1 // SPDX-License-Identifier: GPL-2.0 OR MIT 2 /* 3 * Copyright (C) 2015-2016 The fiat-crypto Authors. 4 * Copyright (C) 2018-2019 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 #include <linux/unaligned.h> 14 #include <crypto/curve25519.h> 15 #include <linux/string.h> 16 17 /* fe means field element. Here the field is \Z/(2^255-19). An element t, 18 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 19 * t[3]+2^102 t[4]+...+2^230 t[9]. 20 * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc. 21 * Multiplication and carrying produce fe from fe_loose. 22 */ 23 typedef struct fe { u32 v[10]; } fe; 24 25 /* fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc 26 * Addition and subtraction produce fe_loose from (fe, fe). 27 */ 28 typedef struct fe_loose { u32 v[10]; } fe_loose; 29 30 static __always_inline void fe_frombytes_impl(u32 h[10], const u8 *s) 31 { 32 /* Ignores top bit of s. */ 33 u32 a0 = get_unaligned_le32(s); 34 u32 a1 = get_unaligned_le32(s+4); 35 u32 a2 = get_unaligned_le32(s+8); 36 u32 a3 = get_unaligned_le32(s+12); 37 u32 a4 = get_unaligned_le32(s+16); 38 u32 a5 = get_unaligned_le32(s+20); 39 u32 a6 = get_unaligned_le32(s+24); 40 u32 a7 = get_unaligned_le32(s+28); 41 h[0] = a0&((1<<26)-1); /* 26 used, 32-26 left. 26 */ 42 h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 = 6+19 = 25 */ 43 h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */ 44 h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) + 6 = 19+ 6 = 25 */ 45 h[4] = (a3>> 6); /* (32- 6) = 26 */ 46 h[5] = a4&((1<<25)-1); /* 25 */ 47 h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 = 7+19 = 26 */ 48 h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */ 49 h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) + 6 = 20+ 6 = 26 */ 50 h[9] = (a7>> 6)&((1<<25)-1); /* 25 */ 51 } 52 53 static __always_inline void fe_frombytes(fe *h, const u8 *s) 54 { 55 fe_frombytes_impl(h->v, s); 56 } 57 58 static __always_inline u8 /*bool*/ 59 addcarryx_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low) 60 { 61 /* This function extracts 25 bits of result and 1 bit of carry 62 * (26 total), so a 32-bit intermediate is sufficient. 63 */ 64 u32 x = a + b + c; 65 *low = x & ((1 << 25) - 1); 66 return (x >> 25) & 1; 67 } 68 69 static __always_inline u8 /*bool*/ 70 addcarryx_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low) 71 { 72 /* This function extracts 26 bits of result and 1 bit of carry 73 * (27 total), so a 32-bit intermediate is sufficient. 74 */ 75 u32 x = a + b + c; 76 *low = x & ((1 << 26) - 1); 77 return (x >> 26) & 1; 78 } 79 80 static __always_inline u8 /*bool*/ 81 subborrow_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low) 82 { 83 /* This function extracts 25 bits of result and 1 bit of borrow 84 * (26 total), so a 32-bit intermediate is sufficient. 85 */ 86 u32 x = a - b - c; 87 *low = x & ((1 << 25) - 1); 88 return x >> 31; 89 } 90 91 static __always_inline u8 /*bool*/ 92 subborrow_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low) 93 { 94 /* This function extracts 26 bits of result and 1 bit of borrow 95 *(27 total), so a 32-bit intermediate is sufficient. 96 */ 97 u32 x = a - b - c; 98 *low = x & ((1 << 26) - 1); 99 return x >> 31; 100 } 101 102 static __always_inline u32 cmovznz32(u32 t, u32 z, u32 nz) 103 { 104 t = -!!t; /* all set if nonzero, 0 if 0 */ 105 return (t&nz) | ((~t)&z); 106 } 107 108 static __always_inline void fe_freeze(u32 out[10], const u32 in1[10]) 109 { 110 { const u32 x17 = in1[9]; 111 { const u32 x18 = in1[8]; 112 { const u32 x16 = in1[7]; 113 { const u32 x14 = in1[6]; 114 { const u32 x12 = in1[5]; 115 { const u32 x10 = in1[4]; 116 { const u32 x8 = in1[3]; 117 { const u32 x6 = in1[2]; 118 { const u32 x4 = in1[1]; 119 { const u32 x2 = in1[0]; 120 { u32 x20; u8/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20); 121 { u32 x23; u8/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23); 122 { u32 x26; u8/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26); 123 { u32 x29; u8/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29); 124 { u32 x32; u8/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32); 125 { u32 x35; u8/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35); 126 { u32 x38; u8/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38); 127 { u32 x41; u8/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41); 128 { u32 x44; u8/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44); 129 { u32 x47; u8/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47); 130 { u32 x49 = cmovznz32(x48, 0x0, 0xffffffff); 131 { u32 x50 = (x49 & 0x3ffffed); 132 { u32 x52; u8/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52); 133 { u32 x54 = (x49 & 0x1ffffff); 134 { u32 x56; u8/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56); 135 { u32 x58 = (x49 & 0x3ffffff); 136 { u32 x60; u8/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60); 137 { u32 x62 = (x49 & 0x1ffffff); 138 { u32 x64; u8/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64); 139 { u32 x66 = (x49 & 0x3ffffff); 140 { u32 x68; u8/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68); 141 { u32 x70 = (x49 & 0x1ffffff); 142 { u32 x72; u8/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72); 143 { u32 x74 = (x49 & 0x3ffffff); 144 { u32 x76; u8/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76); 145 { u32 x78 = (x49 & 0x1ffffff); 146 { u32 x80; u8/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80); 147 { u32 x82 = (x49 & 0x3ffffff); 148 { u32 x84; u8/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84); 149 { u32 x86 = (x49 & 0x1ffffff); 150 { u32 x88; addcarryx_u25(x85, x47, x86, &x88); 151 out[0] = x52; 152 out[1] = x56; 153 out[2] = x60; 154 out[3] = x64; 155 out[4] = x68; 156 out[5] = x72; 157 out[6] = x76; 158 out[7] = x80; 159 out[8] = x84; 160 out[9] = x88; 161 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} 162 } 163 164 static __always_inline void fe_tobytes(u8 s[32], const fe *f) 165 { 166 u32 h[10]; 167 fe_freeze(h, f->v); 168 s[0] = h[0] >> 0; 169 s[1] = h[0] >> 8; 170 s[2] = h[0] >> 16; 171 s[3] = (h[0] >> 24) | (h[1] << 2); 172 s[4] = h[1] >> 6; 173 s[5] = h[1] >> 14; 174 s[6] = (h[1] >> 22) | (h[2] << 3); 175 s[7] = h[2] >> 5; 176 s[8] = h[2] >> 13; 177 s[9] = (h[2] >> 21) | (h[3] << 5); 178 s[10] = h[3] >> 3; 179 s[11] = h[3] >> 11; 180 s[12] = (h[3] >> 19) | (h[4] << 6); 181 s[13] = h[4] >> 2; 182 s[14] = h[4] >> 10; 183 s[15] = h[4] >> 18; 184 s[16] = h[5] >> 0; 185 s[17] = h[5] >> 8; 186 s[18] = h[5] >> 16; 187 s[19] = (h[5] >> 24) | (h[6] << 1); 188 s[20] = h[6] >> 7; 189 s[21] = h[6] >> 15; 190 s[22] = (h[6] >> 23) | (h[7] << 3); 191 s[23] = h[7] >> 5; 192 s[24] = h[7] >> 13; 193 s[25] = (h[7] >> 21) | (h[8] << 4); 194 s[26] = h[8] >> 4; 195 s[27] = h[8] >> 12; 196 s[28] = (h[8] >> 20) | (h[9] << 6); 197 s[29] = h[9] >> 2; 198 s[30] = h[9] >> 10; 199 s[31] = h[9] >> 18; 200 } 201 202 /* h = f */ 203 static __always_inline void fe_copy(fe *h, const fe *f) 204 { 205 memmove(h, f, sizeof(u32) * 10); 206 } 207 208 static __always_inline void fe_copy_lt(fe_loose *h, const fe *f) 209 { 210 memmove(h, f, sizeof(u32) * 10); 211 } 212 213 /* h = 0 */ 214 static __always_inline void fe_0(fe *h) 215 { 216 memset(h, 0, sizeof(u32) * 10); 217 } 218 219 /* h = 1 */ 220 static __always_inline void fe_1(fe *h) 221 { 222 memset(h, 0, sizeof(u32) * 10); 223 h->v[0] = 1; 224 } 225 226 static noinline void fe_add_impl(u32 out[10], const u32 in1[10], const u32 in2[10]) 227 { 228 { const u32 x20 = in1[9]; 229 { const u32 x21 = in1[8]; 230 { const u32 x19 = in1[7]; 231 { const u32 x17 = in1[6]; 232 { const u32 x15 = in1[5]; 233 { const u32 x13 = in1[4]; 234 { const u32 x11 = in1[3]; 235 { const u32 x9 = in1[2]; 236 { const u32 x7 = in1[1]; 237 { const u32 x5 = in1[0]; 238 { const u32 x38 = in2[9]; 239 { const u32 x39 = in2[8]; 240 { const u32 x37 = in2[7]; 241 { const u32 x35 = in2[6]; 242 { const u32 x33 = in2[5]; 243 { const u32 x31 = in2[4]; 244 { const u32 x29 = in2[3]; 245 { const u32 x27 = in2[2]; 246 { const u32 x25 = in2[1]; 247 { const u32 x23 = in2[0]; 248 out[0] = (x5 + x23); 249 out[1] = (x7 + x25); 250 out[2] = (x9 + x27); 251 out[3] = (x11 + x29); 252 out[4] = (x13 + x31); 253 out[5] = (x15 + x33); 254 out[6] = (x17 + x35); 255 out[7] = (x19 + x37); 256 out[8] = (x21 + x39); 257 out[9] = (x20 + x38); 258 }}}}}}}}}}}}}}}}}}}} 259 } 260 261 /* h = f + g 262 * Can overlap h with f or g. 263 */ 264 static __always_inline void fe_add(fe_loose *h, const fe *f, const fe *g) 265 { 266 fe_add_impl(h->v, f->v, g->v); 267 } 268 269 static noinline void fe_sub_impl(u32 out[10], const u32 in1[10], const u32 in2[10]) 270 { 271 { const u32 x20 = in1[9]; 272 { const u32 x21 = in1[8]; 273 { const u32 x19 = in1[7]; 274 { const u32 x17 = in1[6]; 275 { const u32 x15 = in1[5]; 276 { const u32 x13 = in1[4]; 277 { const u32 x11 = in1[3]; 278 { const u32 x9 = in1[2]; 279 { const u32 x7 = in1[1]; 280 { const u32 x5 = in1[0]; 281 { const u32 x38 = in2[9]; 282 { const u32 x39 = in2[8]; 283 { const u32 x37 = in2[7]; 284 { const u32 x35 = in2[6]; 285 { const u32 x33 = in2[5]; 286 { const u32 x31 = in2[4]; 287 { const u32 x29 = in2[3]; 288 { const u32 x27 = in2[2]; 289 { const u32 x25 = in2[1]; 290 { const u32 x23 = in2[0]; 291 out[0] = ((0x7ffffda + x5) - x23); 292 out[1] = ((0x3fffffe + x7) - x25); 293 out[2] = ((0x7fffffe + x9) - x27); 294 out[3] = ((0x3fffffe + x11) - x29); 295 out[4] = ((0x7fffffe + x13) - x31); 296 out[5] = ((0x3fffffe + x15) - x33); 297 out[6] = ((0x7fffffe + x17) - x35); 298 out[7] = ((0x3fffffe + x19) - x37); 299 out[8] = ((0x7fffffe + x21) - x39); 300 out[9] = ((0x3fffffe + x20) - x38); 301 }}}}}}}}}}}}}}}}}}}} 302 } 303 304 /* h = f - g 305 * Can overlap h with f or g. 306 */ 307 static __always_inline void fe_sub(fe_loose *h, const fe *f, const fe *g) 308 { 309 fe_sub_impl(h->v, f->v, g->v); 310 } 311 312 static noinline void fe_mul_impl(u32 out[10], const u32 in1[10], const u32 in2[10]) 313 { 314 { const u32 x20 = in1[9]; 315 { const u32 x21 = in1[8]; 316 { const u32 x19 = in1[7]; 317 { const u32 x17 = in1[6]; 318 { const u32 x15 = in1[5]; 319 { const u32 x13 = in1[4]; 320 { const u32 x11 = in1[3]; 321 { const u32 x9 = in1[2]; 322 { const u32 x7 = in1[1]; 323 { const u32 x5 = in1[0]; 324 { const u32 x38 = in2[9]; 325 { const u32 x39 = in2[8]; 326 { const u32 x37 = in2[7]; 327 { const u32 x35 = in2[6]; 328 { const u32 x33 = in2[5]; 329 { const u32 x31 = in2[4]; 330 { const u32 x29 = in2[3]; 331 { const u32 x27 = in2[2]; 332 { const u32 x25 = in2[1]; 333 { const u32 x23 = in2[0]; 334 { u64 x40 = ((u64)x23 * x5); 335 { u64 x41 = (((u64)x23 * x7) + ((u64)x25 * x5)); 336 { u64 x42 = ((((u64)(0x2 * x25) * x7) + ((u64)x23 * x9)) + ((u64)x27 * x5)); 337 { u64 x43 = (((((u64)x25 * x9) + ((u64)x27 * x7)) + ((u64)x23 * x11)) + ((u64)x29 * x5)); 338 { u64 x44 = (((((u64)x27 * x9) + (0x2 * (((u64)x25 * x11) + ((u64)x29 * x7)))) + ((u64)x23 * x13)) + ((u64)x31 * x5)); 339 { u64 x45 = (((((((u64)x27 * x11) + ((u64)x29 * x9)) + ((u64)x25 * x13)) + ((u64)x31 * x7)) + ((u64)x23 * x15)) + ((u64)x33 * x5)); 340 { u64 x46 = (((((0x2 * ((((u64)x29 * x11) + ((u64)x25 * x15)) + ((u64)x33 * x7))) + ((u64)x27 * x13)) + ((u64)x31 * x9)) + ((u64)x23 * x17)) + ((u64)x35 * x5)); 341 { 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)); 342 { 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)); 343 { 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)); 344 { 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)); 345 { 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)); 346 { u64 x52 = (((((u64)x35 * x17) + (0x2 * (((((u64)x33 * x19) + ((u64)x37 * x15)) + ((u64)x29 * x20)) + ((u64)x38 * x11)))) + ((u64)x31 * x21)) + ((u64)x39 * x13)); 347 { u64 x53 = (((((((u64)x35 * x19) + ((u64)x37 * x17)) + ((u64)x33 * x21)) + ((u64)x39 * x15)) + ((u64)x31 * x20)) + ((u64)x38 * x13)); 348 { u64 x54 = (((0x2 * ((((u64)x37 * x19) + ((u64)x33 * x20)) + ((u64)x38 * x15))) + ((u64)x35 * x21)) + ((u64)x39 * x17)); 349 { u64 x55 = (((((u64)x37 * x21) + ((u64)x39 * x19)) + ((u64)x35 * x20)) + ((u64)x38 * x17)); 350 { u64 x56 = (((u64)x39 * x21) + (0x2 * (((u64)x37 * x20) + ((u64)x38 * x19)))); 351 { u64 x57 = (((u64)x39 * x20) + ((u64)x38 * x21)); 352 { u64 x58 = ((u64)(0x2 * x38) * x20); 353 { u64 x59 = (x48 + (x58 << 0x4)); 354 { u64 x60 = (x59 + (x58 << 0x1)); 355 { u64 x61 = (x60 + x58); 356 { u64 x62 = (x47 + (x57 << 0x4)); 357 { u64 x63 = (x62 + (x57 << 0x1)); 358 { u64 x64 = (x63 + x57); 359 { u64 x65 = (x46 + (x56 << 0x4)); 360 { u64 x66 = (x65 + (x56 << 0x1)); 361 { u64 x67 = (x66 + x56); 362 { u64 x68 = (x45 + (x55 << 0x4)); 363 { u64 x69 = (x68 + (x55 << 0x1)); 364 { u64 x70 = (x69 + x55); 365 { u64 x71 = (x44 + (x54 << 0x4)); 366 { u64 x72 = (x71 + (x54 << 0x1)); 367 { u64 x73 = (x72 + x54); 368 { u64 x74 = (x43 + (x53 << 0x4)); 369 { u64 x75 = (x74 + (x53 << 0x1)); 370 { u64 x76 = (x75 + x53); 371 { u64 x77 = (x42 + (x52 << 0x4)); 372 { u64 x78 = (x77 + (x52 << 0x1)); 373 { u64 x79 = (x78 + x52); 374 { u64 x80 = (x41 + (x51 << 0x4)); 375 { u64 x81 = (x80 + (x51 << 0x1)); 376 { u64 x82 = (x81 + x51); 377 { u64 x83 = (x40 + (x50 << 0x4)); 378 { u64 x84 = (x83 + (x50 << 0x1)); 379 { u64 x85 = (x84 + x50); 380 { u64 x86 = (x85 >> 0x1a); 381 { u32 x87 = ((u32)x85 & 0x3ffffff); 382 { u64 x88 = (x86 + x82); 383 { u64 x89 = (x88 >> 0x19); 384 { u32 x90 = ((u32)x88 & 0x1ffffff); 385 { u64 x91 = (x89 + x79); 386 { u64 x92 = (x91 >> 0x1a); 387 { u32 x93 = ((u32)x91 & 0x3ffffff); 388 { u64 x94 = (x92 + x76); 389 { u64 x95 = (x94 >> 0x19); 390 { u32 x96 = ((u32)x94 & 0x1ffffff); 391 { u64 x97 = (x95 + x73); 392 { u64 x98 = (x97 >> 0x1a); 393 { u32 x99 = ((u32)x97 & 0x3ffffff); 394 { u64 x100 = (x98 + x70); 395 { u64 x101 = (x100 >> 0x19); 396 { u32 x102 = ((u32)x100 & 0x1ffffff); 397 { u64 x103 = (x101 + x67); 398 { u64 x104 = (x103 >> 0x1a); 399 { u32 x105 = ((u32)x103 & 0x3ffffff); 400 { u64 x106 = (x104 + x64); 401 { u64 x107 = (x106 >> 0x19); 402 { u32 x108 = ((u32)x106 & 0x1ffffff); 403 { u64 x109 = (x107 + x61); 404 { u64 x110 = (x109 >> 0x1a); 405 { u32 x111 = ((u32)x109 & 0x3ffffff); 406 { u64 x112 = (x110 + x49); 407 { u64 x113 = (x112 >> 0x19); 408 { u32 x114 = ((u32)x112 & 0x1ffffff); 409 { u64 x115 = (x87 + (0x13 * x113)); 410 { u32 x116 = (u32) (x115 >> 0x1a); 411 { u32 x117 = ((u32)x115 & 0x3ffffff); 412 { u32 x118 = (x116 + x90); 413 { u32 x119 = (x118 >> 0x19); 414 { u32 x120 = (x118 & 0x1ffffff); 415 out[0] = x117; 416 out[1] = x120; 417 out[2] = (x119 + x93); 418 out[3] = x96; 419 out[4] = x99; 420 out[5] = x102; 421 out[6] = x105; 422 out[7] = x108; 423 out[8] = x111; 424 out[9] = x114; 425 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} 426 } 427 428 static __always_inline void fe_mul_ttt(fe *h, const fe *f, const fe *g) 429 { 430 fe_mul_impl(h->v, f->v, g->v); 431 } 432 433 static __always_inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) 434 { 435 fe_mul_impl(h->v, f->v, g->v); 436 } 437 438 static __always_inline void 439 fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) 440 { 441 fe_mul_impl(h->v, f->v, g->v); 442 } 443 444 static noinline void fe_sqr_impl(u32 out[10], const u32 in1[10]) 445 { 446 { const u32 x17 = in1[9]; 447 { const u32 x18 = in1[8]; 448 { const u32 x16 = in1[7]; 449 { const u32 x14 = in1[6]; 450 { const u32 x12 = in1[5]; 451 { const u32 x10 = in1[4]; 452 { const u32 x8 = in1[3]; 453 { const u32 x6 = in1[2]; 454 { const u32 x4 = in1[1]; 455 { const u32 x2 = in1[0]; 456 { u64 x19 = ((u64)x2 * x2); 457 { u64 x20 = ((u64)(0x2 * x2) * x4); 458 { u64 x21 = (0x2 * (((u64)x4 * x4) + ((u64)x2 * x6))); 459 { u64 x22 = (0x2 * (((u64)x4 * x6) + ((u64)x2 * x8))); 460 { u64 x23 = ((((u64)x6 * x6) + ((u64)(0x4 * x4) * x8)) + ((u64)(0x2 * x2) * x10)); 461 { u64 x24 = (0x2 * ((((u64)x6 * x8) + ((u64)x4 * x10)) + ((u64)x2 * x12))); 462 { u64 x25 = (0x2 * (((((u64)x8 * x8) + ((u64)x6 * x10)) + ((u64)x2 * x14)) + ((u64)(0x2 * x4) * x12))); 463 { u64 x26 = (0x2 * (((((u64)x8 * x10) + ((u64)x6 * x12)) + ((u64)x4 * x14)) + ((u64)x2 * x16))); 464 { u64 x27 = (((u64)x10 * x10) + (0x2 * ((((u64)x6 * x14) + ((u64)x2 * x18)) + (0x2 * (((u64)x4 * x16) + ((u64)x8 * x12)))))); 465 { u64 x28 = (0x2 * ((((((u64)x10 * x12) + ((u64)x8 * x14)) + ((u64)x6 * x16)) + ((u64)x4 * x18)) + ((u64)x2 * x17))); 466 { u64 x29 = (0x2 * (((((u64)x12 * x12) + ((u64)x10 * x14)) + ((u64)x6 * x18)) + (0x2 * (((u64)x8 * x16) + ((u64)x4 * x17))))); 467 { u64 x30 = (0x2 * (((((u64)x12 * x14) + ((u64)x10 * x16)) + ((u64)x8 * x18)) + ((u64)x6 * x17))); 468 { u64 x31 = (((u64)x14 * x14) + (0x2 * (((u64)x10 * x18) + (0x2 * (((u64)x12 * x16) + ((u64)x8 * x17)))))); 469 { u64 x32 = (0x2 * ((((u64)x14 * x16) + ((u64)x12 * x18)) + ((u64)x10 * x17))); 470 { u64 x33 = (0x2 * ((((u64)x16 * x16) + ((u64)x14 * x18)) + ((u64)(0x2 * x12) * x17))); 471 { u64 x34 = (0x2 * (((u64)x16 * x18) + ((u64)x14 * x17))); 472 { u64 x35 = (((u64)x18 * x18) + ((u64)(0x4 * x16) * x17)); 473 { u64 x36 = ((u64)(0x2 * x18) * x17); 474 { u64 x37 = ((u64)(0x2 * x17) * x17); 475 { u64 x38 = (x27 + (x37 << 0x4)); 476 { u64 x39 = (x38 + (x37 << 0x1)); 477 { u64 x40 = (x39 + x37); 478 { u64 x41 = (x26 + (x36 << 0x4)); 479 { u64 x42 = (x41 + (x36 << 0x1)); 480 { u64 x43 = (x42 + x36); 481 { u64 x44 = (x25 + (x35 << 0x4)); 482 { u64 x45 = (x44 + (x35 << 0x1)); 483 { u64 x46 = (x45 + x35); 484 { u64 x47 = (x24 + (x34 << 0x4)); 485 { u64 x48 = (x47 + (x34 << 0x1)); 486 { u64 x49 = (x48 + x34); 487 { u64 x50 = (x23 + (x33 << 0x4)); 488 { u64 x51 = (x50 + (x33 << 0x1)); 489 { u64 x52 = (x51 + x33); 490 { u64 x53 = (x22 + (x32 << 0x4)); 491 { u64 x54 = (x53 + (x32 << 0x1)); 492 { u64 x55 = (x54 + x32); 493 { u64 x56 = (x21 + (x31 << 0x4)); 494 { u64 x57 = (x56 + (x31 << 0x1)); 495 { u64 x58 = (x57 + x31); 496 { u64 x59 = (x20 + (x30 << 0x4)); 497 { u64 x60 = (x59 + (x30 << 0x1)); 498 { u64 x61 = (x60 + x30); 499 { u64 x62 = (x19 + (x29 << 0x4)); 500 { u64 x63 = (x62 + (x29 << 0x1)); 501 { u64 x64 = (x63 + x29); 502 { u64 x65 = (x64 >> 0x1a); 503 { u32 x66 = ((u32)x64 & 0x3ffffff); 504 { u64 x67 = (x65 + x61); 505 { u64 x68 = (x67 >> 0x19); 506 { u32 x69 = ((u32)x67 & 0x1ffffff); 507 { u64 x70 = (x68 + x58); 508 { u64 x71 = (x70 >> 0x1a); 509 { u32 x72 = ((u32)x70 & 0x3ffffff); 510 { u64 x73 = (x71 + x55); 511 { u64 x74 = (x73 >> 0x19); 512 { u32 x75 = ((u32)x73 & 0x1ffffff); 513 { u64 x76 = (x74 + x52); 514 { u64 x77 = (x76 >> 0x1a); 515 { u32 x78 = ((u32)x76 & 0x3ffffff); 516 { u64 x79 = (x77 + x49); 517 { u64 x80 = (x79 >> 0x19); 518 { u32 x81 = ((u32)x79 & 0x1ffffff); 519 { u64 x82 = (x80 + x46); 520 { u64 x83 = (x82 >> 0x1a); 521 { u32 x84 = ((u32)x82 & 0x3ffffff); 522 { u64 x85 = (x83 + x43); 523 { u64 x86 = (x85 >> 0x19); 524 { u32 x87 = ((u32)x85 & 0x1ffffff); 525 { u64 x88 = (x86 + x40); 526 { u64 x89 = (x88 >> 0x1a); 527 { u32 x90 = ((u32)x88 & 0x3ffffff); 528 { u64 x91 = (x89 + x28); 529 { u64 x92 = (x91 >> 0x19); 530 { u32 x93 = ((u32)x91 & 0x1ffffff); 531 { u64 x94 = (x66 + (0x13 * x92)); 532 { u32 x95 = (u32) (x94 >> 0x1a); 533 { u32 x96 = ((u32)x94 & 0x3ffffff); 534 { u32 x97 = (x95 + x69); 535 { u32 x98 = (x97 >> 0x19); 536 { u32 x99 = (x97 & 0x1ffffff); 537 out[0] = x96; 538 out[1] = x99; 539 out[2] = (x98 + x72); 540 out[3] = x75; 541 out[4] = x78; 542 out[5] = x81; 543 out[6] = x84; 544 out[7] = x87; 545 out[8] = x90; 546 out[9] = x93; 547 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} 548 } 549 550 static __always_inline void fe_sq_tl(fe *h, const fe_loose *f) 551 { 552 fe_sqr_impl(h->v, f->v); 553 } 554 555 static __always_inline void fe_sq_tt(fe *h, const fe *f) 556 { 557 fe_sqr_impl(h->v, f->v); 558 } 559 560 static __always_inline void fe_loose_invert(fe *out, const fe_loose *z) 561 { 562 fe t0; 563 fe t1; 564 fe t2; 565 fe t3; 566 int i; 567 568 fe_sq_tl(&t0, z); 569 fe_sq_tt(&t1, &t0); 570 for (i = 1; i < 2; ++i) 571 fe_sq_tt(&t1, &t1); 572 fe_mul_tlt(&t1, z, &t1); 573 fe_mul_ttt(&t0, &t0, &t1); 574 fe_sq_tt(&t2, &t0); 575 fe_mul_ttt(&t1, &t1, &t2); 576 fe_sq_tt(&t2, &t1); 577 for (i = 1; i < 5; ++i) 578 fe_sq_tt(&t2, &t2); 579 fe_mul_ttt(&t1, &t2, &t1); 580 fe_sq_tt(&t2, &t1); 581 for (i = 1; i < 10; ++i) 582 fe_sq_tt(&t2, &t2); 583 fe_mul_ttt(&t2, &t2, &t1); 584 fe_sq_tt(&t3, &t2); 585 for (i = 1; i < 20; ++i) 586 fe_sq_tt(&t3, &t3); 587 fe_mul_ttt(&t2, &t3, &t2); 588 fe_sq_tt(&t2, &t2); 589 for (i = 1; i < 10; ++i) 590 fe_sq_tt(&t2, &t2); 591 fe_mul_ttt(&t1, &t2, &t1); 592 fe_sq_tt(&t2, &t1); 593 for (i = 1; i < 50; ++i) 594 fe_sq_tt(&t2, &t2); 595 fe_mul_ttt(&t2, &t2, &t1); 596 fe_sq_tt(&t3, &t2); 597 for (i = 1; i < 100; ++i) 598 fe_sq_tt(&t3, &t3); 599 fe_mul_ttt(&t2, &t3, &t2); 600 fe_sq_tt(&t2, &t2); 601 for (i = 1; i < 50; ++i) 602 fe_sq_tt(&t2, &t2); 603 fe_mul_ttt(&t1, &t2, &t1); 604 fe_sq_tt(&t1, &t1); 605 for (i = 1; i < 5; ++i) 606 fe_sq_tt(&t1, &t1); 607 fe_mul_ttt(out, &t1, &t0); 608 } 609 610 static __always_inline void fe_invert(fe *out, const fe *z) 611 { 612 fe_loose l; 613 fe_copy_lt(&l, z); 614 fe_loose_invert(out, &l); 615 } 616 617 /* Replace (f,g) with (g,f) if b == 1; 618 * replace (f,g) with (f,g) if b == 0. 619 * 620 * Preconditions: b in {0,1} 621 */ 622 static noinline void fe_cswap(fe *f, fe *g, unsigned int b) 623 { 624 unsigned i; 625 b = 0 - b; 626 for (i = 0; i < 10; i++) { 627 u32 x = f->v[i] ^ g->v[i]; 628 x &= b; 629 f->v[i] ^= x; 630 g->v[i] ^= x; 631 } 632 } 633 634 /* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/ 635 static __always_inline void fe_mul_121666_impl(u32 out[10], const u32 in1[10]) 636 { 637 { const u32 x20 = in1[9]; 638 { const u32 x21 = in1[8]; 639 { const u32 x19 = in1[7]; 640 { const u32 x17 = in1[6]; 641 { const u32 x15 = in1[5]; 642 { const u32 x13 = in1[4]; 643 { const u32 x11 = in1[3]; 644 { const u32 x9 = in1[2]; 645 { const u32 x7 = in1[1]; 646 { const u32 x5 = in1[0]; 647 { const u32 x38 = 0; 648 { const u32 x39 = 0; 649 { const u32 x37 = 0; 650 { const u32 x35 = 0; 651 { const u32 x33 = 0; 652 { const u32 x31 = 0; 653 { const u32 x29 = 0; 654 { const u32 x27 = 0; 655 { const u32 x25 = 0; 656 { const u32 x23 = 121666; 657 { u64 x40 = ((u64)x23 * x5); 658 { u64 x41 = (((u64)x23 * x7) + ((u64)x25 * x5)); 659 { u64 x42 = ((((u64)(0x2 * x25) * x7) + ((u64)x23 * x9)) + ((u64)x27 * x5)); 660 { u64 x43 = (((((u64)x25 * x9) + ((u64)x27 * x7)) + ((u64)x23 * x11)) + ((u64)x29 * x5)); 661 { u64 x44 = (((((u64)x27 * x9) + (0x2 * (((u64)x25 * x11) + ((u64)x29 * x7)))) + ((u64)x23 * x13)) + ((u64)x31 * x5)); 662 { u64 x45 = (((((((u64)x27 * x11) + ((u64)x29 * x9)) + ((u64)x25 * x13)) + ((u64)x31 * x7)) + ((u64)x23 * x15)) + ((u64)x33 * x5)); 663 { u64 x46 = (((((0x2 * ((((u64)x29 * x11) + ((u64)x25 * x15)) + ((u64)x33 * x7))) + ((u64)x27 * x13)) + ((u64)x31 * x9)) + ((u64)x23 * x17)) + ((u64)x35 * x5)); 664 { 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)); 665 { 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)); 666 { 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)); 667 { 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)); 668 { 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)); 669 { u64 x52 = (((((u64)x35 * x17) + (0x2 * (((((u64)x33 * x19) + ((u64)x37 * x15)) + ((u64)x29 * x20)) + ((u64)x38 * x11)))) + ((u64)x31 * x21)) + ((u64)x39 * x13)); 670 { u64 x53 = (((((((u64)x35 * x19) + ((u64)x37 * x17)) + ((u64)x33 * x21)) + ((u64)x39 * x15)) + ((u64)x31 * x20)) + ((u64)x38 * x13)); 671 { u64 x54 = (((0x2 * ((((u64)x37 * x19) + ((u64)x33 * x20)) + ((u64)x38 * x15))) + ((u64)x35 * x21)) + ((u64)x39 * x17)); 672 { u64 x55 = (((((u64)x37 * x21) + ((u64)x39 * x19)) + ((u64)x35 * x20)) + ((u64)x38 * x17)); 673 { u64 x56 = (((u64)x39 * x21) + (0x2 * (((u64)x37 * x20) + ((u64)x38 * x19)))); 674 { u64 x57 = (((u64)x39 * x20) + ((u64)x38 * x21)); 675 { u64 x58 = ((u64)(0x2 * x38) * x20); 676 { u64 x59 = (x48 + (x58 << 0x4)); 677 { u64 x60 = (x59 + (x58 << 0x1)); 678 { u64 x61 = (x60 + x58); 679 { u64 x62 = (x47 + (x57 << 0x4)); 680 { u64 x63 = (x62 + (x57 << 0x1)); 681 { u64 x64 = (x63 + x57); 682 { u64 x65 = (x46 + (x56 << 0x4)); 683 { u64 x66 = (x65 + (x56 << 0x1)); 684 { u64 x67 = (x66 + x56); 685 { u64 x68 = (x45 + (x55 << 0x4)); 686 { u64 x69 = (x68 + (x55 << 0x1)); 687 { u64 x70 = (x69 + x55); 688 { u64 x71 = (x44 + (x54 << 0x4)); 689 { u64 x72 = (x71 + (x54 << 0x1)); 690 { u64 x73 = (x72 + x54); 691 { u64 x74 = (x43 + (x53 << 0x4)); 692 { u64 x75 = (x74 + (x53 << 0x1)); 693 { u64 x76 = (x75 + x53); 694 { u64 x77 = (x42 + (x52 << 0x4)); 695 { u64 x78 = (x77 + (x52 << 0x1)); 696 { u64 x79 = (x78 + x52); 697 { u64 x80 = (x41 + (x51 << 0x4)); 698 { u64 x81 = (x80 + (x51 << 0x1)); 699 { u64 x82 = (x81 + x51); 700 { u64 x83 = (x40 + (x50 << 0x4)); 701 { u64 x84 = (x83 + (x50 << 0x1)); 702 { u64 x85 = (x84 + x50); 703 { u64 x86 = (x85 >> 0x1a); 704 { u32 x87 = ((u32)x85 & 0x3ffffff); 705 { u64 x88 = (x86 + x82); 706 { u64 x89 = (x88 >> 0x19); 707 { u32 x90 = ((u32)x88 & 0x1ffffff); 708 { u64 x91 = (x89 + x79); 709 { u64 x92 = (x91 >> 0x1a); 710 { u32 x93 = ((u32)x91 & 0x3ffffff); 711 { u64 x94 = (x92 + x76); 712 { u64 x95 = (x94 >> 0x19); 713 { u32 x96 = ((u32)x94 & 0x1ffffff); 714 { u64 x97 = (x95 + x73); 715 { u64 x98 = (x97 >> 0x1a); 716 { u32 x99 = ((u32)x97 & 0x3ffffff); 717 { u64 x100 = (x98 + x70); 718 { u64 x101 = (x100 >> 0x19); 719 { u32 x102 = ((u32)x100 & 0x1ffffff); 720 { u64 x103 = (x101 + x67); 721 { u64 x104 = (x103 >> 0x1a); 722 { u32 x105 = ((u32)x103 & 0x3ffffff); 723 { u64 x106 = (x104 + x64); 724 { u64 x107 = (x106 >> 0x19); 725 { u32 x108 = ((u32)x106 & 0x1ffffff); 726 { u64 x109 = (x107 + x61); 727 { u64 x110 = (x109 >> 0x1a); 728 { u32 x111 = ((u32)x109 & 0x3ffffff); 729 { u64 x112 = (x110 + x49); 730 { u64 x113 = (x112 >> 0x19); 731 { u32 x114 = ((u32)x112 & 0x1ffffff); 732 { u64 x115 = (x87 + (0x13 * x113)); 733 { u32 x116 = (u32) (x115 >> 0x1a); 734 { u32 x117 = ((u32)x115 & 0x3ffffff); 735 { u32 x118 = (x116 + x90); 736 { u32 x119 = (x118 >> 0x19); 737 { u32 x120 = (x118 & 0x1ffffff); 738 out[0] = x117; 739 out[1] = x120; 740 out[2] = (x119 + x93); 741 out[3] = x96; 742 out[4] = x99; 743 out[5] = x102; 744 out[6] = x105; 745 out[7] = x108; 746 out[8] = x111; 747 out[9] = x114; 748 }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} 749 } 750 751 static __always_inline void fe_mul121666(fe *h, const fe_loose *f) 752 { 753 fe_mul_121666_impl(h->v, f->v); 754 } 755 756 void curve25519_generic(u8 out[CURVE25519_KEY_SIZE], 757 const u8 scalar[CURVE25519_KEY_SIZE], 758 const u8 point[CURVE25519_KEY_SIZE]) 759 { 760 fe x1, x2, z2, x3, z3; 761 fe_loose x2l, z2l, x3l; 762 unsigned swap = 0; 763 int pos; 764 u8 e[32]; 765 766 memcpy(e, scalar, 32); 767 curve25519_clamp_secret(e); 768 769 /* The following implementation was transcribed to Coq and proven to 770 * correspond to unary scalar multiplication in affine coordinates given 771 * that x1 != 0 is the x coordinate of some point on the curve. It was 772 * also checked in Coq that doing a ladderstep with x1 = x3 = 0 gives 773 * z2' = z3' = 0, and z2 = z3 = 0 gives z2' = z3' = 0. The statement was 774 * quantified over the underlying field, so it applies to Curve25519 775 * itself and the quadratic twist of Curve25519. It was not proven in 776 * Coq that prime-field arithmetic correctly simulates extension-field 777 * arithmetic on prime-field values. The decoding of the byte array 778 * representation of e was not considered. 779 * 780 * Specification of Montgomery curves in affine coordinates: 781 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27> 782 * 783 * Proof that these form a group that is isomorphic to a Weierstrass 784 * curve: 785 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35> 786 * 787 * Coq transcription and correctness proof of the loop 788 * (where scalarbits=255): 789 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118> 790 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278> 791 * preconditions: 0 <= e < 2^255 (not necessarily e < order), 792 * fe_invert(0) = 0 793 */ 794 fe_frombytes(&x1, point); 795 fe_1(&x2); 796 fe_0(&z2); 797 fe_copy(&x3, &x1); 798 fe_1(&z3); 799 800 for (pos = 254; pos >= 0; --pos) { 801 fe tmp0, tmp1; 802 fe_loose tmp0l, tmp1l; 803 /* loop invariant as of right before the test, for the case 804 * where x1 != 0: 805 * pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3 806 * is nonzero 807 * let r := e >> (pos+1) in the following equalities of 808 * projective points: 809 * to_xz (r*P) === if swap then (x3, z3) else (x2, z2) 810 * to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3) 811 * x1 is the nonzero x coordinate of the nonzero 812 * point (r*P-(r+1)*P) 813 */ 814 unsigned b = 1 & (e[pos / 8] >> (pos & 7)); 815 swap ^= b; 816 fe_cswap(&x2, &x3, swap); 817 fe_cswap(&z2, &z3, swap); 818 swap = b; 819 /* Coq transcription of ladderstep formula (called from 820 * transcribed loop): 821 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89> 822 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131> 823 * x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217> 824 * x1 = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147> 825 */ 826 fe_sub(&tmp0l, &x3, &z3); 827 fe_sub(&tmp1l, &x2, &z2); 828 fe_add(&x2l, &x2, &z2); 829 fe_add(&z2l, &x3, &z3); 830 fe_mul_tll(&z3, &tmp0l, &x2l); 831 fe_mul_tll(&z2, &z2l, &tmp1l); 832 fe_sq_tl(&tmp0, &tmp1l); 833 fe_sq_tl(&tmp1, &x2l); 834 fe_add(&x3l, &z3, &z2); 835 fe_sub(&z2l, &z3, &z2); 836 fe_mul_ttt(&x2, &tmp1, &tmp0); 837 fe_sub(&tmp1l, &tmp1, &tmp0); 838 fe_sq_tl(&z2, &z2l); 839 fe_mul121666(&z3, &tmp1l); 840 fe_sq_tl(&x3, &x3l); 841 fe_add(&tmp0l, &tmp0, &z3); 842 fe_mul_ttt(&z3, &x1, &z2); 843 fe_mul_tll(&z2, &tmp1l, &tmp0l); 844 } 845 /* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) 846 * else (x2, z2) 847 */ 848 fe_cswap(&x2, &x3, swap); 849 fe_cswap(&z2, &z3, swap); 850 851 fe_invert(&z2, &z2); 852 fe_mul_ttt(&x2, &x2, &z2); 853 fe_tobytes(out, &x2); 854 855 memzero_explicit(&x1, sizeof(x1)); 856 memzero_explicit(&x2, sizeof(x2)); 857 memzero_explicit(&z2, sizeof(z2)); 858 memzero_explicit(&x3, sizeof(x3)); 859 memzero_explicit(&z3, sizeof(z3)); 860 memzero_explicit(&x2l, sizeof(x2l)); 861 memzero_explicit(&z2l, sizeof(z2l)); 862 memzero_explicit(&x3l, sizeof(x3l)); 863 memzero_explicit(&e, sizeof(e)); 864 } 865