar */ | |
| 89 static void fscalar_product(limb *output, const limb *in, const limb scalar) { | |
| 90 unsigned i; | |
| 91 for (i = 0; i < 10; ++i) { | |
| 92 output[i] = in[i] * scalar; | |
| 93 } | |
| 94 } | |
| 95 | |
| 96 /* Multiply two numbers: output = in2 * in | |
| 97 * | |
| 98 * output must be distinct to both inputs. The inputs are reduced coefficient | |
| 99 * form, the output is not. | |
| 100 */ | |
| 101 static void fproduct(limb *output, const limb *in2, const limb *in) { | |
| 102 output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]); | |
| 103 output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) + | |
| 104 ((limb) ((s32) in2[1])) * ((s32) in[0]); | |
| 105 output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) + | |
| 106 ((limb) ((s32) in2[0])) * ((s32) in[2]) + | |
| 107 ((limb) ((s32) in2[2])) * ((s32) in[0]); | |
| 108 output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) + | |
| 109 ((limb) ((s32) in2[2])) * ((s32) in[1]) + | |
| 110 ((limb) ((s32) in2[0])) * ((s32) in[3]) + | |
| 111 ((limb) ((s32) in2[3])) * ((s32) in[0]); | |
| 112 output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) + | |
| 113 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) + | |
| 114 ((limb) ((s32) in2[3])) * ((s32) in[1])) + | |
| 115 ((limb) ((s32) in2[0])) * ((s32) in[4]) + | |
| 116 ((limb) ((s32) in2[4])) * ((s32) in[0]); | |
| 117 output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) + | |
| 118 ((limb) ((s32) in2[3])) * ((s32) in[2]) + | |
| 119 ((limb) ((s32) in2[1])) * ((s32) in[4]) + | |
| 120 ((limb) ((s32) in2[4])) * ((s32) in[1]) + | |
| 121 ((limb) ((s32) in2[0])) * ((s32) in[5]) + | |
| 122 ((limb) ((s32) in2[5])) * ((s32) in[0]); | |
| 123 output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) + | |
| 124 ((limb) ((s32) in2[1])) * ((s32) in[5]) + | |
| 125 ((limb) ((s32) in2[5])) * ((s32) in[1])) + | |
| 126 ((limb) ((s32) in2[2])) * ((s32) in[4]) + | |
| 127 ((limb) ((s32) in2[4])) * ((s32) in[2]) + | |
| 128 ((limb) ((s32) in2[0])) * ((s32) in[6]) + | |
| 129 ((limb) ((s32) in2[6])) * ((s32) in[0]); | |
| 130 output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) + | |
| 131 ((limb) ((s32) in2[4])) * ((s32) in[3]) + | |
| 132 ((limb) ((s32) in2[2])) * ((s32) in[5]) + | |
| 133 ((limb) ((s32) in2[5])) * ((s32) in[2]) + | |
| 134 ((limb) ((s32) in2[1])) * ((s32) in[6]) + | |
| 135 ((limb) ((s32) in2[6])) * ((s32) in[1]) + | |
| 136 ((limb) ((s32) in2[0])) * ((s32) in[7]) + | |
| 137 ((limb) ((s32) in2[7])) * ((s32) in[0]); | |
| 138 output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) + | |
| 139 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) + | |
| 140 ((limb) ((s32) in2[5])) * ((s32) in[3]) + | |
| 141 ((limb) ((s32) in2[1])) * ((s32) in[7]) + | |
| 142 ((limb) ((s32) in2[7])) * ((s32) in[1])) + | |
| 143 ((limb) ((s32) in2[2])) * ((s32) in[6]) + | |
| 144 ((limb) ((s32) in2[6])) * ((s32) in[2]) + | |
| 145 ((limb) ((s32) in2[0])) * ((s32) in[8]) + | |
| 146 ((limb) ((s32) in2[8])) * ((s32) in[0]); | |
| 147 output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) + | |
| 148 ((limb) ((s32) in2[5])) * ((s32) in[4]) + | |
| 149 ((limb) ((s32) in2[3])) * ((s32) in[6]) + | |
| 150 ((limb) ((s32) in2[6])) * ((s32) in[3]) + | |
| 151 ((limb) ((s32) in2[2])) * ((s32) in[7]) + | |
| 152 ((limb) ((s32) in2[7])) * ((s32) in[2]) + | |
| 153 ((limb) ((s32) in2[1])) * ((s32) in[8]) + | |
| 154 ((limb) ((s32) in2[8])) * ((s32) in[1]) + | |
| 155 ((limb) ((s32) in2[0])) * ((s32) in[9]) + | |
| 156 ((limb) ((s32) in2[9])) * ((s32) in[0]); | |
| 157 output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) + | |
| 158 ((limb) ((s32) in2[3])) * ((s32) in[7]) + | |
| 159 ((limb) ((s32) in2[7])) * ((s32) in[3]) + | |
| 160 ((limb) ((s32) in2[1])) * ((s32) in[9]) + | |
| 161 ((limb) ((s32) in2[9])) * ((s32) in[1])) + | |
| 162 ((limb) ((s32) in2[4])) * ((s32) in[6]) + | |
| 163 ((limb) ((s32) in2[6])) * ((s32) in[4]) + | |
| 164 ((limb) ((s32) in2[2])) * ((s32) in[8]) + | |
| 165 ((limb) ((s32) in2[8])) * ((s32) in[2]); | |
| 166 output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) + | |
| 167 ((limb) ((s32) in2[6])) * ((s32) in[5]) + | |
| 168 ((limb) ((s32) in2[4])) * ((s32) in[7]) + | |
| 169 ((limb) ((s32) in2[7])) * ((s32) in[4]) + | |
| 170 ((limb) ((s32) in2[3])) * ((s32) in[8]) + | |
| 171 ((limb) ((s32) in2[8])) * ((s32) in[3]) + | |
| 172 ((limb) ((s32) in2[2])) * ((s32) in[9]) + | |
| 173 ((limb) ((s32) in2[9])) * ((s32) in[2]); | |
| 174 output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) + | |
| 175 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) + | |
| 176 ((limb) ((s32) in2[7])) * ((s32) in[5]) + | |
| 177 ((limb) ((s32) in2[3])) * ((s32) in[9]) + | |
| 178 ((limb) ((s32) in2[9])) * ((s32) in[3])) + | |
| 179 ((limb) ((s32) in2[4])) * ((s32) in[8]) + | |
| 180 ((limb) ((s32) in2[8])) * ((s32) in[4]); | |
| 181 output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) + | |
| 182 ((limb) ((s32) in2[7])) * ((s32) in[6]) + | |
| 183 ((limb) ((s32) in2[5])) * ((s32) in[8]) + | |
| 184 ((limb) ((s32) in2[8])) * ((s32) in[5]) + | |
| 185 ((limb) ((s32) in2[4])) * ((s32) in[9]) + | |
| 186 ((limb) ((s32) in2[9])) * ((s32) in[4]); | |
| 187 output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) + | |
| 188 ((limb) ((s32) in2[5])) * ((s32) in[9]) + | |
| 189 ((limb) ((s32) in2[9])) * ((s32) in[5])) + | |
| 190 ((limb) ((s32) in2[6])) * ((s32) in[8]) + | |
| 191 ((limb) ((s32) in2[8])) * ((s32) in[6]); | |
| 192 output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) + | |
| 193 ((limb) ((s32) in2[8])) * ((s32) in[7]) + | |
| 194 ((limb) ((s32) in2[6])) * ((s32) in[9]) + | |
| 195 ((limb) ((s32) in2[9])) * ((s32) in[6]); | |
| 196 output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) + | |
| 197 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) + | |
| 198 ((limb) ((s32) in2[9])) * ((s32) in[7])); | |
| 199 output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) + | |
| 200 ((limb) ((s32) in2[9])) * ((s32) in[8]); | |
| 201 output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]); | |
| 202 } | |
| 203 | |
| 204 /* Reduce a long form to a short form by taking the input mod 2^255 - 19. */ | |
| 205 static void freduce_degree(limb *output) { | |
| 206 /* Each of these shifts and adds ends up multiplying the value by 19. */ | |
| 207 output[8] += output[18] << 4; | |
| 208 output[8] += output[18] << 1; | |
| 209 output[8] += output[18]; | |
| 210 output[7] += output[17] << 4; | |
| 211 output[7] += output[17] << 1; | |
| 212 output[7] += output[17]; | |
| 213 output[6] += output[16] << 4; | |
| 214 output[6] += output[16] << 1; | |
| 215 output[6] += output[16]; | |
| 216 output[5] += output[15] << 4; | |
| 217 output[5] += output[15] << 1; | |
| 218 output[5] += output[15]; | |
| 219 output[4] += output[14] << 4; | |
| 220 output[4] += output[14] << 1; | |
| 221 output[4] += output[14]; | |
| 222 output[3] += output[13] << 4; | |
| 223 output[3] += output[13] << 1; | |
| 224 output[3] += output[13]; | |
| 225 output[2] += output[12] << 4; | |
| 226 output[2] += output[12] << 1; | |
| 227 output[2] += output[12]; | |
| 228 output[1] += output[11] << 4; | |
| 229 output[1] += output[11] << 1; | |
| 230 output[1] += output[11]; | |
| 231 output[0] += output[10] << 4; | |
| 232 output[0] += output[10] << 1; | |
| 233 output[0] += output[10]; | |
| 234 } | |
| 235 | |
| 236 #if (-1 & 3) != 3 | |
| 237 #error "This code only works on a two's complement system" | |
| 238 #endif | |
| 239 | |
| 240 /* return v / 2^26, using only shifts and adds. */ | |
| 241 static inline limb | |
| 242 div_by_2_26(const limb v) | |
| 243 { | |
| 244 /* High word of v; no shift needed*/ | |
| 245 const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32); | |
| 246 /* Set to all 1s if v was negative; else set to 0s. */ | |
| 247 const int32_t sign = ((int32_t) highword) >> 31; | |
| 248 /* Set to 0x3ffffff if v was negative; else set to 0. */ | |
| 249 const int32_t roundoff = ((uint32_t) sign) >> 6; | |
| 250 /* Should return v / (1<<26) */ | |
| 251 return (v + roundoff) >> 26; | |
| 252 } | |
| 253 | |
| 254 /* return v / (2^25), using only shifts and adds. */ | |
| 255 static inline limb | |
| 256 div_by_2_25(const limb v) | |
| 257 { | |
| 258 /* High word of v; no shift needed*/ | |
| 259 const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32); | |
| 260 /* Set to all 1s if v was negative; else set to 0s. */ | |
| 261 const int32_t sign = ((int32_t) highword) >> 31; | |
| 262 /* Set to 0x1ffffff if v was negative; else set to 0. */ | |
| 263 const int32_t roundoff = ((uint32_t) sign) >> 7; | |
| 264 /* Should return v / (1<<25) */ | |
| 265 return (v + roundoff) >> 25; | |
| 266 } | |
| 267 | |
| 268 static inline s32 | |
| 269 div_s32_by_2_25(const s32 v) | |
| 270 { | |
| 271 const s32 roundoff = ((uint32_t)(v >> 31)) >> 7; | |
| 272 return (v + roundoff) >> 25; | |
| 273 } | |
| 274 | |
| 275 /* Reduce all coefficients of the short form input so that |x| < 2^26. | |
| 276 * | |
| 277 * On entry: |output[i]| < 2^62 | |
| 278 */ | |
| 279 static void freduce_coefficients(limb *output) { | |
| 280 unsigned i; | |
| 281 | |
| 282 output[10] = 0; | |
| 283 | |
| 284 for (i = 0; i < 10; i += 2) { | |
| 285 limb over = div_by_2_26(output[i]); | |
| 286 output[i] -= over << 26; | |
| 287 output[i+1] += over; | |
| 288 | |
| 289 over = div_by_2_25(output[i+1]); | |
| 290 output[i+1] -= over << 25; | |
| 291 output[i+2] += over; | |
| 292 } | |
| 293 /* Now |output[10]| < 2 ^ 38 and all other coefficients are reduced. */ | |
| 294 output[0] += output[10] << 4; | |
| 295 output[0] += output[10] << 1; | |
| 296 output[0] += output[10]; | |
| 297 | |
| 298 output[10] = 0; | |
| 299 | |
| 300 /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19 * 2^38 | |
| 301 * So |over| will be no more than 77825 */ | |
| 302 { | |
| 303 limb over = div_by_2_26(output[0]); | |
| 304 output[0] -= over << 26; | |
| 305 output[1] += over; | |
| 306 } | |
| 307 | |
| 308 /* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 77825 | |
| 309 * So |over| will be no more than 1. */ | |
| 310 { | |
| 311 /* output[1] fits in 32 bits, so we can use div_s32_by_2_25 here. */ | |
| 312 s32 over32 = div_s32_by_2_25((s32) output[1]); | |
| 313 output[1] -= over32 << 25; | |
| 314 output[2] += over32; | |
| 315 } | |
| 316 | |
| 317 /* Finally, output[0,1,3..9] are reduced, and output[2] is "nearly reduced": | |
| 318 * we have |output[2]| <= 2^26. This is good enough for all of our math, | |
| 319 * but it will require an extra freduce_coefficients before fcontract. */ | |
| 320 } | |
| 321 | |
| 322 /* A helpful wrapper around fproduct: output = in * in2. | |
| 323 * | |
| 324 * output must be distinct to both inputs. The output is reduced degree and | |
| 325 * reduced coefficient. | |
| 326 */ | |
| 327 static void | |
| 328 fmul(limb *output, const limb *in, const limb *in2) { | |
| 329 limb t[19]; | |
| 330 fproduct(t, in, in2); | |
| 331 freduce_degree(t); | |
| 332 freduce_coefficients(t); | |
| 333 memcpy(output, t, sizeof(limb) * 10); | |
| 334 } | |
| 335 | |
| 336 static void fsquare_inner(limb *output, const limb *in) { | |
| 337 output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]); | |
| 338 output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]); | |
| 339 output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) + | |
| 340 ((limb) ((s32) in[0])) * ((s32) in[2])); | |
| 341 output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) + | |
| 342 ((limb) ((s32) in[0])) * ((s32) in[3])); | |
| 343 output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) + | |
| 344 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) + | |
| 345 2 * ((limb) ((s32) in[0])) * ((s32) in[4]); | |
| 346 output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) + | |
| 347 ((limb) ((s32) in[1])) * ((s32) in[4]) + | |
| 348 ((limb) ((s32) in[0])) * ((s32) in[5])); | |
| 349 output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) + | |
| 350 ((limb) ((s32) in[2])) * ((s32) in[4]) + | |
| 351 ((limb) ((s32) in[0])) * ((s32) in[6]) + | |
| 352 2 * ((limb) ((s32) in[1])) * ((s32) in[5])); | |
| 353 output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) + | |
| 354 ((limb) ((s32) in[2])) * ((s32) in[5]) + | |
| 355 ((limb) ((s32) in[1])) * ((s32) in[6]) + | |
| 356 ((limb) ((s32) in[0])) * ((s32) in[7])); | |
| 357 output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) + | |
| 358 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) + | |
| 359 ((limb) ((s32) in[0])) * ((s32) in[8]) + | |
| 360 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) + | |
| 361 ((limb) ((s32) in[3])) * ((s32) in[5]))); | |
| 362 output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) + | |
| 363 ((limb) ((s32) in[3])) * ((s32) in[6]) + | |
| 364 ((limb) ((s32) in[2])) * ((s32) in[7]) + | |
| 365 ((limb) ((s32) in[1])) * ((s32) in[8]) + | |
| 366 ((limb) ((s32) in[0])) * ((s32) in[9])); | |
| 367 output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) + | |
| 368 ((limb) ((s32) in[4])) * ((s32) in[6]) + | |
| 369 ((limb) ((s32) in[2])) * ((s32) in[8]) + | |
| 370 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) + | |
| 371 ((limb) ((s32) in[1])) * ((s32) in[9]))); | |
| 372 output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) + | |
| 373 ((limb) ((s32) in[4])) * ((s32) in[7]) + | |
| 374 ((limb) ((s32) in[3])) * ((s32) in[8]) + | |
| 375 ((limb) ((s32) in[2])) * ((s32) in[9])); | |
| 376 output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) + | |
| 377 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) + | |
| 378 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) + | |
| 379 ((limb) ((s32) in[3])) * ((s32) in[9]))); | |
| 380 output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) + | |
| 381 ((limb) ((s32) in[5])) * ((s32) in[8]) + | |
| 382 ((limb) ((s32) in[4])) * ((s32) in[9])); | |
| 383 output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) + | |
| 384 ((limb) ((s32) in[6])) * ((s32) in[8]) + | |
| 385 2 * ((limb) ((s32) in[5])) * ((s32) in[9])); | |
| 386 output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) + | |
| 387 ((limb) ((s32) in[6])) * ((s32) in[9])); | |
| 388 output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) + | |
| 389 4 * ((limb) ((s32) in[7])) * ((s32) in[9]); | |
| 390 output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]); | |
| 391 output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]); | |
| 392 } | |
| 393 | |
| 394 static void | |
| 395 fsquare(limb *output, const limb *in) { | |
| 396 limb t[19]; | |
| 397 fsquare_inner(t, in); | |
| 398 freduce_degree(t); | |
| 399 freduce_coefficients(t); | |
| 400 memcpy(output, t, sizeof(limb) * 10); | |
| 401 } | |
| 402 | |
| 403 /* Take a little-endian, 32-byte number and expand it into polynomial form */ | |
| 404 static void | |
| 405 fexpand(limb *output, const u8 *input) { | |
| 406 #define F(n,start,shift,mask) \ | |
| 407 output[n] = ((((limb) input[start + 0]) | \ | |
| 408 ((limb) input[start + 1]) << 8 | \ | |
| 409 ((limb) input[start + 2]) << 16 | \ | |
| 410 ((limb) input[start + 3]) << 24) >> shift) & mask; | |
| 411 F(0, 0, 0, 0x3ffffff); | |
| 412 F(1, 3, 2, 0x1ffffff); | |
| 413 F(2, 6, 3, 0x3ffffff); | |
| 414 F(3, 9, 5, 0x1ffffff); | |
| 415 F(4, 12, 6, 0x3ffffff); | |
| 416 F(5, 16, 0, 0x1ffffff); | |
| 417 F(6, 19, 1, 0x3ffffff); | |
| 418 F(7, 22, 3, 0x1ffffff); | |
| 419 F(8, 25, 4, 0x3ffffff); | |
| 420 F(9, 28, 6, 0x3ffffff); | |
| 421 #undef F | |
| 422 } | |
| 423 | |
| 424 #if (-32 >> 1) != -16 | |
| 425 #error "This code only works when >> does sign-extension on negative numbers" | |
| 426 #endif | |
| 427 | |
| 428 /* Take a fully reduced polynomial form number and contract it into a | |
| 429 * little-endian, 32-byte array | |
| 430 */ | |
| 431 static void | |
| 432 fcontract(u8 *output, limb *input) { | |
| 433 int i; | |
| 434 int j; | |
| 435 | |
| 436 for (j = 0; j < 2; ++j) { | |
| 437 for (i = 0; i < 9; ++i) { | |
| 438 if ((i & 1) == 1) { | |
| 439 /* This calculation is a time-invariant way to make input[i] positive | |
| 440 by borrowing from the next-larger limb. | |
| 441 */ | |
| 442 const s32 mask = (s32)(input[i]) >> 31; | |
| 443 const s32 carry = -(((s32)(input[i]) & mask) >> 25); | |
| 444 input[i] = (s32)(input[i]) + (carry << 25); | |
| 445 input[i+1] = (s32)(input[i+1]) - carry; | |
| 446 } else { | |
| 447 const s32 mask = (s32)(input[i]) >> 31; | |
| 448 const s32 carry = -(((s32)(input[i]) & mask) >> 26); | |
| 449 input[i] = (s32)(input[i]) + (carry << 26); | |
| 450 input[i+1] = (s32)(input[i+1]) - carry; | |
| 451 } | |
| 452 } | |
| 453 { | |
| 454 const s32 mask = (s32)(input[9]) >> 31; | |
| 455 const s32 carry = -(((s32)(input[9]) & mask) >> 25); | |
| 456 input[9] = (s32)(input[9]) + (carry << 25); | |
| 457 input[0] = (s32)(input[0]) - (carry * 19); | |
| 458 } | |
| 459 } | |
| 460 | |
| 461 /* The first borrow-propagation pass above ended with every limb | |
| 462 except (possibly) input[0] non-negative. | |
| 463 | |
| 464 Since each input limb except input[0] is decreased by at most 1 | |
| 465 by a borrow-propagation pass, the second borrow-propagation pass | |
| 466 could only have wrapped around to decrease input[0] again if the | |
| 467 first pass left input[0] negative *and* input[1] through input[9] | |
| 468 were all zero. In that case, input[1] is now 2^25 - 1, and this | |
| 469 last borrow-propagation step will leave input[1] non-negative. | |
| 470 */ | |
| 471 { | |
| 472 const s32 mask = (s32)(input[0]) >> 31; | |
| 473 const s32 carry = -(((s32)(input[0]) & mask) >> 26); | |
| 474 input[0] = (s32)(input[0]) + (carry << 26); | |
| 475 input[1] = (s32)(input[1]) - carry; | |
| 476 } | |
| 477 | |
| 478 /* Both passes through the above loop, plus the last 0-to-1 step, are | |
| 479 necessary: if input[9] is -1 and input[0] through input[8] are 0, | |
| 480 negative values will remain in the array until the end. | |
| 481 */ | |
| 482 | |
| 483 input[1] <<= 2; | |
| 484 input[2] <<= 3; | |
| 485 input[3] <<= 5; | |
| 486 input[4] <<= 6; | |
| 487 input[6] <<= 1; | |
| 488 input[7] <<= 3; | |
| 489 input[8] <<= 4; | |
| 490 input[9] <<= 6; | |
| 491 #define F(i, s) \ | |
| 492 output[s+0] |= input[i] & 0xff; \ | |
| 493 output[s+1] = (input[i] >> 8) & 0xff; \ | |
| 494 output[s+2] = (input[i] >> 16) & 0xff; \ | |
| 495 output[s+3] = (input[i] >> 24) & 0xff; | |
| 496 output[0] = 0; | |
| 497 output[16] = 0; | |
| 498 F(0,0); | |
| 499 F(1,3); | |
| 500 F(2,6); | |
| 501 F(3,9); | |
| 502 F(4,12); | |
| 503 F(5,16); | |
| 504 F(6,19); | |
| 505 F(7,22); | |
| 506 F(8,25); | |
| 507 F(9,28); | |
| 508 #undef F | |
| 509 } | |
| 510 | |
| 511 /* Input: Q, Q', Q-Q' | |
| 512 * Output: 2Q, Q+Q' | |
| 513 * | |
| 514 * x2 z3: long form | |
| 515 * x3 z3: long form | |
| 516 * x z: short form, destroyed | |
| 517 * xprime zprime: short form, destroyed | |
| 518 * qmqp: short form, preserved | |
| 519 */ | |
| 520 static void fmonty(limb *x2, limb *z2, /* output 2Q */ | |
| 521 limb *x3, limb *z3, /* output Q + Q' */ | |
| 522 limb *x, limb *z, /* input Q */ | |
| 523 limb *xprime, limb *zprime, /* input Q' */ | |
| 524 const limb *qmqp /* input Q - Q' */) { | |
| 525 limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], | |
| 526 zzprime[19], zzzprime[19], xxxprime[19]; | |
| 527 | |
| 528 memcpy(origx, x, 10 * sizeof(limb)); | |
| 529 fsum(x, z); | |
|
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parents:
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diff
changeset
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530 fdifference(z, origx); /* does x - z */ |
| 848 | 531 |
| 532 memcpy(origxprime, xprime, sizeof(limb) * 10); | |
| 533 fsum(xprime, zprime); | |
| 534 fdifference(zprime, origxprime); | |
| 535 fproduct(xxprime, xprime, z); | |
| 536 fproduct(zzprime, x, zprime); | |
| 537 freduce_degree(xxprime); | |
| 538 freduce_coefficients(xxprime); | |
| 539 freduce_degree(zzprime); | |
| 540 freduce_coefficients(zzprime); | |
| 541 memcpy(origxprime, xxprime, sizeof(limb) * 10); | |
| 542 fsum(xxprime, zzprime); | |
| 543 fdifference(zzprime, origxprime); | |
| 544 fsquare(xxxprime, xxprime); | |
| 545 fsquare(zzzprime, zzprime); | |
| 546 fproduct(zzprime, zzzprime, qmqp); | |
| 547 freduce_degree(zzprime); | |
| 548 freduce_coefficients(zzprime); | |
| 549 memcpy(x3, xxxprime, sizeof(limb) * 10); | |
| 550 memcpy(z3, zzprime, sizeof(limb) * 10); | |
| 551 | |
| 552 fsquare(xx, x); | |
| 553 fsquare(zz, z); | |
| 554 fproduct(x2, xx, zz); | |
| 555 freduce_degree(x2); | |
| 556 freduce_coefficients(x2); | |
|
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Thorsten Horstmann <thorsten.horstmann@web.de>
parents:
848
diff
changeset
|
557 fdifference(zz, xx); /* does zz = xx - zz */ |
| 848 | 558 memset(zzz + 10, 0, sizeof(limb) * 9); |
| 559 fscalar_product(zzz, zz, 121665); | |
| 560 /* No need to call freduce_degree here: | |
| 561 fscalar_product doesn't increase the degree of its input. */ | |
| 562 freduce_coefficients(zzz); | |
| 563 fsum(zzz, xx); | |
| 564 fproduct(z2, zz, zzz); | |
| 565 freduce_degree(z2); | |
| 566 freduce_coefficients(z2); | |
| 567 } | |
| 568 | |
| 569 /* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave | |
| 570 * them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid | |
| 571 * side-channel attacks. | |
| 572 * | |
| 573 * NOTE that this function requires that 'iswap' be 1 or 0; other values give | |
| 574 * wrong results. Also, the two limb arrays must be in reduced-coefficient, | |
| 575 * reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped, | |
| 576 * and all all values in a[0..9],b[0..9] must have magnitude less than | |
| 577 * INT32_MAX. | |
| 578 */ | |
| 579 static void | |
| 580 swap_conditional(limb a[19], limb b[19], limb iswap) { | |
| 581 unsigned i; | |
| 582 const s32 swap = (s32) -iswap; | |
| 583 | |
| 584 for (i = 0; i < 10; ++i) { | |
| 585 const s32 x = swap & ( ((s32)a[i]) ^ ((s32)b[i]) ); | |
| 586 a[i] = ((s32)a[i]) ^ x; | |
| 587 b[i] = ((s32)b[i]) ^ x; | |
| 588 } | |
| 589 } | |
| 590 | |
| 591 /* Calculates nQ where Q is the x-coordinate of a point on the curve | |
| 592 * | |
| 593 * resultx/resultz: the x coordinate of the resulting curve point (short form) | |
| 594 * n: a little endian, 32-byte number | |
| 595 * q: a point of the curve (short form) | |
| 596 */ | |
| 597 static void | |
| 598 cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) { | |
| 599 limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0}; | |
| 600 limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t; | |
| 601 limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1}; | |
| 602 limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h; | |
| 603 | |
| 604 unsigned i, j; | |
| 605 | |
| 606 memcpy(nqpqx, q, sizeof(limb) * 10); | |
| 607 | |
| 608 for (i = 0; i < 32; ++i) { | |
| 609 u8 byte = n[31 - i]; | |
| 610 for (j = 0; j < 8; ++j) { | |
| 611 const limb bit = byte >> 7; | |
| 612 | |
| 613 swap_conditional(nqx, nqpqx, bit); | |
| 614 swap_conditional(nqz, nqpqz, bit); | |
| 615 fmonty(nqx2, nqz2, | |
| 616 nqpqx2, nqpqz2, | |
| 617 nqx, nqz, | |
| 618 nqpqx, nqpqz, | |
| 619 q); | |
| 620 swap_conditional(nqx2, nqpqx2, bit); | |
| 621 swap_conditional(nqz2, nqpqz2, bit); | |
| 622 | |
| 623 t = nqx; | |
| 624 nqx = nqx2; | |
| 625 nqx2 = t; | |
| 626 t = nqz; | |
| 627 nqz = nqz2; | |
| 628 nqz2 = t; | |
| 629 t = nqpqx; | |
| 630 nqpqx = nqpqx2; | |
| 631 nqpqx2 = t; | |
| 632 t = nqpqz; | |
| 633 nqpqz = nqpqz2; | |
| 634 nqpqz2 = t; | |
| 635 | |
| 636 byte <<= 1; | |
| 637 } | |
| 638 } | |
| 639 | |
| 640 memcpy(resultx, nqx, sizeof(limb) * 10); | |
| 641 memcpy(resultz, nqz, sizeof(limb) * 10); | |
| 642 } | |
| 643 | |
|
1038
d3925ed45a85
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Thorsten Horstmann <thorsten.horstmann@web.de>
parents:
848
diff
changeset
|
644 /* ----------------------------------------------------------------------------- |
|
d3925ed45a85
Fix for old compilers, variable declarations at beginning of functions
Thorsten Horstmann <thorsten.horstmann@web.de>
parents:
848
diff
changeset
|
645 * Shamelessly copied from djb's code |
|
d3925ed45a85
Fix for old compilers, variable declarations at beginning of functions
Thorsten Horstmann <thorsten.horstmann@web.de>
parents:
848
diff
changeset
|
646 * ----------------------------------------------------------------------------- */ |
| 848 | 647 static void |
| 648 crecip(limb *out, const limb *z) { | |
| 649 limb z2[10]; | |
| 650 limb z9[10]; | |
| 651 limb z11[10]; | |
| 652 limb z2_5_0[10]; | |
| 653 limb z2_10_0[10]; | |
| 654 limb z2_20_0[10]; | |
| 655 limb z2_50_0[10]; | |
| 656 limb z2_100_0[10]; | |
| 657 limb t0[10]; | |
| 658 limb t1[10]; | |
| 659 int i; | |
| 660 | |
| 661 /* 2 */ fsquare(z2,z); | |
| 662 /* 4 */ fsquare(t1,z2); | |
| 663 /* 8 */ fsquare(t0,t1); | |
| 664 /* 9 */ fmul(z9,t0,z); | |
| 665 /* 11 */ fmul(z11,z9,z2); | |
| 666 /* 22 */ fsquare(t0,z11); | |
| 667 /* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9); | |
| 668 | |
| 669 /* 2^6 - 2^1 */ fsquare(t0,z2_5_0); | |
| 670 /* 2^7 - 2^2 */ fsquare(t1,t0); | |
| 671 /* 2^8 - 2^3 */ fsquare(t0,t1); | |
| 672 /* 2^9 - 2^4 */ fsquare(t1,t0); | |
| 673 /* 2^10 - 2^5 */ fsquare(t0,t1); | |
| 674 /* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0); | |
| 675 | |
| 676 /* 2^11 - 2^1 */ fsquare(t0,z2_10_0); | |
| 677 /* 2^12 - 2^2 */ fsquare(t1,t0); | |
| 678 /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } | |
| 679 /* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0); | |
| 680 | |
| 681 /* 2^21 - 2^1 */ fsquare(t0,z2_20_0); | |
| 682 /* 2^22 - 2^2 */ fsquare(t1,t0); | |
| 683 /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } | |
| 684 /* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0); | |
| 685 | |
| 686 /* 2^41 - 2^1 */ fsquare(t1,t0); | |
| 687 /* 2^42 - 2^2 */ fsquare(t0,t1); | |
| 688 /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } | |
| 689 /* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0); | |
| 690 | |
| 691 /* 2^51 - 2^1 */ fsquare(t0,z2_50_0); | |
| 692 /* 2^52 - 2^2 */ fsquare(t1,t0); | |
| 693 /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } | |
| 694 /* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0); | |
| 695 | |
| 696 /* 2^101 - 2^1 */ fsquare(t1,z2_100_0); | |
| 697 /* 2^102 - 2^2 */ fsquare(t0,t1); | |
| 698 /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } | |
| 699 /* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0); | |
| 700 | |
| 701 /* 2^201 - 2^1 */ fsquare(t0,t1); | |
| 702 /* 2^202 - 2^2 */ fsquare(t1,t0); | |
| 703 /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } | |
| 704 /* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0); | |
| 705 | |
| 706 /* 2^251 - 2^1 */ fsquare(t1,t0); | |
| 707 /* 2^252 - 2^2 */ fsquare(t0,t1); | |
| 708 /* 2^253 - 2^3 */ fsquare(t1,t0); | |
| 709 /* 2^254 - 2^4 */ fsquare(t0,t1); | |
| 710 /* 2^255 - 2^5 */ fsquare(t1,t0); | |
| 711 /* 2^255 - 21 */ fmul(out,t1,z11); | |
| 712 } | |
| 713 | |
| 714 int curve25519_donna(u8 *, const u8 *, const u8 *); | |
| 715 | |
| 716 int | |
| 717 curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) { | |
| 718 limb bp[10], x[10], z[11], zmone[10]; | |
| 719 uint8_t e[32]; | |
| 720 int i; | |
| 721 | |
| 722 for (i = 0; i < 32; ++i) e[i] = secret[i]; | |
| 723 e[0] &= 248; | |
| 724 e[31] &= 127; | |
| 725 e[31] |= 64; | |
| 726 | |
| 727 fexpand(bp, basepoint); | |
| 728 cmult(x, z, e, bp); | |
| 729 crecip(zmone, z); | |
| 730 fmul(z, x, zmone); | |
| 731 freduce_coefficients(z); | |
| 732 fcontract(mypublic, z); | |
| 733 return 0; | |
| 734 } |