| OLD | NEW |
|---|
| (Empty) | |
| 1 // Copyright (c) 2013 The Chromium Authors. All rights reserved. |
| 2 // Use of this source code is governed by a BSD-style license that can be |
| 3 // found in the LICENSE file. |
| 4 |
| 5 /* |
| 6 * curve25519-donna: Curve25519 elliptic curve, public key function |
| 7 * |
| 8 * http://code.google.com/p/curve25519-donna/ |
| 9 * |
| 10 * Adam Langley <agl@imperialviolet.org> |
| 11 * |
| 12 * Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to> |
| 13 * |
| 14 * More information about curve25519 can be found here |
| 15 * http://cr.yp.to/ecdh.html |
| 16 * |
| 17 * djb's sample implementation of curve25519 is written in a special assembly |
| 18 * language called qhasm and uses the floating point registers. |
| 19 * |
| 20 * This is, almost, a clean room reimplementation from the curve25519 paper. It |
| 21 * uses many of the tricks described therein. Only the crecip function is taken |
| 22 * from the sample implementation. |
| 23 */ |
| 24 |
| 25 #include <string.h> |
| 26 #include <stdint.h> |
| 27 |
| 28 typedef uint8_t u8; |
| 29 typedef int32_t s32; |
| 30 typedef int64_t limb; |
| 31 |
| 32 /* Field element representation: |
| 33 * |
| 34 * Field elements are written as an array of signed, 64-bit limbs, least |
| 35 * significant first. The value of the field element is: |
| 36 * x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ... |
| 37 * |
| 38 * i.e. the limbs are 26, 25, 26, 25, ... bits wide. |
| 39 */ |
| 40 |
| 41 /* Sum two numbers: output += in */ |
| 42 static void fsum(limb *output, const limb *in) { |
| 43 unsigned i; |
| 44 for (i = 0; i < 10; i += 2) { |
| 45 output[0+i] = (output[0+i] + in[0+i]); |
| 46 output[1+i] = (output[1+i] + in[1+i]); |
| 47 } |
| 48 } |
| 49 |
| 50 /* Find the difference of two numbers: output = in - output |
| 51 * (note the order of the arguments!) |
| 52 */ |
| 53 static void fdifference(limb *output, const limb *in) { |
| 54 unsigned i; |
| 55 for (i = 0; i < 10; ++i) { |
| 56 output[i] = (in[i] - output[i]); |
| 57 } |
| 58 } |
| 59 |
| 60 /* Multiply a number my a scalar: output = in * scalar */ |
| 61 static void fscalar_product(limb *output, const limb *in, const limb scalar) { |
| 62 unsigned i; |
| 63 for (i = 0; i < 10; ++i) { |
| 64 output[i] = in[i] * scalar; |
| 65 } |
| 66 } |
| 67 |
| 68 /* Multiply two numbers: output = in2 * in |
| 69 * |
| 70 * output must be distinct to both inputs. The inputs are reduced coefficient |
| 71 * form, the output is not. |
| 72 */ |
| 73 static void fproduct(limb *output, const limb *in2, const limb *in) { |
| 74 output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]); |
| 75 output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) + |
| 76 ((limb) ((s32) in2[1])) * ((s32) in[0]); |
| 77 output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) + |
| 78 ((limb) ((s32) in2[0])) * ((s32) in[2]) + |
| 79 ((limb) ((s32) in2[2])) * ((s32) in[0]); |
| 80 output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) + |
| 81 ((limb) ((s32) in2[2])) * ((s32) in[1]) + |
| 82 ((limb) ((s32) in2[0])) * ((s32) in[3]) + |
| 83 ((limb) ((s32) in2[3])) * ((s32) in[0]); |
| 84 output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) + |
| 85 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) + |
| 86 ((limb) ((s32) in2[3])) * ((s32) in[1])) + |
| 87 ((limb) ((s32) in2[0])) * ((s32) in[4]) + |
| 88 ((limb) ((s32) in2[4])) * ((s32) in[0]); |
| 89 output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) + |
| 90 ((limb) ((s32) in2[3])) * ((s32) in[2]) + |
| 91 ((limb) ((s32) in2[1])) * ((s32) in[4]) + |
| 92 ((limb) ((s32) in2[4])) * ((s32) in[1]) + |
| 93 ((limb) ((s32) in2[0])) * ((s32) in[5]) + |
| 94 ((limb) ((s32) in2[5])) * ((s32) in[0]); |
| 95 output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) + |
| 96 ((limb) ((s32) in2[1])) * ((s32) in[5]) + |
| 97 ((limb) ((s32) in2[5])) * ((s32) in[1])) + |
| 98 ((limb) ((s32) in2[2])) * ((s32) in[4]) + |
| 99 ((limb) ((s32) in2[4])) * ((s32) in[2]) + |
| 100 ((limb) ((s32) in2[0])) * ((s32) in[6]) + |
| 101 ((limb) ((s32) in2[6])) * ((s32) in[0]); |
| 102 output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) + |
| 103 ((limb) ((s32) in2[4])) * ((s32) in[3]) + |
| 104 ((limb) ((s32) in2[2])) * ((s32) in[5]) + |
| 105 ((limb) ((s32) in2[5])) * ((s32) in[2]) + |
| 106 ((limb) ((s32) in2[1])) * ((s32) in[6]) + |
| 107 ((limb) ((s32) in2[6])) * ((s32) in[1]) + |
| 108 ((limb) ((s32) in2[0])) * ((s32) in[7]) + |
| 109 ((limb) ((s32) in2[7])) * ((s32) in[0]); |
| 110 output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) + |
| 111 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) + |
| 112 ((limb) ((s32) in2[5])) * ((s32) in[3]) + |
| 113 ((limb) ((s32) in2[1])) * ((s32) in[7]) + |
| 114 ((limb) ((s32) in2[7])) * ((s32) in[1])) + |
| 115 ((limb) ((s32) in2[2])) * ((s32) in[6]) + |
| 116 ((limb) ((s32) in2[6])) * ((s32) in[2]) + |
| 117 ((limb) ((s32) in2[0])) * ((s32) in[8]) + |
| 118 ((limb) ((s32) in2[8])) * ((s32) in[0]); |
| 119 output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) + |
| 120 ((limb) ((s32) in2[5])) * ((s32) in[4]) + |
| 121 ((limb) ((s32) in2[3])) * ((s32) in[6]) + |
| 122 ((limb) ((s32) in2[6])) * ((s32) in[3]) + |
| 123 ((limb) ((s32) in2[2])) * ((s32) in[7]) + |
| 124 ((limb) ((s32) in2[7])) * ((s32) in[2]) + |
| 125 ((limb) ((s32) in2[1])) * ((s32) in[8]) + |
| 126 ((limb) ((s32) in2[8])) * ((s32) in[1]) + |
| 127 ((limb) ((s32) in2[0])) * ((s32) in[9]) + |
| 128 ((limb) ((s32) in2[9])) * ((s32) in[0]); |
| 129 output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) + |
| 130 ((limb) ((s32) in2[3])) * ((s32) in[7]) + |
| 131 ((limb) ((s32) in2[7])) * ((s32) in[3]) + |
| 132 ((limb) ((s32) in2[1])) * ((s32) in[9]) + |
| 133 ((limb) ((s32) in2[9])) * ((s32) in[1])) + |
| 134 ((limb) ((s32) in2[4])) * ((s32) in[6]) + |
| 135 ((limb) ((s32) in2[6])) * ((s32) in[4]) + |
| 136 ((limb) ((s32) in2[2])) * ((s32) in[8]) + |
| 137 ((limb) ((s32) in2[8])) * ((s32) in[2]); |
| 138 output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) + |
| 139 ((limb) ((s32) in2[6])) * ((s32) in[5]) + |
| 140 ((limb) ((s32) in2[4])) * ((s32) in[7]) + |
| 141 ((limb) ((s32) in2[7])) * ((s32) in[4]) + |
| 142 ((limb) ((s32) in2[3])) * ((s32) in[8]) + |
| 143 ((limb) ((s32) in2[8])) * ((s32) in[3]) + |
| 144 ((limb) ((s32) in2[2])) * ((s32) in[9]) + |
| 145 ((limb) ((s32) in2[9])) * ((s32) in[2]); |
| 146 output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) + |
| 147 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) + |
| 148 ((limb) ((s32) in2[7])) * ((s32) in[5]) + |
| 149 ((limb) ((s32) in2[3])) * ((s32) in[9]) + |
| 150 ((limb) ((s32) in2[9])) * ((s32) in[3])) + |
| 151 ((limb) ((s32) in2[4])) * ((s32) in[8]) + |
| 152 ((limb) ((s32) in2[8])) * ((s32) in[4]); |
| 153 output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) + |
| 154 ((limb) ((s32) in2[7])) * ((s32) in[6]) + |
| 155 ((limb) ((s32) in2[5])) * ((s32) in[8]) + |
| 156 ((limb) ((s32) in2[8])) * ((s32) in[5]) + |
| 157 ((limb) ((s32) in2[4])) * ((s32) in[9]) + |
| 158 ((limb) ((s32) in2[9])) * ((s32) in[4]); |
| 159 output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) + |
| 160 ((limb) ((s32) in2[5])) * ((s32) in[9]) + |
| 161 ((limb) ((s32) in2[9])) * ((s32) in[5])) + |
| 162 ((limb) ((s32) in2[6])) * ((s32) in[8]) + |
| 163 ((limb) ((s32) in2[8])) * ((s32) in[6]); |
| 164 output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) + |
| 165 ((limb) ((s32) in2[8])) * ((s32) in[7]) + |
| 166 ((limb) ((s32) in2[6])) * ((s32) in[9]) + |
| 167 ((limb) ((s32) in2[9])) * ((s32) in[6]); |
| 168 output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) + |
| 169 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) + |
| 170 ((limb) ((s32) in2[9])) * ((s32) in[7])); |
| 171 output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) + |
| 172 ((limb) ((s32) in2[9])) * ((s32) in[8]); |
| 173 output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]); |
| 174 } |
| 175 |
| 176 /* Reduce a long form to a short form by taking the input mod 2^255 - 19. */ |
| 177 static void freduce_degree(limb *output) { |
| 178 /* Each of these shifts and adds ends up multiplying the value by 19. */ |
| 179 output[8] += output[18] << 4; |
| 180 output[8] += output[18] << 1; |
| 181 output[8] += output[18]; |
| 182 output[7] += output[17] << 4; |
| 183 output[7] += output[17] << 1; |
| 184 output[7] += output[17]; |
| 185 output[6] += output[16] << 4; |
| 186 output[6] += output[16] << 1; |
| 187 output[6] += output[16]; |
| 188 output[5] += output[15] << 4; |
| 189 output[5] += output[15] << 1; |
| 190 output[5] += output[15]; |
| 191 output[4] += output[14] << 4; |
| 192 output[4] += output[14] << 1; |
| 193 output[4] += output[14]; |
| 194 output[3] += output[13] << 4; |
| 195 output[3] += output[13] << 1; |
| 196 output[3] += output[13]; |
| 197 output[2] += output[12] << 4; |
| 198 output[2] += output[12] << 1; |
| 199 output[2] += output[12]; |
| 200 output[1] += output[11] << 4; |
| 201 output[1] += output[11] << 1; |
| 202 output[1] += output[11]; |
| 203 output[0] += output[10] << 4; |
| 204 output[0] += output[10] << 1; |
| 205 output[0] += output[10]; |
| 206 } |
| 207 |
| 208 /* Reduce all coefficients of the short form input so that |x| < 2^26. |
| 209 * |
| 210 * On entry: |output[i]| < 2^62 |
| 211 */ |
| 212 static void freduce_coefficients(limb *output) { |
| 213 unsigned i; |
| 214 do { |
| 215 output[10] = 0; |
| 216 |
| 217 for (i = 0; i < 10; i += 2) { |
| 218 limb over = output[i] / 0x4000000l; |
| 219 output[i+1] += over; |
| 220 output[i] -= over * 0x4000000l; |
| 221 |
| 222 over = output[i+1] / 0x2000000; |
| 223 output[i+2] += over; |
| 224 output[i+1] -= over * 0x2000000; |
| 225 } |
| 226 output[0] += 19 * output[10]; |
| 227 } while (output[10]); |
| 228 } |
| 229 |
| 230 /* A helpful wrapper around fproduct: output = in * in2. |
| 231 * |
| 232 * output must be distinct to both inputs. The output is reduced degree and |
| 233 * reduced coefficient. |
| 234 */ |
| 235 static void |
| 236 fmul(limb *output, const limb *in, const limb *in2) { |
| 237 limb t[19]; |
| 238 fproduct(t, in, in2); |
| 239 freduce_degree(t); |
| 240 freduce_coefficients(t); |
| 241 memcpy(output, t, sizeof(limb) * 10); |
| 242 } |
| 243 |
| 244 static void fsquare_inner(limb *output, const limb *in) { |
| 245 output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]); |
| 246 output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]); |
| 247 output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) + |
| 248 ((limb) ((s32) in[0])) * ((s32) in[2])); |
| 249 output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) + |
| 250 ((limb) ((s32) in[0])) * ((s32) in[3])); |
| 251 output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) + |
| 252 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) + |
| 253 2 * ((limb) ((s32) in[0])) * ((s32) in[4]); |
| 254 output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) + |
| 255 ((limb) ((s32) in[1])) * ((s32) in[4]) + |
| 256 ((limb) ((s32) in[0])) * ((s32) in[5])); |
| 257 output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) + |
| 258 ((limb) ((s32) in[2])) * ((s32) in[4]) + |
| 259 ((limb) ((s32) in[0])) * ((s32) in[6]) + |
| 260 2 * ((limb) ((s32) in[1])) * ((s32) in[5])); |
| 261 output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) + |
| 262 ((limb) ((s32) in[2])) * ((s32) in[5]) + |
| 263 ((limb) ((s32) in[1])) * ((s32) in[6]) + |
| 264 ((limb) ((s32) in[0])) * ((s32) in[7])); |
| 265 output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) + |
| 266 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) + |
| 267 ((limb) ((s32) in[0])) * ((s32) in[8]) + |
| 268 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) + |
| 269 ((limb) ((s32) in[3])) * ((s32) in[5]))); |
| 270 output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) + |
| 271 ((limb) ((s32) in[3])) * ((s32) in[6]) + |
| 272 ((limb) ((s32) in[2])) * ((s32) in[7]) + |
| 273 ((limb) ((s32) in[1])) * ((s32) in[8]) + |
| 274 ((limb) ((s32) in[0])) * ((s32) in[9])); |
| 275 output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) + |
| 276 ((limb) ((s32) in[4])) * ((s32) in[6]) + |
| 277 ((limb) ((s32) in[2])) * ((s32) in[8]) + |
| 278 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) + |
| 279 ((limb) ((s32) in[1])) * ((s32) in[9]))); |
| 280 output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) + |
| 281 ((limb) ((s32) in[4])) * ((s32) in[7]) + |
| 282 ((limb) ((s32) in[3])) * ((s32) in[8]) + |
| 283 ((limb) ((s32) in[2])) * ((s32) in[9])); |
| 284 output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) + |
| 285 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) + |
| 286 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) + |
| 287 ((limb) ((s32) in[3])) * ((s32) in[9]))); |
| 288 output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) + |
| 289 ((limb) ((s32) in[5])) * ((s32) in[8]) + |
| 290 ((limb) ((s32) in[4])) * ((s32) in[9])); |
| 291 output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) + |
| 292 ((limb) ((s32) in[6])) * ((s32) in[8]) + |
| 293 2 * ((limb) ((s32) in[5])) * ((s32) in[9])); |
| 294 output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) + |
| 295 ((limb) ((s32) in[6])) * ((s32) in[9])); |
| 296 output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) + |
| 297 4 * ((limb) ((s32) in[7])) * ((s32) in[9]); |
| 298 output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]); |
| 299 output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]); |
| 300 } |
| 301 |
| 302 static void |
| 303 fsquare(limb *output, const limb *in) { |
| 304 limb t[19]; |
| 305 fsquare_inner(t, in); |
| 306 freduce_degree(t); |
| 307 freduce_coefficients(t); |
| 308 memcpy(output, t, sizeof(limb) * 10); |
| 309 } |
| 310 |
| 311 /* Take a little-endian, 32-byte number and expand it into polynomial form */ |
| 312 static void |
| 313 fexpand(limb *output, const u8 *input) { |
| 314 #define F(n,start,shift,mask) \ |
| 315 output[n] = ((((limb) input[start + 0]) | \ |
| 316 ((limb) input[start + 1]) << 8 | \ |
| 317 ((limb) input[start + 2]) << 16 | \ |
| 318 ((limb) input[start + 3]) << 24) >> shift) & mask; |
| 319 F(0, 0, 0, 0x3ffffff); |
| 320 F(1, 3, 2, 0x1ffffff); |
| 321 F(2, 6, 3, 0x3ffffff); |
| 322 F(3, 9, 5, 0x1ffffff); |
| 323 F(4, 12, 6, 0x3ffffff); |
| 324 F(5, 16, 0, 0x1ffffff); |
| 325 F(6, 19, 1, 0x3ffffff); |
| 326 F(7, 22, 3, 0x1ffffff); |
| 327 F(8, 25, 4, 0x3ffffff); |
| 328 F(9, 28, 6, 0x1ffffff); |
| 329 #undef F |
| 330 } |
| 331 |
| 332 /* Take a fully reduced polynomial form number and contract it into a |
| 333 * little-endian, 32-byte array |
| 334 */ |
| 335 static void |
| 336 fcontract(u8 *output, limb *input) { |
| 337 int i; |
| 338 |
| 339 do { |
| 340 for (i = 0; i < 9; ++i) { |
| 341 if ((i & 1) == 1) { |
| 342 while (input[i] < 0) { |
| 343 input[i] += 0x2000000; |
| 344 input[i + 1]--; |
| 345 } |
| 346 } else { |
| 347 while (input[i] < 0) { |
| 348 input[i] += 0x4000000; |
| 349 input[i + 1]--; |
| 350 } |
| 351 } |
| 352 } |
| 353 while (input[9] < 0) { |
| 354 input[9] += 0x2000000; |
| 355 input[0] -= 19; |
| 356 } |
| 357 } while (input[0] < 0); |
| 358 |
| 359 input[1] <<= 2; |
| 360 input[2] <<= 3; |
| 361 input[3] <<= 5; |
| 362 input[4] <<= 6; |
| 363 input[6] <<= 1; |
| 364 input[7] <<= 3; |
| 365 input[8] <<= 4; |
| 366 input[9] <<= 6; |
| 367 #define F(i, s) \ |
| 368 output[s+0] |= input[i] & 0xff; \ |
| 369 output[s+1] = (input[i] >> 8) & 0xff; \ |
| 370 output[s+2] = (input[i] >> 16) & 0xff; \ |
| 371 output[s+3] = (input[i] >> 24) & 0xff; |
| 372 output[0] = 0; |
| 373 output[16] = 0; |
| 374 F(0,0); |
| 375 F(1,3); |
| 376 F(2,6); |
| 377 F(3,9); |
| 378 F(4,12); |
| 379 F(5,16); |
| 380 F(6,19); |
| 381 F(7,22); |
| 382 F(8,25); |
| 383 F(9,28); |
| 384 #undef F |
| 385 } |
| 386 |
| 387 /* Input: Q, Q', Q-Q' |
| 388 * Output: 2Q, Q+Q' |
| 389 * |
| 390 * x2 z3: long form |
| 391 * x3 z3: long form |
| 392 * x z: short form, destroyed |
| 393 * xprime zprime: short form, destroyed |
| 394 * qmqp: short form, preserved |
| 395 */ |
| 396 static void fmonty(limb *x2, limb *z2, /* output 2Q */ |
| 397 limb *x3, limb *z3, /* output Q + Q' */ |
| 398 limb *x, limb *z, /* input Q */ |
| 399 limb *xprime, limb *zprime, /* input Q' */ |
| 400 const limb *qmqp /* input Q - Q' */) { |
| 401 limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], |
| 402 zzprime[19], zzzprime[19], xxxprime[19]; |
| 403 |
| 404 memcpy(origx, x, 10 * sizeof(limb)); |
| 405 fsum(x, z); |
| 406 fdifference(z, origx); // does x - z |
| 407 |
| 408 memcpy(origxprime, xprime, sizeof(limb) * 10); |
| 409 fsum(xprime, zprime); |
| 410 fdifference(zprime, origxprime); |
| 411 fproduct(xxprime, xprime, z); |
| 412 fproduct(zzprime, x, zprime); |
| 413 freduce_degree(xxprime); |
| 414 freduce_coefficients(xxprime); |
| 415 freduce_degree(zzprime); |
| 416 freduce_coefficients(zzprime); |
| 417 memcpy(origxprime, xxprime, sizeof(limb) * 10); |
| 418 fsum(xxprime, zzprime); |
| 419 fdifference(zzprime, origxprime); |
| 420 fsquare(xxxprime, xxprime); |
| 421 fsquare(zzzprime, zzprime); |
| 422 fproduct(zzprime, zzzprime, qmqp); |
| 423 freduce_degree(zzprime); |
| 424 freduce_coefficients(zzprime); |
| 425 memcpy(x3, xxxprime, sizeof(limb) * 10); |
| 426 memcpy(z3, zzprime, sizeof(limb) * 10); |
| 427 |
| 428 fsquare(xx, x); |
| 429 fsquare(zz, z); |
| 430 fproduct(x2, xx, zz); |
| 431 freduce_degree(x2); |
| 432 freduce_coefficients(x2); |
| 433 fdifference(zz, xx); // does zz = xx - zz |
| 434 memset(zzz + 10, 0, sizeof(limb) * 9); |
| 435 fscalar_product(zzz, zz, 121665); |
| 436 freduce_degree(zzz); |
| 437 freduce_coefficients(zzz); |
| 438 fsum(zzz, xx); |
| 439 fproduct(z2, zz, zzz); |
| 440 freduce_degree(z2); |
| 441 freduce_coefficients(z2); |
| 442 } |
| 443 |
| 444 /* Calculates nQ where Q is the x-coordinate of a point on the curve |
| 445 * |
| 446 * resultx/resultz: the x coordinate of the resulting curve point (short form) |
| 447 * n: a little endian, 32-byte number |
| 448 * q: a point of the curve (short form) |
| 449 */ |
| 450 static void |
| 451 cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) { |
| 452 limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0}; |
| 453 limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t; |
| 454 limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1}; |
| 455 limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h; |
| 456 |
| 457 unsigned i, j; |
| 458 |
| 459 memcpy(nqpqx, q, sizeof(limb) * 10); |
| 460 |
| 461 for (i = 0; i < 32; ++i) { |
| 462 u8 byte = n[31 - i]; |
| 463 for (j = 0; j < 8; ++j) { |
| 464 if (byte & 0x80) { |
| 465 fmonty(nqpqx2, nqpqz2, |
| 466 nqx2, nqz2, |
| 467 nqpqx, nqpqz, |
| 468 nqx, nqz, |
| 469 q); |
| 470 } else { |
| 471 fmonty(nqx2, nqz2, |
| 472 nqpqx2, nqpqz2, |
| 473 nqx, nqz, |
| 474 nqpqx, nqpqz, |
| 475 q); |
| 476 } |
| 477 |
| 478 t = nqx; |
| 479 nqx = nqx2; |
| 480 nqx2 = t; |
| 481 t = nqz; |
| 482 nqz = nqz2; |
| 483 nqz2 = t; |
| 484 t = nqpqx; |
| 485 nqpqx = nqpqx2; |
| 486 nqpqx2 = t; |
| 487 t = nqpqz; |
| 488 nqpqz = nqpqz2; |
| 489 nqpqz2 = t; |
| 490 |
| 491 byte <<= 1; |
| 492 } |
| 493 } |
| 494 |
| 495 memcpy(resultx, nqx, sizeof(limb) * 10); |
| 496 memcpy(resultz, nqz, sizeof(limb) * 10); |
| 497 } |
| 498 |
| 499 // ----------------------------------------------------------------------------- |
| 500 // Shamelessly copied from djb's code |
| 501 // ----------------------------------------------------------------------------- |
| 502 static void |
| 503 crecip(limb *out, const limb *z) { |
| 504 limb z2[10]; |
| 505 limb z9[10]; |
| 506 limb z11[10]; |
| 507 limb z2_5_0[10]; |
| 508 limb z2_10_0[10]; |
| 509 limb z2_20_0[10]; |
| 510 limb z2_50_0[10]; |
| 511 limb z2_100_0[10]; |
| 512 limb t0[10]; |
| 513 limb t1[10]; |
| 514 int i; |
| 515 |
| 516 /* 2 */ fsquare(z2,z); |
| 517 /* 4 */ fsquare(t1,z2); |
| 518 /* 8 */ fsquare(t0,t1); |
| 519 /* 9 */ fmul(z9,t0,z); |
| 520 /* 11 */ fmul(z11,z9,z2); |
| 521 /* 22 */ fsquare(t0,z11); |
| 522 /* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9); |
| 523 |
| 524 /* 2^6 - 2^1 */ fsquare(t0,z2_5_0); |
| 525 /* 2^7 - 2^2 */ fsquare(t1,t0); |
| 526 /* 2^8 - 2^3 */ fsquare(t0,t1); |
| 527 /* 2^9 - 2^4 */ fsquare(t1,t0); |
| 528 /* 2^10 - 2^5 */ fsquare(t0,t1); |
| 529 /* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0); |
| 530 |
| 531 /* 2^11 - 2^1 */ fsquare(t0,z2_10_0); |
| 532 /* 2^12 - 2^2 */ fsquare(t1,t0); |
| 533 /* 2^20 - 2^10 */ |
| 534 for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
| 535 /* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0); |
| 536 |
| 537 /* 2^21 - 2^1 */ fsquare(t0,z2_20_0); |
| 538 /* 2^22 - 2^2 */ fsquare(t1,t0); |
| 539 /* 2^40 - 2^20 */ |
| 540 for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
| 541 /* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0); |
| 542 |
| 543 /* 2^41 - 2^1 */ fsquare(t1,t0); |
| 544 /* 2^42 - 2^2 */ fsquare(t0,t1); |
| 545 /* 2^50 - 2^10 */ |
| 546 for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } |
| 547 /* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0); |
| 548 |
| 549 /* 2^51 - 2^1 */ fsquare(t0,z2_50_0); |
| 550 /* 2^52 - 2^2 */ fsquare(t1,t0); |
| 551 /* 2^100 - 2^50 */ |
| 552 for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
| 553 /* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0); |
| 554 |
| 555 /* 2^101 - 2^1 */ fsquare(t1,z2_100_0); |
| 556 /* 2^102 - 2^2 */ fsquare(t0,t1); |
| 557 /* 2^200 - 2^100 */ |
| 558 for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } |
| 559 /* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0); |
| 560 |
| 561 /* 2^201 - 2^1 */ fsquare(t0,t1); |
| 562 /* 2^202 - 2^2 */ fsquare(t1,t0); |
| 563 /* 2^250 - 2^50 */ |
| 564 for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
| 565 /* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0); |
| 566 |
| 567 /* 2^251 - 2^1 */ fsquare(t1,t0); |
| 568 /* 2^252 - 2^2 */ fsquare(t0,t1); |
| 569 /* 2^253 - 2^3 */ fsquare(t1,t0); |
| 570 /* 2^254 - 2^4 */ fsquare(t0,t1); |
| 571 /* 2^255 - 2^5 */ fsquare(t1,t0); |
| 572 /* 2^255 - 21 */ fmul(out,t1,z11); |
| 573 } |
| 574 |
| 575 int |
| 576 curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) { |
| 577 limb bp[10], x[10], z[10], zmone[10]; |
| 578 uint8_t e[32]; |
| 579 int i; |
| 580 |
| 581 for (i = 0; i < 32; ++i) e[i] = secret[i]; |
| 582 e[0] &= 248; |
| 583 e[31] &= 127; |
| 584 e[31] |= 64; |
| 585 |
| 586 fexpand(bp, basepoint); |
| 587 cmult(x, z, e, bp); |
| 588 crecip(zmone, z); |
| 589 fmul(z, x, zmone); |
| 590 fcontract(mypublic, z); |
| 591 return 0; |
| 592 } |
| OLD | NEW |
|---|
Chromium Code Reviews
