2 * Copyright (c) 2020, SUSE LLC.
4 * This program is licensed under the BSD license, read LICENSE.BSD
5 * for further information
8 /* simple and slow ed25519 verification code. */
10 #ifndef LIBSOLV_CHKSUM_H
14 #define MPED25519_LEN (32 / MP_T_BYTES)
17 # define MPED25519_CONST1(x) (mp_t)x
19 # define MPED25519_CONST1(x) (mp_t)(x >> 0), (mp_t)(x >> 8), (mp_t)(x >> 16), (mp_t)(x >> 24)
22 #define MPED25519_CONST(a, b, c, d, e, f, g, h) { \
23 MPED25519_CONST1(h), MPED25519_CONST1(g), MPED25519_CONST1(f), MPED25519_CONST1(e), \
24 MPED25519_CONST1(d), MPED25519_CONST1(c), MPED25519_CONST1(b), MPED25519_CONST1(a) \
27 static mp_t ed25519_q[] = /* mod prime */
28 MPED25519_CONST(0x7FFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFED);
29 static mp_t ed25519_d[] = /* -(121665/121666) */
30 MPED25519_CONST(0x52036CEE, 0x2B6FFE73, 0x8CC74079, 0x7779E898, 0x00700A4D, 0x4141D8AB, 0x75EB4DCA, 0x135978A3);
31 static mp_t ed25519_sqrtm1[] = /* sqrt(-1) */
32 MPED25519_CONST(0x2B832480, 0x4FC1DF0B, 0x2B4D0099, 0x3DFBD7A7, 0x2F431806, 0xAD2FE478, 0xC4EE1B27, 0x4A0EA0B0);
33 static mp_t ed25519_l[] = /* order of base point */
34 MPED25519_CONST(0x10000000, 0x00000000, 0x00000000, 0x00000000, 0x14DEF9DE, 0xA2F79CD6, 0x5812631A, 0x5CF5D3ED);
35 static mp_t ed25519_gx[] = /* base point */
36 MPED25519_CONST(0x216936D3, 0xCD6E53FE, 0xC0A4E231, 0xFDD6DC5C, 0x692CC760, 0x9525A7B2, 0xC9562D60, 0x8F25D51A);
37 static mp_t ed25519_gy[] = /* base point */
38 MPED25519_CONST(0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666658);
39 static mp_t ed25519_one[] = /* 1 */
40 MPED25519_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000001);
42 /* small helpers to save some typing */
44 mped25519_add(mp_t *target, mp_t *m1, mp_t *m2)
46 mpadd(MPED25519_LEN, target, m1, m2, ed25519_q);
50 mped25519_sub(mp_t *target, mp_t *m1, mp_t *m2)
52 mpsub(MPED25519_LEN, target, m1, m2, ed25519_q);
55 /* target = 512 bit input modulo ed25519_q */
57 mped25519_reduce512(mp_t *target, mp_t *a)
62 for (x = 0, i = 0; i < MPED25519_LEN; i++)
64 x += (mp2_t)a[i] + (mp2_t)a[i + MPED25519_LEN] * 38;
69 if ((target[MPED25519_LEN - 1] & (1 << (MP_T_BITS - 1))) != 0)
72 target[MPED25519_LEN - 1] -= 1 << (MP_T_BITS - 1);
74 for (i = 0; x && i < MPED25519_LEN; i++)
76 x += (mp2_t)target[i];
80 if (target[MPED25519_LEN - 1] > ed25519_q[MPED25519_LEN - 1] ||
81 (target[MPED25519_LEN - 1] == ed25519_q[MPED25519_LEN - 1] && !mpisless(MPED25519_LEN - 1, target, ed25519_q)))
82 mpsubmod(MPED25519_LEN, target, ed25519_q);
86 mped25519_mul(mp_t *target, mp_t *m1, mp_t *m2)
88 mp_t tmp[MPED25519_LEN * 2];
92 mpzero(MPED25519_LEN * 2, tmp);
93 for (i = 0; i < MPED25519_LEN; i++)
95 for (x = 0, j = 0; j < MPED25519_LEN; j++)
97 x += (mp2_t)tmp[i + j] + (mp2_t)m1[i] * m2[j];
103 mped25519_reduce512(target, tmp);
107 mped25519_sqr(mp_t *target, mp_t *m)
109 mped25519_mul(target, m, m);
112 /* target = a ^ (2^252 - 4), a11 = a ^ 11 */
114 mped25519_pow_252_4(mp_t *target, mp_t *a, mp_t *a_11)
116 static const int todo[16] = { 0, 5, 1, 10, 2, 20, 3, 10, 2, 50, 5, 100, 6, 50, 5, 2 };
117 mp_t data[9][MPED25519_LEN];
120 mpcpy(MPED25519_LEN, target, a);
121 mped25519_sqr(target, target);
122 mpcpy(MPED25519_LEN, a_11, target);
123 mped25519_sqr(target, target);
124 mped25519_sqr(target, target);
125 mped25519_mul(data[0], target, a); /* data[0] = 9 */
126 mped25519_mul(a_11, data[0], a_11); /* a_11 = 11 */
127 mped25519_mul(target, a_11, a_11); /* target = 22 */
128 for (i = 0; i < 8; i++)
130 mped25519_mul(target, target, data[todo[i * 2]]);
131 mpcpy(MPED25519_LEN, data[i + 1], target);
132 for (j = todo[i * 2 + 1]; j-- > 0;)
133 mped25519_sqr(target, target);
137 /* target = a ^ (2^252 - 3) */
139 mped25519_pow_252_3(mp_t *target, mp_t *a)
141 mp_t t11[MPED25519_LEN];
142 mped25519_pow_252_4(target, a, t11);
143 mped25519_mul(target, target, a);
146 /* target = a ^ -1 = a ^ (2^255 - 21) */
148 mped25519_inv(mp_t *target, mp_t *a)
150 mp_t t[MPED25519_LEN], t11[MPED25519_LEN];
151 mped25519_pow_252_4(t, a, t11);
154 mped25519_sqr(t, t); /* 2^255 - 32 */
155 mped25519_mul(target, t, t11);
159 mped25519_reduce512_l(mp_t *target, mp_t *a)
161 mp_t tmp[MPED25519_LEN];
162 mpzero(MPED25519_LEN, target);
163 mpmul_add(MPED25519_LEN, target, ed25519_one, MPED25519_LEN * 2, a, tmp, ed25519_l);
166 /* recover x coordinate from y and sign */
168 mped25519_recover_x(mp_t *x, mp_t *y, int sign)
170 mp_t num[MPED25519_LEN], den[MPED25519_LEN];
171 mp_t tmp1[MPED25519_LEN], tmp2[MPED25519_LEN];
173 if (!mpisless(MPED25519_LEN, y, ed25519_q))
175 /* calculate num=y^2-1 and den=dy^2+1 */
176 mped25519_sqr(num, y);
177 mped25519_mul(den, num, ed25519_d);
178 mped25519_sub(num, num, ed25519_one);
179 mped25519_add(den, den, ed25519_one);
181 /* calculate x = num*den^3 * (num*den^7)^((q-5)/8) */
182 mped25519_sqr(tmp1, den); /* tmp1 = den^2 */
183 mped25519_mul(tmp2, tmp1, den); /* tmp2 = den^3 */
184 mped25519_sqr(tmp1, tmp2); /* tmp1 = den^6 */
185 mped25519_mul(x, tmp1, den); /* x = den^7 */
186 mped25519_mul(tmp1, x, num); /* tmp1 = num * den^7 */
187 mped25519_pow_252_3(x, tmp1); /* x = tmp1^((q-5)/8) */
188 mped25519_mul(tmp1, x, tmp2); /* tmp1 = x * den^3 */
189 mped25519_mul(x, tmp1, num); /* x = tmp1 * num */
191 /* check if den*x^2 == num */
192 mped25519_sqr(tmp2, x);
193 mped25519_mul(tmp1, tmp2, den);
194 if (!mpisequal(MPED25519_LEN, tmp1, num)) {
195 mped25519_mul(x, x, ed25519_sqrtm1); /* x = x * sqrt(-1) */
196 mped25519_sqr(tmp2, x);
197 mped25519_mul(tmp1, tmp2, den);
198 if (!mpisequal(MPED25519_LEN, tmp1, num))
201 if (mpiszero(MPED25519_LEN, x))
202 return 0; /* (0,1) is bad */
203 if ((x[0] & 1) != sign)
204 mped25519_sub(x, ed25519_q, x);
208 /* see https://hyperelliptic.org/EFD/g1p/auto-twisted-projective.html */
211 mped25519_ptdouble(mp_t *p_x, mp_t *p_y, mp_t *p_z)
213 mp_t B[MPED25519_LEN], C[MPED25519_LEN], D[MPED25519_LEN];
214 mp_t F[MPED25519_LEN], H[MPED25519_LEN], J[MPED25519_LEN];
216 mped25519_add(C, p_x, p_y);
218 mped25519_sqr(C, p_x);
219 mped25519_sqr(D, p_y);
220 mped25519_sub(F, C, D);
221 mped25519_sqr(H, p_z);
222 mped25519_add(H, H, H);
223 mped25519_add(J, F, H);
224 mped25519_add(H, C, D);
225 mped25519_mul(p_y, H, F);
226 mped25519_mul(p_z, J, F);
227 mped25519_sub(H, H, B);
228 mped25519_mul(p_x, J, H);
233 mped25519_ptadd(mp_t *p_x, mp_t *p_y, mp_t *p_z, mp_t *q_x, mp_t *q_y, mp_t *q_z)
235 mp_t A[MPED25519_LEN], B[MPED25519_LEN], C[MPED25519_LEN];
236 mp_t D[MPED25519_LEN], E[MPED25519_LEN], F[MPED25519_LEN];
237 mp_t G[MPED25519_LEN], H[MPED25519_LEN], J[MPED25519_LEN];
239 mped25519_mul(A, p_z, q_z);
241 mped25519_mul(C, p_x, q_x);
242 mped25519_mul(D, p_y, q_y);
243 mped25519_mul(F, ed25519_d, C);
244 mped25519_mul(E, F, D);
245 mped25519_sub(F, B, E);
246 mped25519_add(G, B, E);
247 mped25519_add(H, p_x, p_y);
248 mped25519_add(J, q_x, q_y);
249 mped25519_mul(p_x, H, J);
250 mped25519_sub(p_x, p_x, C);
251 mped25519_sub(p_x, p_x, D);
252 mped25519_mul(H, p_x, F);
253 mped25519_mul(p_x, H, A);
254 mped25519_add(H, D, C);
255 mped25519_mul(J, H, G);
256 mped25519_mul(p_y, J, A);
257 mped25519_mul(p_z, F, G);
261 mped25519_ptcpy(mp_t *p_x, mp_t *p_y, mp_t *p_z, mp_t *q_x, mp_t *q_y, mp_t *q_z)
263 mpcpy(MPED25519_LEN, p_x, q_x);
264 mpcpy(MPED25519_LEN, p_y, q_y);
265 mpcpy(MPED25519_LEN, p_z, q_z);
270 mped25519_mpdump(mp_t *p, char *s, int c)
273 fprintf(stderr, "%c.", c);
274 mpdump(MPED25519_LEN, p, s);
278 mped25519_ptdump(mp_t *p_x, mp_t *p_y, mp_t *p_z, char *s)
280 mp_t zi[MPED25519_LEN], px[MPED25519_LEN], py[MPED25519_LEN];
281 mped25519_mpdump(p_x, s, 'X');
282 mped25519_mpdump(p_y, s, 'Y');
283 mped25519_mpdump(p_z, s, 'Z');
284 mped25519_inv(zi, p_z);
285 mped25519_mul(px, p_x, zi);
286 mped25519_mul(py, p_y, zi);
287 mped25519_mpdump(px, s, 'x');
288 mped25519_mpdump(py, s, 'y');
293 /* scalar multiplication and add: r = s1*p1 + s2*p2 */
294 /* needs about 13 + (256 - 32) / 2 = 125 point additions */
296 mped25519_scmult2(mp_t *r_x, mp_t *r_y, mp_t *s1, mp_t *p1_x, mp_t * p1_y, mp_t *s2, mp_t *p2_x, mp_t * p2_y)
298 mp_t p_x[MPED25519_LEN], p_y[MPED25519_LEN], p_z[MPED25519_LEN];
299 mp_t pi_z[MPED25519_LEN];
300 mp_t tabx[16][MPED25519_LEN], taby[16][MPED25519_LEN], tabz[16][MPED25519_LEN];
301 int i, x, dodouble = 0;
303 mpzero(MPED25519_LEN, p_x);
304 mpzero(MPED25519_LEN, p_y);
305 mpzero(MPED25519_LEN, p_z);
308 /* setup table: tab[i * 4 + j] = i * p1 + j * p2 */
309 mped25519_ptcpy(tabx[0], taby[0], tabz[0], p_x, p_y, p_z);
310 for (i = 4; i < 16; i += 4)
311 mped25519_ptcpy(tabx[i], taby[i], tabz[i], p1_x, p1_y, ed25519_one);
312 mped25519_ptdouble(tabx[8], taby[8], tabz[8]);
313 mped25519_ptadd(tabx[12], taby[12], tabz[12], tabx[8], taby[8], tabz[8]);
314 mped25519_ptcpy(tabx[1], taby[1], tabz[1], p2_x, p2_y, ed25519_one);
315 for (i = 2; i < 16; i++)
319 mped25519_ptcpy(tabx[i], taby[i], tabz[i], tabx[i - 1], taby[i - 1], tabz[i - 1]);
320 mped25519_ptadd(tabx[i], taby[i], tabz[i], p2_x, p2_y, ed25519_one);
322 /* now do the scalar multiplication */
323 for (i = 255; i >= 0; i--)
326 mped25519_ptdouble(p_x, p_y, p_z);
327 x = s1[i / MP_T_BITS] & (1 << (i % MP_T_BITS)) ? 4 : 0;
328 x |= s2[i / MP_T_BITS] & (1 << (i % MP_T_BITS)) ? 1 : 0;
335 mped25519_ptdouble(p_x, p_y, p_z);
337 x |= s1[i / MP_T_BITS] & (1 << (i % MP_T_BITS)) ? 4 : 0;
338 x |= s2[i / MP_T_BITS] & (1 << (i % MP_T_BITS)) ? 1 : 0;
340 mped25519_ptadd(p_x, p_y, p_z, tabx[x], taby[x], tabz[x]);
344 mped25519_ptdump(p_x, p_y, p_z, "r = ");
346 mped25519_inv(pi_z, p_z);
347 mped25519_mul(r_x, p_x, pi_z);
348 mped25519_mul(r_y, p_y, pi_z);
349 return mpiszero(MPED25519_LEN, p_z) ? 0 : 1;
353 mped25519_setfromle(int len, mp_t *out, const unsigned char *buf, int bufl, int highmask)
355 unsigned char bebuf[64]; /* bufl must be <= 64 */
357 for (i = 0; i < bufl; i++)
358 bebuf[bufl - 1 - i] = buf[i];
359 bebuf[0] &= highmask;
360 mpsetfrombe(len, out, bebuf, bufl);
364 mped25519(const unsigned char *pub, const unsigned char *sig, const unsigned char *data, unsigned int datal)
366 unsigned char hbuf[64], rbuf[32];
368 mp_t pub_x[MPED25519_LEN], pub_y[MPED25519_LEN];
369 mp_t h[MPED25519_LEN], s[MPED25519_LEN], h2[MPED25519_LEN * 2];
370 mp_t r_x[MPED25519_LEN], r_y[MPED25519_LEN];
373 mped25519_setfromle(MPED25519_LEN, s, sig + 32, 32, 0xff);
374 if (!mpisless(MPED25519_LEN, s, ed25519_l))
375 return 0; /* bad s */
376 /* uncompress pubkey, we invert the sign to get -pub */
377 mped25519_setfromle(MPED25519_LEN, pub_y, pub, 32, 0x7f);
378 if (!mped25519_recover_x(pub_x, pub_y, pub[31] & 0x80 ? 0 : 1))
379 return 0; /* bad pubkey */
381 mped25519_mpdump(pub_x, "-pubx = ", 0);
382 mped25519_mpdump(pub_y, "puby = ", 0);
384 /* calculate h = H(sig[0..31]|pub|data) mod l */
385 chk = solv_chksum_create(REPOKEY_TYPE_SHA512);
388 solv_chksum_add(chk, sig, 32);
389 solv_chksum_add(chk, pub, 32);
390 solv_chksum_add(chk, data, datal);
391 solv_chksum_free(chk, hbuf);
392 mped25519_setfromle(MPED25519_LEN * 2, h2, hbuf, 64, 0xff);
393 mped25519_reduce512_l(h, h2);
395 mped25519_mpdump(s, "s = ", 0);
396 mped25519_mpdump(h, "h = ", 0);
398 /* calculate r = s * G - h * pub */
399 if (!mped25519_scmult2(r_x, r_y, s, ed25519_gx, ed25519_gy, h, pub_x, pub_y))
401 /* compress r into rbuf and verify that it matches sig */
402 for (i = 0; i < 32; i++)
403 rbuf[i] = r_y[i / MP_T_BYTES] >> (8 * (i % MP_T_BYTES));
404 if ((r_x[0] & 1) != 0)
406 return memcmp(sig, rbuf, 32) == 0 ? 1 : 0;