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1// SPDX-License-Identifier: GPL-2.0 OR MIT2/*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 Curve255197 * ECDH from: <https://github.com/mit-plv/fiat-crypto>. Though originally8 * 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 efficiently10 * 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]+2^7719 * 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 */23typedef 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,etc26 * Addition and subtraction produce fe_loose from (fe, fe).27 */28typedef struct fe_loose { u32 v[10]; } fe_loose;29 30static __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 53static __always_inline void fe_frombytes(fe *h, const u8 *s)54{55 fe_frombytes_impl(h->v, s);56}57 58static __always_inline u8 /*bool*/59addcarryx_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low)60{61 /* This function extracts 25 bits of result and 1 bit of carry62 * (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 69static __always_inline u8 /*bool*/70addcarryx_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low)71{72 /* This function extracts 26 bits of result and 1 bit of carry73 * (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 80static __always_inline u8 /*bool*/81subborrow_u25(u8 /*bool*/ c, u32 a, u32 b, u32 *low)82{83 /* This function extracts 25 bits of result and 1 bit of borrow84 * (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 91static __always_inline u8 /*bool*/92subborrow_u26(u8 /*bool*/ c, u32 a, u32 b, u32 *low)93{94 /* This function extracts 26 bits of result and 1 bit of borrow95 *(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 102static __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 108static __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 164static __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 */203static __always_inline void fe_copy(fe *h, const fe *f)204{205 memmove(h, f, sizeof(u32) * 10);206}207 208static __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 */214static __always_inline void fe_0(fe *h)215{216 memset(h, 0, sizeof(u32) * 10);217}218 219/* h = 1 */220static __always_inline void fe_1(fe *h)221{222 memset(h, 0, sizeof(u32) * 10);223 h->v[0] = 1;224}225 226static 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 + g262 * Can overlap h with f or g.263 */264static __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 269static 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 - g305 * Can overlap h with f or g.306 */307static __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 312static 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 428static __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 433static __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 438static __always_inline void439fe_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 444static 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 550static __always_inline void fe_sq_tl(fe *h, const fe_loose *f)551{552 fe_sqr_impl(h->v, f->v);553}554 555static __always_inline void fe_sq_tt(fe *h, const fe *f)556{557 fe_sqr_impl(h->v, f->v);558}559 560static __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 610static __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 */622static 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.*/635static __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 751static __always_inline void fe_mul121666(fe *h, const fe_loose *f)752{753 fe_mul_121666_impl(h->v, f->v);754}755 756void 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 to770 * correspond to unary scalar multiplication in affine coordinates given771 * that x1 != 0 is the x coordinate of some point on the curve. It was772 * also checked in Coq that doing a ladderstep with x1 = x3 = 0 gives773 * z2' = z3' = 0, and z2 = z3 = 0 gives z2' = z3' = 0. The statement was774 * quantified over the underlying field, so it applies to Curve25519775 * itself and the quadratic twist of Curve25519. It was not proven in776 * Coq that prime-field arithmetic correctly simulates extension-field777 * arithmetic on prime-field values. The decoding of the byte array778 * 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 Weierstrass784 * 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 loop788 * (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) = 0793 */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 case804 * where x1 != 0:805 * pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3806 * is nonzero807 * let r := e >> (pos+1) in the following equalities of808 * 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 nonzero812 * 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 from820 * 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