1// SPDX-License-Identifier: GPL-2.0 OR MIT 2/* 3 * Copyright (C) 2015-2016 The fiat-crypto Authors. 4 * Copyright (C) 2018-2020 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved. 5 * 6 * This is a machine-generated formally verified implementation of Curve25519 7 * ECDH from: <https://github.com/mit-plv/fiat-crypto>. Though originally 8 * machine generated, it has been tweaked to be suitable for use in the kernel. 9 * It is optimized for 32-bit machines and machines that cannot work efficiently 10 * with 128-bit integer types. 11 */ 12 13/* fe means field element. Here the field is \Z/(2^255-19). An element t, 14 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 15 * t[3]+2^102 t[4]+...+2^230 t[9]. 16 * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc. 17 * Multiplication and carrying produce fe from fe_loose. 18 */ 19typedef struct fe { u32 v[10]; } fe; 20 21/* fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc 22 * Addition and subtraction produce fe_loose from (fe, fe). 23 */ 24typedef struct fe_loose { u32 v[10]; } fe_loose; 25 26static __always_inline void fe_frombytes_impl(u32 h[10], const u8 *s) 27{ 28 /* Ignores top bit of s. */ 29 u32 a0 = get_unaligned_le32(s); 30 u32 a1 = get_unaligned_le32(s+4); 31 u32 a2 = get_unaligned_le32(s+8); 32 u32 a3 = get_unaligned_le32(s+12); 33 u32 a4 = get_unaligned_le32(s+16); 34 u32 a5 = get_unaligned_le32(s+20); 35 u32 a6 = get_unaligned_le32(s+24); 36 u32 a7 = get_unaligned_le32(s+28); 37 h[0] = a0&((1<<26)-1); /* 26 used, 32-26 left. 26 */ 38 h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 = 6+19 = 25 */ 39 h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */ 40 h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) + 6 = 19+ 6 = 25 */ 41 h[4] = (a3>> 6); /* (32- 6) = 26 */ 42 h[5] = a4&((1<<25)-1); /* 25 */ 43 h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 = 7+19 = 26 */ 44 h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */ 45 h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) + 6 = 20+ 6 = 26 */ 46 h[9] = (a7>> 6)&((1<<25)-1); /* 25 */ 47} 48 49static __always_inline void fe_frombytes(fe *h, const u8 *s) 50{ 51 fe_frombytes_impl(h->v, s); 52} 53 54static __always_inline u8 /*bool*/ 55addcarryx_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low) 56{ 57 /* This function extracts 25 bits of result and 1 bit of carry 58 * (26 total), so a 32-bit intermediate is sufficient. 59 */ 60 u32 x = a + b + c; 61 *low = x & ((1 << 25) - 1); 62 return (x >> 25) & 1; 63} 64 65static __always_inline u8 /*bool*/ 66addcarryx_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low) 67{ 68 /* This function extracts 26 bits of result and 1 bit of carry 69 * (27 total), so a 32-bit intermediate is sufficient. 70 */ 71 u32 x = a + b + c; 72 *low = x & ((1 << 26) - 1); 73 return (x >> 26) & 1; 74} 75 76static __always_inline u8 /*bool*/ 77subborrow_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low) 78{ 79 /* This function extracts 25 bits of result and 1 bit of borrow 80 * (26 total), so a 32-bit intermediate is sufficient. 81 */ 82 u32 x = a - b - c; 83 *low = x & ((1 << 25) - 1); 84 return x >> 31; 85} 86 87static __always_inline u8 /*bool*/ 88subborrow_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low) 89{ 90 /* This function extracts 26 bits of result and 1 bit of borrow 91 *(27 total), so a 32-bit intermediate is sufficient. 92 */ 93 u32 x = a - b - c; 94 *low = x & ((1 << 26) - 1); 95 return x >> 31; 96} 97 98static __always_inline u32 cmovznz32(u32 t, u32 z, u32 nz) 99{ 100 t = -!!t; /* all set if nonzero, 0 if 0 */ 101 return (t&nz) | ((~t)&z); 102} 103 104static __always_inline void fe_freeze(u32 out[10], const u32 in1[10]) 105{ 106 { const u32 x17 = in1[9]; 107 { const u32 x18 = in1[8]; 108 { const u32 x16 = in1[7]; 109 { const u32 x14 = in1[6]; 110 { const u32 x12 = in1[5]; 111 { const u32 x10 = in1[4]; 112 { const u32 x8 = in1[3]; 113 { const u32 x6 = in1[2]; 114 { const u32 x4 = in1[1]; 115 { const u32 x2 = in1[0]; 116 { u32 x20; u8/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20); 117 { u32 x23; u8/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23); 118 { u32 x26; u8/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26); 119 { u32 x29; u8/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29); 120 { u32 x32; u8/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32); 121 { u32 x35; u8/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35); 122 { u32 x38; u8/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38); 123 { u32 x41; u8/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41); 124 { u32 x44; u8/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44); 125 { u32 x47; u8/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47); 126 { u32 x49 = cmovznz32(x48, 0x0, 0xffffffff); 127 { u32 x50 = (x49 & 0x3ffffed); 128 { u32 x52; u8/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52); 129 { u32 x54 = (x49 & 0x1ffffff); 130 { u32 x56; u8/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56); 131 { u32 x58 = (x49 & 0x3ffffff); 132 { u32 x60; u8/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60); 133 { u32 x62 = (x49 & 0x1ffffff); 134 { u32 x64; u8/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64); 135 { u32 x66 = (x49 & 0x3ffffff); 136 { u32 x68; u8/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68); 137 { u32 x70 = (x49 & 0x1ffffff); 138 { u32 x72; u8/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72); 139 { u32 x74 = (x49 & 0x3ffffff); 140 { u32 x76; u8/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76); 141 { u32 x78 = (x49 & 0x1ffffff); 142 { u32 x80; u8/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80); 143 { u32 x82 = (x49 & 0x3ffffff); 144 { u32 x84; u8/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84); 145 { u32 x86 = (x49 & 0x1ffffff); 146 { u32 x88; addcarryx_u25(x85, x47, x86, &x88); 147 out[0] = x52; 148 out[1] = x56; 149 out[2] = x60; 150 out[3] = x64; 151 out[4] = x68; 152 out[5] = x72; 153 out[6] = x76; 154 out[7] = x80; 155 out[8] = x84; 156 out[9] = x88; 157 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} 158} 159 160static __always_inline void fe_tobytes(u8 s[32], const fe *f) 161{ 162 u32 h[10]; 163 fe_freeze(h, f->v); 164 s[0] = h[0] >> 0; 165 s[1] = h[0] >> 8; 166 s[2] = h[0] >> 16; 167 s[3] = (h[0] >> 24) | (h[1] << 2); 168 s[4] = h[1] >> 6; 169 s[5] = h[1] >> 14; 170 s[6] = (h[1] >> 22) | (h[2] << 3); 171 s[7] = h[2] >> 5; 172 s[8] = h[2] >> 13; 173 s[9] = (h[2] >> 21) | (h[3] << 5); 174 s[10] = h[3] >> 3; 175 s[11] = h[3] >> 11; 176 s[12] = (h[3] >> 19) | (h[4] << 6); 177 s[13] = h[4] >> 2; 178 s[14] = h[4] >> 10; 179 s[15] = h[4] >> 18; 180 s[16] = h[5] >> 0; 181 s[17] = h[5] >> 8; 182 s[18] = h[5] >> 16; 183 s[19] = (h[5] >> 24) | (h[6] << 1); 184 s[20] = h[6] >> 7; 185 s[21] = h[6] >> 15; 186 s[22] = (h[6] >> 23) | (h[7] << 3); 187 s[23] = h[7] >> 5; 188 s[24] = h[7] >> 13; 189 s[25] = (h[7] >> 21) | (h[8] << 4); 190 s[26] = h[8] >> 4; 191 s[27] = h[8] >> 12; 192 s[28] = (h[8] >> 20) | (h[9] << 6); 193 s[29] = h[9] >> 2; 194 s[30] = h[9] >> 10; 195 s[31] = h[9] >> 18; 196} 197 198/* h = f */ 199static __always_inline void fe_copy(fe *h, const fe *f) 200{ 201 memmove(h, f, sizeof(u32) * 10); 202} 203 204static __always_inline void fe_copy_lt(fe_loose *h, const fe *f) 205{ 206 memmove(h, f, sizeof(u32) * 10); 207} 208 209/* h = 0 */ 210static __always_inline void fe_0(fe *h) 211{ 212 memset(h, 0, sizeof(u32) * 10); 213} 214 215/* h = 1 */ 216static __always_inline void fe_1(fe *h) 217{ 218 memset(h, 0, sizeof(u32) * 10); 219 h->v[0] = 1; 220} 221 222static void fe_add_impl(u32 out[10], const u32 in1[10], const u32 in2[10]) 223{ 224 { const u32 x20 = in1[9]; 225 { const u32 x21 = in1[8]; 226 { const u32 x19 = in1[7]; 227 { const u32 x17 = in1[6]; 228 { const u32 x15 = in1[5]; 229 { const u32 x13 = in1[4]; 230 { const u32 x11 = in1[3]; 231 { const u32 x9 = in1[2]; 232 { const u32 x7 = in1[1]; 233 { const u32 x5 = in1[0]; 234 { const u32 x38 = in2[9]; 235 { const u32 x39 = in2[8]; 236 { const u32 x37 = in2[7]; 237 { const u32 x35 = in2[6]; 238 { const u32 x33 = in2[5]; 239 { const u32 x31 = in2[4]; 240 { const u32 x29 = in2[3]; 241 { const u32 x27 = in2[2]; 242 { const u32 x25 = in2[1]; 243 { const u32 x23 = in2[0]; 244 out[0] = (x5 + x23); 245 out[1] = (x7 + x25); 246 out[2] = (x9 + x27); 247 out[3] = (x11 + x29); 248 out[4] = (x13 + x31); 249 out[5] = (x15 + x33); 250 out[6] = (x17 + x35); 251 out[7] = (x19 + x37); 252 out[8] = (x21 + x39); 253 out[9] = (x20 + x38); 254 }}}}}}}}}}}}}}}}}}}} 255} 256 257/* h = f + g 258 * Can overlap h with f or g. 259 */ 260static __always_inline void fe_add(fe_loose *h, const fe *f, const fe *g) 261{ 262 fe_add_impl(h->v, f->v, g->v); 263} 264 265static void fe_sub_impl(u32 out[10], const u32 in1[10], const u32 in2[10]) 266{ 267 { const u32 x20 = in1[9]; 268 { const u32 x21 = in1[8]; 269 { const u32 x19 = in1[7]; 270 { const u32 x17 = in1[6]; 271 { const u32 x15 = in1[5]; 272 { const u32 x13 = in1[4]; 273 { const u32 x11 = in1[3]; 274 { const u32 x9 = in1[2]; 275 { const u32 x7 = in1[1]; 276 { const u32 x5 = in1[0]; 277 { const u32 x38 = in2[9]; 278 { const u32 x39 = in2[8]; 279 { const u32 x37 = in2[7]; 280 { const u32 x35 = in2[6]; 281 { const u32 x33 = in2[5]; 282 { const u32 x31 = in2[4]; 283 { const u32 x29 = in2[3]; 284 { const u32 x27 = in2[2]; 285 { const u32 x25 = in2[1]; 286 { const u32 x23 = in2[0]; 287 out[0] = ((0x7ffffda + x5) - x23); 288 out[1] = ((0x3fffffe + x7) - x25); 289 out[2] = ((0x7fffffe + x9) - x27); 290 out[3] = ((0x3fffffe + x11) - x29); 291 out[4] = ((0x7fffffe + x13) - x31); 292 out[5] = ((0x3fffffe + x15) - x33); 293 out[6] = ((0x7fffffe + x17) - x35); 294 out[7] = ((0x3fffffe + x19) - x37); 295 out[8] = ((0x7fffffe + x21) - x39); 296 out[9] = ((0x3fffffe + x20) - x38); 297 }}}}}}}}}}}}}}}}}}}} 298} 299 300/* h = f - g 301 * Can overlap h with f or g. 302 */ 303static __always_inline void fe_sub(fe_loose *h, const fe *f, const fe *g) 304{ 305 fe_sub_impl(h->v, f->v, g->v); 306} 307 308static void fe_mul_impl(u32 out[10], const u32 in1[10], const u32 in2[10]) 309{ 310 { const u32 x20 = in1[9]; 311 { const u32 x21 = in1[8]; 312 { const u32 x19 = in1[7]; 313 { const u32 x17 = in1[6]; 314 { const u32 x15 = in1[5]; 315 { const u32 x13 = in1[4]; 316 { const u32 x11 = in1[3]; 317 { const u32 x9 = in1[2]; 318 { const u32 x7 = in1[1]; 319 { const u32 x5 = in1[0]; 320 { const u32 x38 = in2[9]; 321 { const u32 x39 = in2[8]; 322 { const u32 x37 = in2[7]; 323 { const u32 x35 = in2[6]; 324 { const u32 x33 = in2[5]; 325 { const u32 x31 = in2[4]; 326 { const u32 x29 = in2[3]; 327 { const u32 x27 = in2[2]; 328 { const u32 x25 = in2[1]; 329 { const u32 x23 = in2[0]; 330 { u64 x40 = ((u64)x23 * x5); 331 { u64 x41 = (((u64)x23 * x7) + ((u64)x25 * x5)); 332 { u64 x42 = ((((u64)(0x2 * x25) * x7) + ((u64)x23 * x9)) + ((u64)x27 * x5)); 333 { u64 x43 = (((((u64)x25 * x9) + ((u64)x27 * x7)) + ((u64)x23 * x11)) + ((u64)x29 * x5)); 334 { u64 x44 = (((((u64)x27 * x9) + (0x2 * (((u64)x25 * x11) + ((u64)x29 * x7)))) + ((u64)x23 * x13)) + ((u64)x31 * x5)); 335 { u64 x45 = (((((((u64)x27 * x11) + ((u64)x29 * x9)) + ((u64)x25 * x13)) + ((u64)x31 * x7)) + ((u64)x23 * x15)) + ((u64)x33 * x5)); 336 { u64 x46 = (((((0x2 * ((((u64)x29 * x11) + ((u64)x25 * x15)) + ((u64)x33 * x7))) + ((u64)x27 * x13)) + ((u64)x31 * x9)) + ((u64)x23 * x17)) + ((u64)x35 * x5)); 337 { u64 x47 = (((((((((u64)x29 * x13) + ((u64)x31 * x11)) + ((u64)x27 * x15)) + ((u64)x33 * x9)) + ((u64)x25 * x17)) + ((u64)x35 * x7)) + ((u64)x23 * x19)) + ((u64)x37 * x5)); 338 { u64 x48 = (((((((u64)x31 * x13) + (0x2 * (((((u64)x29 * x15) + ((u64)x33 * x11)) + ((u64)x25 * x19)) + ((u64)x37 * x7)))) + ((u64)x27 * x17)) + ((u64)x35 * x9)) + ((u64)x23 * x21)) + ((u64)x39 * x5)); 339 { u64 x49 = (((((((((((u64)x31 * x15) + ((u64)x33 * x13)) + ((u64)x29 * x17)) + ((u64)x35 * x11)) + ((u64)x27 * x19)) + ((u64)x37 * x9)) + ((u64)x25 * x21)) + ((u64)x39 * x7)) + ((u64)x23 * x20)) + ((u64)x38 * x5)); 340 { u64 x50 = (((((0x2 * ((((((u64)x33 * x15) + ((u64)x29 * x19)) + ((u64)x37 * x11)) + ((u64)x25 * x20)) + ((u64)x38 * x7))) + ((u64)x31 * x17)) + ((u64)x35 * x13)) + ((u64)x27 * x21)) + ((u64)x39 * x9)); 341 { u64 x51 = (((((((((u64)x33 * x17) + ((u64)x35 * x15)) + ((u64)x31 * x19)) + ((u64)x37 * x13)) + ((u64)x29 * x21)) + ((u64)x39 * x11)) + ((u64)x27 * x20)) + ((u64)x38 * x9)); 342 { u64 x52 = (((((u64)x35 * x17) + (0x2 * (((((u64)x33 * x19) + ((u64)x37 * x15)) + ((u64)x29 * x20)) + ((u64)x38 * x11)))) + ((u64)x31 * x21)) + ((u64)x39 * x13)); 343 { u64 x53 = (((((((u64)x35 * x19) + ((u64)x37 * x17)) + ((u64)x33 * x21)) + ((u64)x39 * x15)) + ((u64)x31 * x20)) + ((u64)x38 * x13)); 344 { u64 x54 = (((0x2 * ((((u64)x37 * x19) + ((u64)x33 * x20)) + ((u64)x38 * x15))) + ((u64)x35 * x21)) + ((u64)x39 * x17)); 345 { u64 x55 = (((((u64)x37 * x21) + ((u64)x39 * x19)) + ((u64)x35 * x20)) + ((u64)x38 * x17)); 346 { u64 x56 = (((u64)x39 * x21) + (0x2 * (((u64)x37 * x20) + ((u64)x38 * x19)))); 347 { u64 x57 = (((u64)x39 * x20) + ((u64)x38 * x21)); 348 { u64 x58 = ((u64)(0x2 * x38) * x20); 349 { u64 x59 = (x48 + (x58 << 0x4)); 350 { u64 x60 = (x59 + (x58 << 0x1)); 351 { u64 x61 = (x60 + x58); 352 { u64 x62 = (x47 + (x57 << 0x4)); 353 { u64 x63 = (x62 + (x57 << 0x1)); 354 { u64 x64 = (x63 + x57); 355 { u64 x65 = (x46 + (x56 << 0x4)); 356 { u64 x66 = (x65 + (x56 << 0x1)); 357 { u64 x67 = (x66 + x56); 358 { u64 x68 = (x45 + (x55 << 0x4)); 359 { u64 x69 = (x68 + (x55 << 0x1)); 360 { u64 x70 = (x69 + x55); 361 { u64 x71 = (x44 + (x54 << 0x4)); 362 { u64 x72 = (x71 + (x54 << 0x1)); 363 { u64 x73 = (x72 + x54); 364 { u64 x74 = (x43 + (x53 << 0x4)); 365 { u64 x75 = (x74 + (x53 << 0x1)); 366 { u64 x76 = (x75 + x53); 367 { u64 x77 = (x42 + (x52 << 0x4)); 368 { u64 x78 = (x77 + (x52 << 0x1)); 369 { u64 x79 = (x78 + x52); 370 { u64 x80 = (x41 + (x51 << 0x4)); 371 { u64 x81 = (x80 + (x51 << 0x1)); 372 { u64 x82 = (x81 + x51); 373 { u64 x83 = (x40 + (x50 << 0x4)); 374 { u64 x84 = (x83 + (x50 << 0x1)); 375 { u64 x85 = (x84 + x50); 376 { u64 x86 = (x85 >> 0x1a); 377 { u32 x87 = ((u32)x85 & 0x3ffffff); 378 { u64 x88 = (x86 + x82); 379 { u64 x89 = (x88 >> 0x19); 380 { u32 x90 = ((u32)x88 & 0x1ffffff); 381 { u64 x91 = (x89 + x79); 382 { u64 x92 = (x91 >> 0x1a); 383 { u32 x93 = ((u32)x91 & 0x3ffffff); 384 { u64 x94 = (x92 + x76); 385 { u64 x95 = (x94 >> 0x19); 386 { u32 x96 = ((u32)x94 & 0x1ffffff); 387 { u64 x97 = (x95 + x73); 388 { u64 x98 = (x97 >> 0x1a); 389 { u32 x99 = ((u32)x97 & 0x3ffffff); 390 { u64 x100 = (x98 + x70); 391 { u64 x101 = (x100 >> 0x19); 392 { u32 x102 = ((u32)x100 & 0x1ffffff); 393 { u64 x103 = (x101 + x67); 394 { u64 x104 = (x103 >> 0x1a); 395 { u32 x105 = ((u32)x103 & 0x3ffffff); 396 { u64 x106 = (x104 + x64); 397 { u64 x107 = (x106 >> 0x19); 398 { u32 x108 = ((u32)x106 & 0x1ffffff); 399 { u64 x109 = (x107 + x61); 400 { u64 x110 = (x109 >> 0x1a); 401 { u32 x111 = ((u32)x109 & 0x3ffffff); 402 { u64 x112 = (x110 + x49); 403 { u64 x113 = (x112 >> 0x19); 404 { u32 x114 = ((u32)x112 & 0x1ffffff); 405 { u64 x115 = (x87 + (0x13 * x113)); 406 { u32 x116 = (u32) (x115 >> 0x1a); 407 { u32 x117 = ((u32)x115 & 0x3ffffff); 408 { u32 x118 = (x116 + x90); 409 { u32 x119 = (x118 >> 0x19); 410 { u32 x120 = (x118 & 0x1ffffff); 411 out[0] = x117; 412 out[1] = x120; 413 out[2] = (x119 + x93); 414 out[3] = x96; 415 out[4] = x99; 416 out[5] = x102; 417 out[6] = x105; 418 out[7] = x108; 419 out[8] = x111; 420 out[9] = x114; 421 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} 422} 423 424static __always_inline void fe_mul_ttt(fe *h, const fe *f, const fe *g) 425{ 426 fe_mul_impl(h->v, f->v, g->v); 427} 428 429static __always_inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) 430{ 431 fe_mul_impl(h->v, f->v, g->v); 432} 433 434static __always_inline void 435fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) 436{ 437 fe_mul_impl(h->v, f->v, g->v); 438} 439 440static void fe_sqr_impl(u32 out[10], const u32 in1[10]) 441{ 442 { const u32 x17 = in1[9]; 443 { const u32 x18 = in1[8]; 444 { const u32 x16 = in1[7]; 445 { const u32 x14 = in1[6]; 446 { const u32 x12 = in1[5]; 447 { const u32 x10 = in1[4]; 448 { const u32 x8 = in1[3]; 449 { const u32 x6 = in1[2]; 450 { const u32 x4 = in1[1]; 451 { const u32 x2 = in1[0]; 452 { u64 x19 = ((u64)x2 * x2); 453 { u64 x20 = ((u64)(0x2 * x2) * x4); 454 { u64 x21 = (0x2 * (((u64)x4 * x4) + ((u64)x2 * x6))); 455 { u64 x22 = (0x2 * (((u64)x4 * x6) + ((u64)x2 * x8))); 456 { u64 x23 = ((((u64)x6 * x6) + ((u64)(0x4 * x4) * x8)) + ((u64)(0x2 * x2) * x10)); 457 { u64 x24 = (0x2 * ((((u64)x6 * x8) + ((u64)x4 * x10)) + ((u64)x2 * x12))); 458 { u64 x25 = (0x2 * (((((u64)x8 * x8) + ((u64)x6 * x10)) + ((u64)x2 * x14)) + ((u64)(0x2 * x4) * x12))); 459 { u64 x26 = (0x2 * (((((u64)x8 * x10) + ((u64)x6 * x12)) + ((u64)x4 * x14)) + ((u64)x2 * x16))); 460 { u64 x27 = (((u64)x10 * x10) + (0x2 * ((((u64)x6 * x14) + ((u64)x2 * x18)) + (0x2 * (((u64)x4 * x16) + ((u64)x8 * x12)))))); 461 { u64 x28 = (0x2 * ((((((u64)x10 * x12) + ((u64)x8 * x14)) + ((u64)x6 * x16)) + ((u64)x4 * x18)) + ((u64)x2 * x17))); 462 { u64 x29 = (0x2 * (((((u64)x12 * x12) + ((u64)x10 * x14)) + ((u64)x6 * x18)) + (0x2 * (((u64)x8 * x16) + ((u64)x4 * x17))))); 463 { u64 x30 = (0x2 * (((((u64)x12 * x14) + ((u64)x10 * x16)) + ((u64)x8 * x18)) + ((u64)x6 * x17))); 464 { u64 x31 = (((u64)x14 * x14) + (0x2 * (((u64)x10 * x18) + (0x2 * (((u64)x12 * x16) + ((u64)x8 * x17)))))); 465 { u64 x32 = (0x2 * ((((u64)x14 * x16) + ((u64)x12 * x18)) + ((u64)x10 * x17))); 466 { u64 x33 = (0x2 * ((((u64)x16 * x16) + ((u64)x14 * x18)) + ((u64)(0x2 * x12) * x17))); 467 { u64 x34 = (0x2 * (((u64)x16 * x18) + ((u64)x14 * x17))); 468 { u64 x35 = (((u64)x18 * x18) + ((u64)(0x4 * x16) * x17)); 469 { u64 x36 = ((u64)(0x2 * x18) * x17); 470 { u64 x37 = ((u64)(0x2 * x17) * x17); 471 { u64 x38 = (x27 + (x37 << 0x4)); 472 { u64 x39 = (x38 + (x37 << 0x1)); 473 { u64 x40 = (x39 + x37); 474 { u64 x41 = (x26 + (x36 << 0x4)); 475 { u64 x42 = (x41 + (x36 << 0x1)); 476 { u64 x43 = (x42 + x36); 477 { u64 x44 = (x25 + (x35 << 0x4)); 478 { u64 x45 = (x44 + (x35 << 0x1)); 479 { u64 x46 = (x45 + x35); 480 { u64 x47 = (x24 + (x34 << 0x4)); 481 { u64 x48 = (x47 + (x34 << 0x1)); 482 { u64 x49 = (x48 + x34); 483 { u64 x50 = (x23 + (x33 << 0x4)); 484 { u64 x51 = (x50 + (x33 << 0x1)); 485 { u64 x52 = (x51 + x33); 486 { u64 x53 = (x22 + (x32 << 0x4)); 487 { u64 x54 = (x53 + (x32 << 0x1)); 488 { u64 x55 = (x54 + x32); 489 { u64 x56 = (x21 + (x31 << 0x4)); 490 { u64 x57 = (x56 + (x31 << 0x1)); 491 { u64 x58 = (x57 + x31); 492 { u64 x59 = (x20 + (x30 << 0x4)); 493 { u64 x60 = (x59 + (x30 << 0x1)); 494 { u64 x61 = (x60 + x30); 495 { u64 x62 = (x19 + (x29 << 0x4)); 496 { u64 x63 = (x62 + (x29 << 0x1)); 497 { u64 x64 = (x63 + x29); 498 { u64 x65 = (x64 >> 0x1a); 499 { u32 x66 = ((u32)x64 & 0x3ffffff); 500 { u64 x67 = (x65 + x61); 501 { u64 x68 = (x67 >> 0x19); 502 { u32 x69 = ((u32)x67 & 0x1ffffff); 503 { u64 x70 = (x68 + x58); 504 { u64 x71 = (x70 >> 0x1a); 505 { u32 x72 = ((u32)x70 & 0x3ffffff); 506 { u64 x73 = (x71 + x55); 507 { u64 x74 = (x73 >> 0x19); 508 { u32 x75 = ((u32)x73 & 0x1ffffff); 509 { u64 x76 = (x74 + x52); 510 { u64 x77 = (x76 >> 0x1a); 511 { u32 x78 = ((u32)x76 & 0x3ffffff); 512 { u64 x79 = (x77 + x49); 513 { u64 x80 = (x79 >> 0x19); 514 { u32 x81 = ((u32)x79 & 0x1ffffff); 515 { u64 x82 = (x80 + x46); 516 { u64 x83 = (x82 >> 0x1a); 517 { u32 x84 = ((u32)x82 & 0x3ffffff); 518 { u64 x85 = (x83 + x43); 519 { u64 x86 = (x85 >> 0x19); 520 { u32 x87 = ((u32)x85 & 0x1ffffff); 521 { u64 x88 = (x86 + x40); 522 { u64 x89 = (x88 >> 0x1a); 523 { u32 x90 = ((u32)x88 & 0x3ffffff); 524 { u64 x91 = (x89 + x28); 525 { u64 x92 = (x91 >> 0x19); 526 { u32 x93 = ((u32)x91 & 0x1ffffff); 527 { u64 x94 = (x66 + (0x13 * x92)); 528 { u32 x95 = (u32) (x94 >> 0x1a); 529 { u32 x96 = ((u32)x94 & 0x3ffffff); 530 { u32 x97 = (x95 + x69); 531 { u32 x98 = (x97 >> 0x19); 532 { u32 x99 = (x97 & 0x1ffffff); 533 out[0] = x96; 534 out[1] = x99; 535 out[2] = (x98 + x72); 536 out[3] = x75; 537 out[4] = x78; 538 out[5] = x81; 539 out[6] = x84; 540 out[7] = x87; 541 out[8] = x90; 542 out[9] = x93; 543 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} 544} 545 546static __always_inline void fe_sq_tl(fe *h, const fe_loose *f) 547{ 548 fe_sqr_impl(h->v, f->v); 549} 550 551static __always_inline void fe_sq_tt(fe *h, const fe *f) 552{ 553 fe_sqr_impl(h->v, f->v); 554} 555 556static __always_inline void fe_loose_invert(fe *out, const fe_loose *z) 557{ 558 fe t0; 559 fe t1; 560 fe t2; 561 fe t3; 562 int i; 563 564 fe_sq_tl(&t0, z); 565 fe_sq_tt(&t1, &t0); 566 for (i = 1; i < 2; ++i) 567 fe_sq_tt(&t1, &t1); 568 fe_mul_tlt(&t1, z, &t1); 569 fe_mul_ttt(&t0, &t0, &t1); 570 fe_sq_tt(&t2, &t0); 571 fe_mul_ttt(&t1, &t1, &t2); 572 fe_sq_tt(&t2, &t1); 573 for (i = 1; i < 5; ++i) 574 fe_sq_tt(&t2, &t2); 575 fe_mul_ttt(&t1, &t2, &t1); 576 fe_sq_tt(&t2, &t1); 577 for (i = 1; i < 10; ++i) 578 fe_sq_tt(&t2, &t2); 579 fe_mul_ttt(&t2, &t2, &t1); 580 fe_sq_tt(&t3, &t2); 581 for (i = 1; i < 20; ++i) 582 fe_sq_tt(&t3, &t3); 583 fe_mul_ttt(&t2, &t3, &t2); 584 fe_sq_tt(&t2, &t2); 585 for (i = 1; i < 10; ++i) 586 fe_sq_tt(&t2, &t2); 587 fe_mul_ttt(&t1, &t2, &t1); 588 fe_sq_tt(&t2, &t1); 589 for (i = 1; i < 50; ++i) 590 fe_sq_tt(&t2, &t2); 591 fe_mul_ttt(&t2, &t2, &t1); 592 fe_sq_tt(&t3, &t2); 593 for (i = 1; i < 100; ++i) 594 fe_sq_tt(&t3, &t3); 595 fe_mul_ttt(&t2, &t3, &t2); 596 fe_sq_tt(&t2, &t2); 597 for (i = 1; i < 50; ++i) 598 fe_sq_tt(&t2, &t2); 599 fe_mul_ttt(&t1, &t2, &t1); 600 fe_sq_tt(&t1, &t1); 601 for (i = 1; i < 5; ++i) 602 fe_sq_tt(&t1, &t1); 603 fe_mul_ttt(out, &t1, &t0); 604} 605 606static __always_inline void fe_invert(fe *out, const fe *z) 607{ 608 fe_loose l; 609 fe_copy_lt(&l, z); 610 fe_loose_invert(out, &l); 611} 612 613/* Replace (f,g) with (g,f) if b == 1; 614 * replace (f,g) with (f,g) if b == 0. 615 * 616 * Preconditions: b in {0,1} 617 */ 618static __always_inline void fe_cswap(fe *f, fe *g, unsigned int b) 619{ 620 unsigned i; 621 b = 0 - b; 622 for (i = 0; i < 10; i++) { 623 u32 x = f->v[i] ^ g->v[i]; 624 x &= b; 625 f->v[i] ^= x; 626 g->v[i] ^= x; 627 } 628} 629 630/* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/ 631static __always_inline void fe_mul_121666_impl(u32 out[10], const u32 in1[10]) 632{ 633 { const u32 x20 = in1[9]; 634 { const u32 x21 = in1[8]; 635 { const u32 x19 = in1[7]; 636 { const u32 x17 = in1[6]; 637 { const u32 x15 = in1[5]; 638 { const u32 x13 = in1[4]; 639 { const u32 x11 = in1[3]; 640 { const u32 x9 = in1[2]; 641 { const u32 x7 = in1[1]; 642 { const u32 x5 = in1[0]; 643 { const u32 x38 = 0; 644 { const u32 x39 = 0; 645 { const u32 x37 = 0; 646 { const u32 x35 = 0; 647 { const u32 x33 = 0; 648 { const u32 x31 = 0; 649 { const u32 x29 = 0; 650 { const u32 x27 = 0; 651 { const u32 x25 = 0; 652 { const u32 x23 = 121666; 653 { u64 x40 = ((u64)x23 * x5); 654 { u64 x41 = (((u64)x23 * x7) + ((u64)x25 * x5)); 655 { u64 x42 = ((((u64)(0x2 * x25) * x7) + ((u64)x23 * x9)) + ((u64)x27 * x5)); 656 { u64 x43 = (((((u64)x25 * x9) + ((u64)x27 * x7)) + ((u64)x23 * x11)) + ((u64)x29 * x5)); 657 { u64 x44 = (((((u64)x27 * x9) + (0x2 * (((u64)x25 * x11) + ((u64)x29 * x7)))) + ((u64)x23 * x13)) + ((u64)x31 * x5)); 658 { u64 x45 = (((((((u64)x27 * x11) + ((u64)x29 * x9)) + ((u64)x25 * x13)) + ((u64)x31 * x7)) + ((u64)x23 * x15)) + ((u64)x33 * x5)); 659 { u64 x46 = (((((0x2 * ((((u64)x29 * x11) + ((u64)x25 * x15)) + ((u64)x33 * x7))) + ((u64)x27 * x13)) + ((u64)x31 * x9)) + ((u64)x23 * x17)) + ((u64)x35 * x5)); 660 { u64 x47 = (((((((((u64)x29 * x13) + ((u64)x31 * x11)) + ((u64)x27 * x15)) + ((u64)x33 * x9)) + ((u64)x25 * x17)) + ((u64)x35 * x7)) + ((u64)x23 * x19)) + ((u64)x37 * x5)); 661 { u64 x48 = (((((((u64)x31 * x13) + (0x2 * (((((u64)x29 * x15) + ((u64)x33 * x11)) + ((u64)x25 * x19)) + ((u64)x37 * x7)))) + ((u64)x27 * x17)) + ((u64)x35 * x9)) + ((u64)x23 * x21)) + ((u64)x39 * x5)); 662 { u64 x49 = (((((((((((u64)x31 * x15) + ((u64)x33 * x13)) + ((u64)x29 * x17)) + ((u64)x35 * x11)) + ((u64)x27 * x19)) + ((u64)x37 * x9)) + ((u64)x25 * x21)) + ((u64)x39 * x7)) + ((u64)x23 * x20)) + ((u64)x38 * x5)); 663 { u64 x50 = (((((0x2 * ((((((u64)x33 * x15) + ((u64)x29 * x19)) + ((u64)x37 * x11)) + ((u64)x25 * x20)) + ((u64)x38 * x7))) + ((u64)x31 * x17)) + ((u64)x35 * x13)) + ((u64)x27 * x21)) + ((u64)x39 * x9)); 664 { u64 x51 = (((((((((u64)x33 * x17) + ((u64)x35 * x15)) + ((u64)x31 * x19)) + ((u64)x37 * x13)) + ((u64)x29 * x21)) + ((u64)x39 * x11)) + ((u64)x27 * x20)) + ((u64)x38 * x9)); 665 { u64 x52 = (((((u64)x35 * x17) + (0x2 * (((((u64)x33 * x19) + ((u64)x37 * x15)) + ((u64)x29 * x20)) + ((u64)x38 * x11)))) + ((u64)x31 * x21)) + ((u64)x39 * x13)); 666 { u64 x53 = (((((((u64)x35 * x19) + ((u64)x37 * x17)) + ((u64)x33 * x21)) + ((u64)x39 * x15)) + ((u64)x31 * x20)) + ((u64)x38 * x13)); 667 { u64 x54 = (((0x2 * ((((u64)x37 * x19) + ((u64)x33 * x20)) + ((u64)x38 * x15))) + ((u64)x35 * x21)) + ((u64)x39 * x17)); 668 { u64 x55 = (((((u64)x37 * x21) + ((u64)x39 * x19)) + ((u64)x35 * x20)) + ((u64)x38 * x17)); 669 { u64 x56 = (((u64)x39 * x21) + (0x2 * (((u64)x37 * x20) + ((u64)x38 * x19)))); 670 { u64 x57 = (((u64)x39 * x20) + ((u64)x38 * x21)); 671 { u64 x58 = ((u64)(0x2 * x38) * x20); 672 { u64 x59 = (x48 + (x58 << 0x4)); 673 { u64 x60 = (x59 + (x58 << 0x1)); 674 { u64 x61 = (x60 + x58); 675 { u64 x62 = (x47 + (x57 << 0x4)); 676 { u64 x63 = (x62 + (x57 << 0x1)); 677 { u64 x64 = (x63 + x57); 678 { u64 x65 = (x46 + (x56 << 0x4)); 679 { u64 x66 = (x65 + (x56 << 0x1)); 680 { u64 x67 = (x66 + x56); 681 { u64 x68 = (x45 + (x55 << 0x4)); 682 { u64 x69 = (x68 + (x55 << 0x1)); 683 { u64 x70 = (x69 + x55); 684 { u64 x71 = (x44 + (x54 << 0x4)); 685 { u64 x72 = (x71 + (x54 << 0x1)); 686 { u64 x73 = (x72 + x54); 687 { u64 x74 = (x43 + (x53 << 0x4)); 688 { u64 x75 = (x74 + (x53 << 0x1)); 689 { u64 x76 = (x75 + x53); 690 { u64 x77 = (x42 + (x52 << 0x4)); 691 { u64 x78 = (x77 + (x52 << 0x1)); 692 { u64 x79 = (x78 + x52); 693 { u64 x80 = (x41 + (x51 << 0x4)); 694 { u64 x81 = (x80 + (x51 << 0x1)); 695 { u64 x82 = (x81 + x51); 696 { u64 x83 = (x40 + (x50 << 0x4)); 697 { u64 x84 = (x83 + (x50 << 0x1)); 698 { u64 x85 = (x84 + x50); 699 { u64 x86 = (x85 >> 0x1a); 700 { u32 x87 = ((u32)x85 & 0x3ffffff); 701 { u64 x88 = (x86 + x82); 702 { u64 x89 = (x88 >> 0x19); 703 { u32 x90 = ((u32)x88 & 0x1ffffff); 704 { u64 x91 = (x89 + x79); 705 { u64 x92 = (x91 >> 0x1a); 706 { u32 x93 = ((u32)x91 & 0x3ffffff); 707 { u64 x94 = (x92 + x76); 708 { u64 x95 = (x94 >> 0x19); 709 { u32 x96 = ((u32)x94 & 0x1ffffff); 710 { u64 x97 = (x95 + x73); 711 { u64 x98 = (x97 >> 0x1a); 712 { u32 x99 = ((u32)x97 & 0x3ffffff); 713 { u64 x100 = (x98 + x70); 714 { u64 x101 = (x100 >> 0x19); 715 { u32 x102 = ((u32)x100 & 0x1ffffff); 716 { u64 x103 = (x101 + x67); 717 { u64 x104 = (x103 >> 0x1a); 718 { u32 x105 = ((u32)x103 & 0x3ffffff); 719 { u64 x106 = (x104 + x64); 720 { u64 x107 = (x106 >> 0x19); 721 { u32 x108 = ((u32)x106 & 0x1ffffff); 722 { u64 x109 = (x107 + x61); 723 { u64 x110 = (x109 >> 0x1a); 724 { u32 x111 = ((u32)x109 & 0x3ffffff); 725 { u64 x112 = (x110 + x49); 726 { u64 x113 = (x112 >> 0x19); 727 { u32 x114 = ((u32)x112 & 0x1ffffff); 728 { u64 x115 = (x87 + (0x13 * x113)); 729 { u32 x116 = (u32) (x115 >> 0x1a); 730 { u32 x117 = ((u32)x115 & 0x3ffffff); 731 { u32 x118 = (x116 + x90); 732 { u32 x119 = (x118 >> 0x19); 733 { u32 x120 = (x118 & 0x1ffffff); 734 out[0] = x117; 735 out[1] = x120; 736 out[2] = (x119 + x93); 737 out[3] = x96; 738 out[4] = x99; 739 out[5] = x102; 740 out[6] = x105; 741 out[7] = x108; 742 out[8] = x111; 743 out[9] = x114; 744 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} 745} 746 747static __always_inline void fe_mul121666(fe *h, const fe_loose *f) 748{ 749 fe_mul_121666_impl(h->v, f->v); 750} 751 752static void curve25519_generic(u8 out[CURVE25519_KEY_SIZE], 753 const u8 scalar[CURVE25519_KEY_SIZE], 754 const u8 point[CURVE25519_KEY_SIZE]) 755{ 756 fe x1, x2, z2, x3, z3; 757 fe_loose x2l, z2l, x3l; 758 unsigned swap = 0; 759 int pos; 760 u8 e[32]; 761 762 memcpy(e, scalar, 32); 763 curve25519_clamp_secret(e); 764 765 /* The following implementation was transcribed to Coq and proven to 766 * correspond to unary scalar multiplication in affine coordinates given 767 * that x1 != 0 is the x coordinate of some point on the curve. It was 768 * also checked in Coq that doing a ladderstep with x1 = x3 = 0 gives 769 * z2' = z3' = 0, and z2 = z3 = 0 gives z2' = z3' = 0. The statement was 770 * quantified over the underlying field, so it applies to Curve25519 771 * itself and the quadratic twist of Curve25519. It was not proven in 772 * Coq that prime-field arithmetic correctly simulates extension-field 773 * arithmetic on prime-field values. The decoding of the byte array 774 * representation of e was not considered. 775 * 776 * Specification of Montgomery curves in affine coordinates: 777 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27> 778 * 779 * Proof that these form a group that is isomorphic to a Weierstrass 780 * curve: 781 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35> 782 * 783 * Coq transcription and correctness proof of the loop 784 * (where scalarbits=255): 785 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118> 786 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278> 787 * preconditions: 0 <= e < 2^255 (not necessarily e < order), 788 * fe_invert(0) = 0 789 */ 790 fe_frombytes(&x1, point); 791 fe_1(&x2); 792 fe_0(&z2); 793 fe_copy(&x3, &x1); 794 fe_1(&z3); 795 796 for (pos = 254; pos >= 0; --pos) { 797 fe tmp0, tmp1; 798 fe_loose tmp0l, tmp1l; 799 /* loop invariant as of right before the test, for the case 800 * where x1 != 0: 801 * pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3 802 * is nonzero 803 * let r := e >> (pos+1) in the following equalities of 804 * projective points: 805 * to_xz (r*P) === if swap then (x3, z3) else (x2, z2) 806 * to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3) 807 * x1 is the nonzero x coordinate of the nonzero 808 * point (r*P-(r+1)*P) 809 */ 810 unsigned b = 1 & (e[pos / 8] >> (pos & 7)); 811 swap ^= b; 812 fe_cswap(&x2, &x3, swap); 813 fe_cswap(&z2, &z3, swap); 814 swap = b; 815 /* Coq transcription of ladderstep formula (called from 816 * transcribed loop): 817 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89> 818 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131> 819 * x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217> 820 * x1 = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147> 821 */ 822 fe_sub(&tmp0l, &x3, &z3); 823 fe_sub(&tmp1l, &x2, &z2); 824 fe_add(&x2l, &x2, &z2); 825 fe_add(&z2l, &x3, &z3); 826 fe_mul_tll(&z3, &tmp0l, &x2l); 827 fe_mul_tll(&z2, &z2l, &tmp1l); 828 fe_sq_tl(&tmp0, &tmp1l); 829 fe_sq_tl(&tmp1, &x2l); 830 fe_add(&x3l, &z3, &z2); 831 fe_sub(&z2l, &z3, &z2); 832 fe_mul_ttt(&x2, &tmp1, &tmp0); 833 fe_sub(&tmp1l, &tmp1, &tmp0); 834 fe_sq_tl(&z2, &z2l); 835 fe_mul121666(&z3, &tmp1l); 836 fe_sq_tl(&x3, &x3l); 837 fe_add(&tmp0l, &tmp0, &z3); 838 fe_mul_ttt(&z3, &x1, &z2); 839 fe_mul_tll(&z2, &tmp1l, &tmp0l); 840 } 841 /* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) 842 * else (x2, z2) 843 */ 844 fe_cswap(&x2, &x3, swap); 845 fe_cswap(&z2, &z3, swap); 846 847 fe_invert(&z2, &z2); 848 fe_mul_ttt(&x2, &x2, &z2); 849 fe_tobytes(out, &x2); 850 851 memzero_explicit(&x1, sizeof(x1)); 852 memzero_explicit(&x2, sizeof(x2)); 853 memzero_explicit(&z2, sizeof(z2)); 854 memzero_explicit(&x3, sizeof(x3)); 855 memzero_explicit(&z3, sizeof(z3)); 856 memzero_explicit(&x2l, sizeof(x2l)); 857 memzero_explicit(&z2l, sizeof(z2l)); 858 memzero_explicit(&x3l, sizeof(x3l)); 859 memzero_explicit(&e, sizeof(e)); 860} 861