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ed25519.inc

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1// SHA-512 (FIPS 180-4) and Ed25519 (RFC 8032) for Safe Actions.
2//
3// The Ed25519 arithmetic follows TweetNaCl (Bernstein, van Gastel, Janssen,
4// Lange, Schwabe, Smetsers; public domain): small, constant-time in the secret
5// scalar for signing, and easy to audit. Two changes for verification: S must be
6// canonical (S < L, RFC 8032 section 5.1.7), and shifts of possibly negative
7// values are written as multiplication. Checked against the RFC 8032 vectors
8// and against independent implementations in tests/safe_actions_tests.cpp.
9
10namespace ckey_crypto {
11
12// ---------------------------------------------------------------- SHA-512
13
14static const uint64_t kSha512K[80] = {
15 0x428a2f98d728ae22ULL, 0x7137449123ef65cdULL, 0xb5c0fbcfec4d3b2fULL, 0xe9b5dba58189dbbcULL, 0x3956c25bf348b538ULL,
16 0x59f111f1b605d019ULL, 0x923f82a4af194f9bULL, 0xab1c5ed5da6d8118ULL, 0xd807aa98a3030242ULL, 0x12835b0145706fbeULL,
17 0x243185be4ee4b28cULL, 0x550c7dc3d5ffb4e2ULL, 0x72be5d74f27b896fULL, 0x80deb1fe3b1696b1ULL, 0x9bdc06a725c71235ULL,
18 0xc19bf174cf692694ULL, 0xe49b69c19ef14ad2ULL, 0xefbe4786384f25e3ULL, 0x0fc19dc68b8cd5b5ULL, 0x240ca1cc77ac9c65ULL,
19 0x2de92c6f592b0275ULL, 0x4a7484aa6ea6e483ULL, 0x5cb0a9dcbd41fbd4ULL, 0x76f988da831153b5ULL, 0x983e5152ee66dfabULL,
20 0xa831c66d2db43210ULL, 0xb00327c898fb213fULL, 0xbf597fc7beef0ee4ULL, 0xc6e00bf33da88fc2ULL, 0xd5a79147930aa725ULL,
21 0x06ca6351e003826fULL, 0x142929670a0e6e70ULL, 0x27b70a8546d22ffcULL, 0x2e1b21385c26c926ULL, 0x4d2c6dfc5ac42aedULL,
22 0x53380d139d95b3dfULL, 0x650a73548baf63deULL, 0x766a0abb3c77b2a8ULL, 0x81c2c92e47edaee6ULL, 0x92722c851482353bULL,
23 0xa2bfe8a14cf10364ULL, 0xa81a664bbc423001ULL, 0xc24b8b70d0f89791ULL, 0xc76c51a30654be30ULL, 0xd192e819d6ef5218ULL,
24 0xd69906245565a910ULL, 0xf40e35855771202aULL, 0x106aa07032bbd1b8ULL, 0x19a4c116b8d2d0c8ULL, 0x1e376c085141ab53ULL,
25 0x2748774cdf8eeb99ULL, 0x34b0bcb5e19b48a8ULL, 0x391c0cb3c5c95a63ULL, 0x4ed8aa4ae3418acbULL, 0x5b9cca4f7763e373ULL,
26 0x682e6ff3d6b2b8a3ULL, 0x748f82ee5defb2fcULL, 0x78a5636f43172f60ULL, 0x84c87814a1f0ab72ULL, 0x8cc702081a6439ecULL,
27 0x90befffa23631e28ULL, 0xa4506cebde82bde9ULL, 0xbef9a3f7b2c67915ULL, 0xc67178f2e372532bULL, 0xca273eceea26619cULL,
28 0xd186b8c721c0c207ULL, 0xeada7dd6cde0eb1eULL, 0xf57d4f7fee6ed178ULL, 0x06f067aa72176fbaULL, 0x0a637dc5a2c898a6ULL,
29 0x113f9804bef90daeULL, 0x1b710b35131c471bULL, 0x28db77f523047d84ULL, 0x32caab7b40c72493ULL, 0x3c9ebe0a15c9bebcULL,
30 0x431d67c49c100d4cULL, 0x4cc5d4becb3e42b6ULL, 0x597f299cfc657e2aULL, 0x5fcb6fab3ad6faecULL, 0x6c44198c4a475817ULL};
31
32static inline uint64_t ror64(uint64_t x, int n) { return (x >> n) | (x << (64 - n)); }
33
34struct Sha512 {
35 uint64_t h[8] = {0x6a09e667f3bcc908ULL, 0xbb67ae8584caa73bULL, 0x3c6ef372fe94f82bULL, 0xa54ff53a5f1d36f1ULL,
36 0x510e527fade682d1ULL, 0x9b05688c2b3e6c1fULL, 0x1f83d9abfb41bd6bULL, 0x5be0cd19137e2179ULL};
37 uint8_t buf[128] = {};
38 size_t used = 0;
39 uint64_t total = 0;
40
41 void block(const uint8_t *p) {
42 uint64_t w[80];
43 for (int i = 0; i < 16; ++i) {
44 w[i] = 0;
45 for (int j = 0; j < 8; ++j) w[i] = (w[i] << 8) | p[8 * i + j];
46 }
47 for (int i = 16; i < 80; ++i) {
48 const uint64_t s0 = ror64(w[i - 15], 1) ^ ror64(w[i - 15], 8) ^ (w[i - 15] >> 7);
49 const uint64_t s1 = ror64(w[i - 2], 19) ^ ror64(w[i - 2], 61) ^ (w[i - 2] >> 6);
50 w[i] = w[i - 16] + s0 + w[i - 7] + s1;
51 }
52 uint64_t a = h[0], b = h[1], c = h[2], d = h[3], e = h[4], f = h[5], g = h[6], k = h[7];
53 for (int i = 0; i < 80; ++i) {
54 const uint64_t t1 = k + (ror64(e, 14) ^ ror64(e, 18) ^ ror64(e, 41)) + ((e & f) ^ (~e & g)) + kSha512K[i] + w[i];
55 const uint64_t t2 = (ror64(a, 28) ^ ror64(a, 34) ^ ror64(a, 39)) + ((a & b) ^ (a & c) ^ (b & c));
56 k = g; g = f; f = e; e = d + t1; d = c; c = b; b = a; a = t1 + t2;
57 }
58 h[0] += a; h[1] += b; h[2] += c; h[3] += d; h[4] += e; h[5] += f; h[6] += g; h[7] += k;
59 }
60 void update(const uint8_t *p, size_t n) {
61 total += n;
62 while (n) {
63 const size_t take = std::min(n, sizeof(buf) - used);
64 std::memcpy(buf + used, p, take);
65 used += take; p += take; n -= take;
66 if (used == sizeof(buf)) { block(buf); used = 0; }
67 }
68 }
69 void finish(uint8_t out[64]) {
70 const uint64_t bits = total * 8;
71 const uint8_t one = 0x80;
72 update(&one, 1);
73 const uint8_t zero = 0;
74 while (used != 112) update(&zero, 1);
75 uint8_t len[16] = {};
76 for (int i = 0; i < 8; ++i) len[15 - i] = static_cast<uint8_t>(bits >> (8 * i));
77 update(len, 16);
78 for (int i = 0; i < 8; ++i)
79 for (int j = 0; j < 8; ++j) out[8 * i + j] = static_cast<uint8_t>(h[i] >> (56 - 8 * j));
80 }
81};
82
83static void sha512(uint8_t out[64], const uint8_t *a, size_t an, const uint8_t *b = nullptr, size_t bn = 0,
84 const uint8_t *c = nullptr, size_t cn = 0) {
85 Sha512 s;
86 s.update(a, an);
87 if (b) s.update(b, bn);
88 if (c) s.update(c, cn);
89 s.finish(out);
90}
91
92// ---------------------------------------------------------------- field arithmetic mod 2^255 - 19
93
94typedef int64_t gf[16];
95static const gf gf0 = {0};
96static const gf gf1 = {1};
97static const gf kD = {0x78a3, 0x1359, 0x4dca, 0x75eb, 0xd8ab, 0x4141, 0x0a4d, 0x0070, 0xe898, 0x7779, 0x4079, 0x8cc7, 0xfe73, 0x2b6f, 0x6cee, 0x5203};
98static const gf kD2 = {0xf159, 0x26b2, 0x9b94, 0xebd6, 0xb156, 0x8283, 0x149a, 0x00e0, 0xd130, 0xeef3, 0x80f2, 0x198e, 0xfce7, 0x56df, 0xd9dc, 0x2406};
99static const gf kX = {0xd51a, 0x8f25, 0x2d60, 0xc956, 0xa7b2, 0x9525, 0xc760, 0x692c, 0xdc5c, 0xfdd6, 0xe231, 0xc0a4, 0x53fe, 0xcd6e, 0x36d3, 0x2169};
100static const gf kY = {0x6658, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666};
101static const gf kI = {0xa0b0, 0x4a0e, 0x1b27, 0xc4ee, 0xe478, 0xad2f, 0x1806, 0x2f43, 0xd7a7, 0x3dfb, 0x0099, 0x2b4d, 0xdf0b, 0x4fc1, 0x2480, 0x2b83};
102
103static void set25519(gf r, const gf a) { for (int i = 0; i < 16; ++i) r[i] = a[i]; }
104
105static void car25519(gf o) {
106 for (int i = 0; i < 16; ++i) {
107 o[i] += (int64_t{1} << 16);
108 const int64_t c = o[i] >> 16; // arithmetic shift (C++20)
109 o[(i + 1) * (i < 15)] += c - 1 + 37 * (c - 1) * (i == 15);
110 o[i] -= c * 65536;
111 }
112}
113
114static void sel25519(gf p, gf q, int b) {
115 const int64_t c = ~(int64_t(b) - 1);
116 for (int i = 0; i < 16; ++i) {
117 const int64_t t = c & (p[i] ^ q[i]);
118 p[i] ^= t;
119 q[i] ^= t;
120 }
121}
122
123static void pack25519(uint8_t *o, const gf n) {
124 gf m, t;
125 set25519(t, n);
126 car25519(t); car25519(t); car25519(t);
127 for (int j = 0; j < 2; ++j) {
128 m[0] = t[0] - 0xffed;
129 for (int i = 1; i < 15; ++i) {
130 m[i] = t[i] - 0xffff - ((m[i - 1] >> 16) & 1);
131 m[i - 1] &= 0xffff;
132 }
133 m[15] = t[15] - 0x7fff - ((m[14] >> 16) & 1);
134 const int b = static_cast<int>((m[15] >> 16) & 1);
135 m[14] &= 0xffff;
136 sel25519(t, m, 1 - b);
137 }
138 for (int i = 0; i < 16; ++i) {
139 o[2 * i] = static_cast<uint8_t>(t[i] & 0xff);
140 o[2 * i + 1] = static_cast<uint8_t>(t[i] >> 8);
141 }
142}
143
144static int verify32(const uint8_t *x, const uint8_t *y) {
145 unsigned d = 0;
146 for (int i = 0; i < 32; ++i) d |= x[i] ^ y[i];
147 return (1 & ((d - 1) >> 8)) - 1; // 0 when equal, -1 otherwise
148}
149
150static int neq25519(const gf a, const gf b) {
151 uint8_t c[32], d[32];
152 pack25519(c, a);
153 pack25519(d, b);
154 return verify32(c, d);
155}
156
157static uint8_t par25519(const gf a) {
158 uint8_t d[32];
159 pack25519(d, a);
160 return d[0] & 1;
161}
162
163static void unpack25519(gf o, const uint8_t *n) {
164 for (int i = 0; i < 16; ++i) o[i] = n[2 * i] + (int64_t(n[2 * i + 1]) << 8);
165 o[15] &= 0x7fff;
166}
167
168static void fadd(gf o, const gf a, const gf b) { for (int i = 0; i < 16; ++i) o[i] = a[i] + b[i]; }
169static void fsub(gf o, const gf a, const gf b) { for (int i = 0; i < 16; ++i) o[i] = a[i] - b[i]; }
170
171static void fmul(gf o, const gf a, const gf b) {
172 int64_t t[31] = {0};
173 for (int i = 0; i < 16; ++i)
174 for (int j = 0; j < 16; ++j) t[i + j] += a[i] * b[j];
175 for (int i = 0; i < 15; ++i) t[i] += 38 * t[i + 16];
176 for (int i = 0; i < 16; ++i) o[i] = t[i];
177 car25519(o);
178 car25519(o);
179}
180
181static void fsq(gf o, const gf a) { fmul(o, a, a); }
182
183static void inv25519(gf o, const gf in) {
184 gf c;
185 set25519(c, in);
186 for (int a = 253; a >= 0; --a) {
187 fsq(c, c);
188 if (a != 2 && a != 4) fmul(c, c, in);
189 }
190 set25519(o, c);
191}
192
193static void pow2523(gf o, const gf in) {
194 gf c;
195 set25519(c, in);
196 for (int a = 250; a >= 0; --a) {
197 fsq(c, c);
198 if (a != 1) fmul(c, c, in);
199 }
200 set25519(o, c);
201}
202
203// ---------------------------------------------------------------- the Edwards curve
204
205static void point_add(gf p[4], gf q[4]) {
206 gf a, b, c, d, t, e, f, g, h;
207 fsub(a, p[1], p[0]);
208 fsub(t, q[1], q[0]);
209 fmul(a, a, t);
210 fadd(b, p[0], p[1]);
211 fadd(t, q[0], q[1]);
212 fmul(b, b, t);
213 fmul(c, p[3], q[3]);
214 fmul(c, c, kD2);
215 fmul(d, p[2], q[2]);
216 fadd(d, d, d);
217 fsub(e, b, a);
218 fsub(f, d, c);
219 fadd(g, d, c);
220 fadd(h, b, a);
221 fmul(p[0], e, f);
222 fmul(p[1], h, g);
223 fmul(p[2], g, f);
224 fmul(p[3], e, h);
225}
226
227static void cswap(gf p[4], gf q[4], uint8_t b) {
228 for (int i = 0; i < 4; ++i) sel25519(p[i], q[i], b);
229}
230
231static void pack_point(uint8_t *r, gf p[4]) {
232 gf tx, ty, zi;
233 inv25519(zi, p[2]);
234 fmul(tx, p[0], zi);
235 fmul(ty, p[1], zi);
236 pack25519(r, ty);
237 r[31] ^= static_cast<uint8_t>(par25519(tx) << 7);
238}
239
240static void scalarmult(gf p[4], gf q[4], const uint8_t *s) {
241 set25519(p[0], gf0);
242 set25519(p[1], gf1);
243 set25519(p[2], gf1);
244 set25519(p[3], gf0);
245 for (int i = 255; i >= 0; --i) {
246 const uint8_t b = (s[i / 8] >> (i & 7)) & 1;
247 cswap(p, q, b);
248 point_add(q, p);
249 point_add(p, p);
250 cswap(p, q, b);
251 }
252}
253
254static void scalarbase(gf p[4], const uint8_t *s) {
255 gf q[4];
256 set25519(q[0], kX);
257 set25519(q[1], kY);
258 set25519(q[2], gf1);
259 fmul(q[3], kX, kY);
260 scalarmult(p, q, s);
261}
262
263static const int64_t kL[32] = {0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
264 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0x10};
265
266static void modL(uint8_t *r, int64_t x[64]) {
267 for (int i = 63; i >= 32; --i) {
268 int64_t carry = 0;
269 int j;
270 for (j = i - 32; j < i - 12; ++j) {
271 x[j] += carry - 16 * x[i] * kL[j - (i - 32)];
272 carry = (x[j] + 128) >> 8;
273 x[j] -= carry * 256;
274 }
275 x[j] += carry;
276 x[i] = 0;
277 }
278 int64_t carry = 0;
279 for (int j = 0; j < 32; ++j) {
280 x[j] += carry - (x[31] >> 4) * kL[j];
281 carry = x[j] >> 8;
282 x[j] &= 255;
283 }
284 for (int j = 0; j < 32; ++j) x[j] -= carry * kL[j];
285 for (int i = 0; i < 32; ++i) {
286 x[i + 1] += x[i] >> 8;
287 r[i] = static_cast<uint8_t>(x[i] & 255);
288 }
289}
290
291static void reduce64(uint8_t *r) {
292 int64_t x[64];
293 for (int i = 0; i < 64; ++i) x[i] = r[i];
294 for (int i = 0; i < 64; ++i) r[i] = 0;
295 modL(r, x);
296}
297
298static int unpackneg(gf r[4], const uint8_t p[32]) {
299 gf t, chk, num, den, den2, den4, den6;
300 set25519(r[2], gf1);
301 unpack25519(r[1], p);
302 fsq(num, r[1]);
303 fmul(den, num, kD);
304 fsub(num, num, r[2]);
305 fadd(den, r[2], den);
306 fsq(den2, den);
307 fsq(den4, den2);
308 fmul(den6, den4, den2);
309 fmul(t, den6, num);
310 fmul(t, t, den);
311 pow2523(t, t);
312 fmul(t, t, num);
313 fmul(t, t, den);
314 fmul(t, t, den);
315 fmul(r[0], t, den);
316 fsq(chk, r[0]);
317 fmul(chk, chk, den);
318 if (neq25519(chk, num)) fmul(r[0], r[0], kI);
319 fsq(chk, r[0]);
320 fmul(chk, chk, den);
321 if (neq25519(chk, num)) return -1;
322 if (par25519(r[0]) == (p[31] >> 7)) fsub(r[0], gf0, r[0]);
323 fmul(r[3], r[0], r[1]);
324 return 0;
325}
326
327/** The public key for a 32-byte seed. */
328static void ed25519_public_key(uint8_t pk[32], const uint8_t seed[32]) {
329 uint8_t d[64];
330 gf p[4];
331 sha512(d, seed, 32);
332 d[0] &= 248;
333 d[31] &= 127;
334 d[31] |= 64;
335 scalarbase(p, d);
336 pack_point(pk, p);
337}
338
339/** A detached RFC 8032 signature of msg with a 32-byte seed. */
340static void ed25519_sign(uint8_t sig[64], const uint8_t *msg, size_t n, const uint8_t seed[32]) {
341 uint8_t d[64], r[64], h[64], pk[32];
342 gf p[4];
343 sha512(d, seed, 32);
344 d[0] &= 248;
345 d[31] &= 127;
346 d[31] |= 64;
347 ed25519_public_key(pk, seed);
348 sha512(r, d + 32, 32, msg, n);
349 reduce64(r);
350 scalarbase(p, r);
351 pack_point(sig, p);
352 sha512(h, sig, 32, pk, 32, msg, n);
353 reduce64(h);
354 int64_t x[64] = {0};
355 for (int i = 0; i < 32; ++i) x[i] = r[i];
356 for (int i = 0; i < 32; ++i)
357 for (int j = 0; j < 32; ++j) x[i + j] += int64_t(h[i]) * int64_t(d[j]);
358 modL(sig + 32, x);
359}
360
361/** True when S < L, the group order (little-endian comparison). */
362static bool scalar_canonical(const uint8_t s[32]) {
363 for (int i = 31; i >= 0; --i) {
364 if (s[i] < kL[i]) return true;
365 if (s[i] > kL[i]) return false;
366 }
367 return false; // equal to L
368}
369
370/** Verifies a detached signature. */
371static bool ed25519_verify(const uint8_t sig[64], const uint8_t *msg, size_t n, const uint8_t pk[32]) {
372 if (!scalar_canonical(sig + 32)) return false;
373 gf p[4], q[4];
374 if (unpackneg(q, pk)) return false;
375 uint8_t h[64], t[32];
376 sha512(h, sig, 32, pk, 32, msg, n);
377 reduce64(h);
378 scalarmult(p, q, h);
379 scalarbase(q, sig + 32);
380 point_add(p, q);
381 pack_point(t, p);
382 return verify32(sig, t) == 0;
383}
384
385} // namespace ckey_crypto