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1 : : // Copyright (c) 2017-2022 The Bitcoin Core developers
2 : : // Distributed under the MIT software license, see the accompanying
3 : : // file COPYING or http://www.opensource.org/licenses/mit-license.php.
4 : :
5 : : #include <crypto/muhash.h>
6 : :
7 : : #include <crypto/chacha20.h>
8 : : #include <crypto/common.h>
9 : : #include <hash.h>
10 : : #include <util/check.h>
11 : :
12 : : #include <bit>
13 : : #include <cassert>
14 : : #include <cstdio>
15 : : #include <limits>
16 : :
17 : : namespace {
18 : :
19 : : using limb_t = Num3072::limb_t;
20 : : using signed_limb_t = Num3072::signed_limb_t;
21 : : using double_limb_t = Num3072::double_limb_t;
22 : : using signed_double_limb_t = Num3072::signed_double_limb_t;
23 : : constexpr int LIMB_SIZE = Num3072::LIMB_SIZE;
24 : : constexpr int SIGNED_LIMB_SIZE = Num3072::SIGNED_LIMB_SIZE;
25 : : constexpr int LIMBS = Num3072::LIMBS;
26 : : constexpr int SIGNED_LIMBS = Num3072::SIGNED_LIMBS;
27 : : constexpr int FINAL_LIMB_POSITION = 3072 / SIGNED_LIMB_SIZE;
28 : : constexpr int FINAL_LIMB_MODULUS_BITS = 3072 % SIGNED_LIMB_SIZE;
29 : : constexpr limb_t MAX_LIMB = (limb_t)(-1);
30 : : constexpr limb_t MAX_SIGNED_LIMB = (((limb_t)1) << SIGNED_LIMB_SIZE) - 1;
31 : : /** 2^3072 - 1103717, the largest 3072-bit safe prime number, is used as the modulus. */
32 : : constexpr limb_t MAX_PRIME_DIFF = 1103717;
33 : : /** The modular inverse of (2**3072 - MAX_PRIME_DIFF) mod (MAX_SIGNED_LIMB + 1). */
34 : : constexpr limb_t MODULUS_INVERSE = limb_t(0x70a1421da087d93);
35 : :
36 : :
37 : : /** Extract the lowest limb of [c0,c1,c2] into n, and left shift the number by 1 limb. */
38 : 1181232 : inline void extract3(limb_t& c0, limb_t& c1, limb_t& c2, limb_t& n)
39 : : {
40 : 1181232 : n = c0;
41 : 1181232 : c0 = c1;
42 : 1181232 : c1 = c2;
43 : 1181232 : c2 = 0;
44 : : }
45 : :
46 : : /** [c0,c1] = a * b */
47 : 1156623 : inline void mul(limb_t& c0, limb_t& c1, const limb_t& a, const limb_t& b)
48 : : {
49 : 1156623 : double_limb_t t = (double_limb_t)a * b;
50 : 1156623 : c1 = t >> LIMB_SIZE;
51 : 1156623 : c0 = t;
52 : : }
53 : :
54 : : /* [c0,c1,c2] += n * [d0,d1,d2]. c2 is 0 initially */
55 : 1156623 : inline void mulnadd3(limb_t& c0, limb_t& c1, limb_t& c2, limb_t& d0, limb_t& d1, limb_t& d2, const limb_t& n)
56 : : {
57 : 1156623 : double_limb_t t = (double_limb_t)d0 * n + c0;
58 : 1156623 : c0 = t;
59 : 1156623 : t >>= LIMB_SIZE;
60 : 1156623 : t += (double_limb_t)d1 * n + c1;
61 : 1156623 : c1 = t;
62 : 1156623 : t >>= LIMB_SIZE;
63 : 1156623 : c2 = t + d2 * n;
64 : 1156623 : }
65 : :
66 : : /* [c0,c1] *= n */
67 : 24609 : inline void muln2(limb_t& c0, limb_t& c1, const limb_t& n)
68 : : {
69 : 24609 : double_limb_t t = (double_limb_t)c0 * n;
70 : 24609 : c0 = t;
71 : 24609 : t >>= LIMB_SIZE;
72 : 24609 : t += (double_limb_t)c1 * n;
73 : 24609 : c1 = t;
74 : : }
75 : :
76 : : /** [c0,c1,c2] += a * b */
77 : 55542513 : inline void muladd3(limb_t& c0, limb_t& c1, limb_t& c2, const limb_t& a, const limb_t& b)
78 : : {
79 : 55542513 : double_limb_t t = (double_limb_t)a * b;
80 : 55542513 : limb_t th = t >> LIMB_SIZE;
81 : 55542513 : limb_t tl = t;
82 : :
83 : 55542513 : c0 += tl;
84 [ + + ]: 55542513 : th += (c0 < tl) ? 1 : 0;
85 : 55542513 : c1 += th;
86 [ + + ]: 55542513 : c2 += (c1 < th) ? 1 : 0;
87 : 55542513 : }
88 : :
89 : : /**
90 : : * Add limb a to [c0,c1]: [c0,c1] += a. Then extract the lowest
91 : : * limb of [c0,c1] into n, and left shift the number by 1 limb.
92 : : * */
93 : 1181760 : inline void addnextract2(limb_t& c0, limb_t& c1, const limb_t& a, limb_t& n)
94 : : {
95 : 1181760 : limb_t c2 = 0;
96 : :
97 : : // add
98 : 1181760 : c0 += a;
99 [ + + ]: 1181760 : if (c0 < a) {
100 : 6860 : c1 += 1;
101 : :
102 : : // Handle case when c1 has overflown
103 [ - + ]: 6860 : if (c1 == 0) c2 = 1;
104 : : }
105 : :
106 : : // extract
107 : 1181760 : n = c0;
108 : 1181760 : c0 = c1;
109 : 1181760 : c1 = c2;
110 : 1181760 : }
111 : :
112 : : } // namespace
113 : :
114 : : /** Indicates whether d is larger than the modulus. */
115 : 58266 : bool Num3072::IsOverflow() const
116 : : {
117 [ + + ]: 58266 : if (this->limbs[0] <= std::numeric_limits<limb_t>::max() - MAX_PRIME_DIFF) return false;
118 [ + + ]: 528 : for (int i = 1; i < LIMBS; ++i) {
119 [ + - ]: 517 : if (this->limbs[i] != std::numeric_limits<limb_t>::max()) return false;
120 : : }
121 : : return true;
122 : : }
123 : :
124 : 11 : void Num3072::FullReduce()
125 : : {
126 : 11 : limb_t c0 = MAX_PRIME_DIFF;
127 : 11 : limb_t c1 = 0;
128 [ + + ]: 539 : for (int i = 0; i < LIMBS; ++i) {
129 : 528 : addnextract2(c0, c1, this->limbs[i], this->limbs[i]);
130 : : }
131 : 11 : }
132 : :
133 : : namespace {
134 : : /** A type representing a number in signed limb representation. */
135 : : struct Num3072Signed
136 : : {
137 : : /** The represented value is sum(limbs[i]*2^(SIGNED_LIMB_SIZE*i), i=0..SIGNED_LIMBS-1).
138 : : * Note that limbs may be negative, or exceed 2^SIGNED_LIMB_SIZE-1. */
139 : : signed_limb_t limbs[SIGNED_LIMBS];
140 : :
141 : : /** Construct a Num3072Signed with value 0. */
142 : 44876 : Num3072Signed()
143 : 44876 : {
144 : 44876 : memset(limbs, 0, sizeof(limbs));
145 : 44876 : }
146 : :
147 : : /** Convert a Num3072 to a Num3072Signed. Output will be normalized and in
148 : : * range 0..2^3072-1. */
149 : 11219 : void FromNum3072(const Num3072& in)
150 : : {
151 : 11219 : double_limb_t c = 0;
152 : 11219 : int b = 0, outpos = 0;
153 [ + + ]: 549731 : for (int i = 0; i < LIMBS; ++i) {
154 : 538512 : c += double_limb_t{in.limbs[i]} << b;
155 : 538512 : b += LIMB_SIZE;
156 [ + + ]: 1088243 : while (b >= SIGNED_LIMB_SIZE) {
157 : 549731 : limbs[outpos++] = limb_t(c) & MAX_SIGNED_LIMB;
158 : 549731 : c >>= SIGNED_LIMB_SIZE;
159 : 549731 : b -= SIGNED_LIMB_SIZE;
160 : : }
161 : : }
162 : 11219 : Assume(outpos == SIGNED_LIMBS - 1);
163 : 11219 : limbs[SIGNED_LIMBS - 1] = c;
164 : 11219 : c >>= SIGNED_LIMB_SIZE;
165 : 11219 : Assume(c == 0);
166 : 11219 : }
167 : :
168 : : /** Convert a Num3072Signed to a Num3072. Input must be in range 0..modulus-1. */
169 : 11219 : void ToNum3072(Num3072& out) const
170 : : {
171 : 11219 : double_limb_t c = 0;
172 : 11219 : int b = 0, outpos = 0;
173 [ + + ]: 572169 : for (int i = 0; i < SIGNED_LIMBS; ++i) {
174 : 560950 : c += double_limb_t(limbs[i]) << b;
175 : 560950 : b += SIGNED_LIMB_SIZE;
176 [ + + ]: 560950 : if (b >= LIMB_SIZE) {
177 : 538512 : out.limbs[outpos++] = c;
178 : 538512 : c >>= LIMB_SIZE;
179 : 538512 : b -= LIMB_SIZE;
180 : : }
181 : : }
182 : 11219 : Assume(outpos == LIMBS);
183 : 11219 : Assume(c == 0);
184 : 11219 : }
185 : :
186 : : /** Take a Num3072Signed in range 1-2*2^3072..2^3072-1, and:
187 : : * - optionally negate it (if negate is true)
188 : : * - reduce it modulo the modulus (2^3072 - MAX_PRIME_DIFF)
189 : : * - produce output with all limbs in range 0..2^SIGNED_LIMB_SIZE-1
190 : : */
191 : 11219 : void Normalize(bool negate)
192 : : {
193 : : // Add modulus if this was negative. This brings the range of *this to 1-2^3072..2^3072-1.
194 : 11219 : signed_limb_t cond_add = limbs[SIGNED_LIMBS-1] >> (LIMB_SIZE-1); // -1 if this is negative; 0 otherwise
195 : 11219 : limbs[0] += signed_limb_t(-MAX_PRIME_DIFF) & cond_add;
196 : 11219 : limbs[FINAL_LIMB_POSITION] += (signed_limb_t(1) << FINAL_LIMB_MODULUS_BITS) & cond_add;
197 : : // Next negate all limbs if negate was set. This does not change the range of *this.
198 : 11219 : signed_limb_t cond_negate = -signed_limb_t(negate); // -1 if this negate is true; 0 otherwise
199 [ + + ]: 572169 : for (int i = 0; i < SIGNED_LIMBS; ++i) {
200 : 560950 : limbs[i] = (limbs[i] ^ cond_negate) - cond_negate;
201 : : }
202 : : // Perform carry (make all limbs except the top one be in range 0..2^SIGNED_LIMB_SIZE-1).
203 [ + + ]: 560950 : for (int i = 0; i < SIGNED_LIMBS - 1; ++i) {
204 : 549731 : limbs[i + 1] += limbs[i] >> SIGNED_LIMB_SIZE;
205 : 549731 : limbs[i] &= MAX_SIGNED_LIMB;
206 : : }
207 : : // Again add modulus if *this was negative. This brings the range of *this to 0..2^3072-1.
208 : 11219 : cond_add = limbs[SIGNED_LIMBS-1] >> (LIMB_SIZE-1); // -1 if this is negative; 0 otherwise
209 : 11219 : limbs[0] += signed_limb_t(-MAX_PRIME_DIFF) & cond_add;
210 : 11219 : limbs[FINAL_LIMB_POSITION] += (signed_limb_t(1) << FINAL_LIMB_MODULUS_BITS) & cond_add;
211 : : // Perform another carry. Now all limbs are in range 0..2^SIGNED_LIMB_SIZE-1.
212 [ + + ]: 560950 : for (int i = 0; i < SIGNED_LIMBS - 1; ++i) {
213 : 549731 : limbs[i + 1] += limbs[i] >> SIGNED_LIMB_SIZE;
214 : 549731 : limbs[i] &= MAX_SIGNED_LIMB;
215 : : }
216 : 11219 : }
217 : : };
218 : :
219 : : /** 2x2 transformation matrix with signed_limb_t elements. */
220 : : struct SignedMatrix
221 : : {
222 : : signed_limb_t u, v, q, r;
223 : : };
224 : :
225 : : /** Compute the transformation matrix for SIGNED_LIMB_SIZE divsteps.
226 : : *
227 : : * eta: initial eta value
228 : : * f: bottom SIGNED_LIMB_SIZE bits of initial f value
229 : : * g: bottom SIGNED_LIMB_SIZE bits of initial g value
230 : : * out: resulting transformation matrix, scaled by 2^SIGNED_LIMB_SIZE
231 : : * return: eta value after SIGNED_LIMB_SIZE divsteps
232 : : */
233 : 1123143 : inline limb_t ComputeDivstepMatrix(signed_limb_t eta, limb_t f, limb_t g, SignedMatrix& out)
234 : : {
235 : : /** inv256[i] = -1/(2*i+1) (mod 256) */
236 : 1123143 : static const uint8_t NEGINV256[128] = {
237 : : 0xFF, 0x55, 0x33, 0x49, 0xC7, 0x5D, 0x3B, 0x11, 0x0F, 0xE5, 0xC3, 0x59,
238 : : 0xD7, 0xED, 0xCB, 0x21, 0x1F, 0x75, 0x53, 0x69, 0xE7, 0x7D, 0x5B, 0x31,
239 : : 0x2F, 0x05, 0xE3, 0x79, 0xF7, 0x0D, 0xEB, 0x41, 0x3F, 0x95, 0x73, 0x89,
240 : : 0x07, 0x9D, 0x7B, 0x51, 0x4F, 0x25, 0x03, 0x99, 0x17, 0x2D, 0x0B, 0x61,
241 : : 0x5F, 0xB5, 0x93, 0xA9, 0x27, 0xBD, 0x9B, 0x71, 0x6F, 0x45, 0x23, 0xB9,
242 : : 0x37, 0x4D, 0x2B, 0x81, 0x7F, 0xD5, 0xB3, 0xC9, 0x47, 0xDD, 0xBB, 0x91,
243 : : 0x8F, 0x65, 0x43, 0xD9, 0x57, 0x6D, 0x4B, 0xA1, 0x9F, 0xF5, 0xD3, 0xE9,
244 : : 0x67, 0xFD, 0xDB, 0xB1, 0xAF, 0x85, 0x63, 0xF9, 0x77, 0x8D, 0x6B, 0xC1,
245 : : 0xBF, 0x15, 0xF3, 0x09, 0x87, 0x1D, 0xFB, 0xD1, 0xCF, 0xA5, 0x83, 0x19,
246 : : 0x97, 0xAD, 0x8B, 0xE1, 0xDF, 0x35, 0x13, 0x29, 0xA7, 0x3D, 0x1B, 0xF1,
247 : : 0xEF, 0xC5, 0xA3, 0x39, 0xB7, 0xCD, 0xAB, 0x01
248 : : };
249 : : // Coefficients of returned SignedMatrix; starts off as identity matrix. */
250 : 1123143 : limb_t u = 1, v = 0, q = 0, r = 1;
251 : : // The number of divsteps still left.
252 : 1123143 : int i = SIGNED_LIMB_SIZE;
253 : 11364931 : while (true) {
254 : : /* Use a sentinel bit to count zeros only up to i. */
255 [ + - ]: 6244037 : int zeros = std::countr_zero(g | (MAX_LIMB << i));
256 : : /* Perform zeros divsteps at once; they all just divide g by two. */
257 : 6244037 : g >>= zeros;
258 : 6244037 : u <<= zeros;
259 : 6244037 : v <<= zeros;
260 : 6244037 : eta -= zeros;
261 : 6244037 : i -= zeros;
262 : : /* We're done once we've performed SIGNED_LIMB_SIZE divsteps. */
263 [ + + ]: 6244037 : if (i == 0) break;
264 : : /* If eta is negative, negate it and replace f,g with g,-f. */
265 [ + + ]: 5120894 : if (eta < 0) {
266 : 850314 : limb_t tmp;
267 : 850314 : eta = -eta;
268 : 850314 : tmp = f; f = g; g = -tmp;
269 : 850314 : tmp = u; u = q; q = -tmp;
270 : 850314 : tmp = v; v = r; r = -tmp;
271 : : }
272 : : /* eta is now >= 0. In what follows we're going to cancel out the bottom bits of g. No more
273 : : * than i can be cancelled out (as we'd be done before that point), and no more than eta+1
274 : : * can be done as its sign will flip once that happens. */
275 [ + + ]: 5120894 : int limit = ((int)eta + 1) > i ? i : ((int)eta + 1);
276 : : /* m is a mask for the bottom min(limit, 8) bits (our table only supports 8 bits). */
277 : 5120894 : limb_t m = (MAX_LIMB >> (LIMB_SIZE - limit)) & 255U;
278 : : /* Find what multiple of f must be added to g to cancel its bottom min(limit, 8) bits. */
279 : 5120894 : limb_t w = (g * NEGINV256[(f >> 1) & 127]) & m;
280 : : /* Do so. */
281 : 5120894 : g += f * w;
282 : 5120894 : q += u * w;
283 : 5120894 : r += v * w;
284 : 5120894 : }
285 : 1123143 : out.u = (signed_limb_t)u;
286 : 1123143 : out.v = (signed_limb_t)v;
287 : 1123143 : out.q = (signed_limb_t)q;
288 : 1123143 : out.r = (signed_limb_t)r;
289 : 1123143 : return eta;
290 : : }
291 : :
292 : : /** Apply matrix t/2^SIGNED_LIMB_SIZE to vector [d,e], modulo modulus.
293 : : *
294 : : * On input and output, d and e are in range 1-2*modulus..modulus-1.
295 : : */
296 : 1123143 : inline void UpdateDE(Num3072Signed& d, Num3072Signed& e, const SignedMatrix& t)
297 : : {
298 : 1123143 : const signed_limb_t u = t.u, v=t.v, q=t.q, r=t.r;
299 : :
300 : : /* [md,me] start as zero; plus [u,q] if d is negative; plus [v,r] if e is negative. */
301 : 1123143 : signed_limb_t sd = d.limbs[SIGNED_LIMBS - 1] >> (LIMB_SIZE - 1);
302 : 1123143 : signed_limb_t se = e.limbs[SIGNED_LIMBS - 1] >> (LIMB_SIZE - 1);
303 : 1123143 : signed_limb_t md = (u & sd) + (v & se);
304 : 1123143 : signed_limb_t me = (q & sd) + (r & se);
305 : : /* Begin computing t*[d,e]. */
306 : 1123143 : signed_limb_t di = d.limbs[0], ei = e.limbs[0];
307 : 1123143 : signed_double_limb_t cd = (signed_double_limb_t)u * di + (signed_double_limb_t)v * ei;
308 : 1123143 : signed_double_limb_t ce = (signed_double_limb_t)q * di + (signed_double_limb_t)r * ei;
309 : : /* Correct md,me so that t*[d,e]+modulus*[md,me] has SIGNED_LIMB_SIZE zero bottom bits. */
310 : 1123143 : md -= (MODULUS_INVERSE * limb_t(cd) + md) & MAX_SIGNED_LIMB;
311 : 1123143 : me -= (MODULUS_INVERSE * limb_t(ce) + me) & MAX_SIGNED_LIMB;
312 : : /* Update the beginning of computation for t*[d,e]+modulus*[md,me] now md,me are known. */
313 : 1123143 : cd -= (signed_double_limb_t)1103717 * md;
314 : 1123143 : ce -= (signed_double_limb_t)1103717 * me;
315 : : /* Verify that the low SIGNED_LIMB_SIZE bits of the computation are indeed zero, and then throw them away. */
316 : 1123143 : Assume((cd & MAX_SIGNED_LIMB) == 0);
317 : 1123143 : Assume((ce & MAX_SIGNED_LIMB) == 0);
318 : 1123143 : cd >>= SIGNED_LIMB_SIZE;
319 : 1123143 : ce >>= SIGNED_LIMB_SIZE;
320 : : /* Now iteratively compute limb i=1..SIGNED_LIMBS-2 of t*[d,e]+modulus*[md,me], and store them in output
321 : : * limb i-1 (shifting down by SIGNED_LIMB_SIZE bits). The corresponding limbs in modulus are all zero,
322 : : * so modulus/md/me are not actually involved here. */
323 [ + + ]: 55034007 : for (int i = 1; i < SIGNED_LIMBS - 1; ++i) {
324 : 53910864 : di = d.limbs[i];
325 : 53910864 : ei = e.limbs[i];
326 : 53910864 : cd += (signed_double_limb_t)u * di + (signed_double_limb_t)v * ei;
327 : 53910864 : ce += (signed_double_limb_t)q * di + (signed_double_limb_t)r * ei;
328 : 53910864 : d.limbs[i - 1] = (signed_limb_t)cd & MAX_SIGNED_LIMB; cd >>= SIGNED_LIMB_SIZE;
329 : 53910864 : e.limbs[i - 1] = (signed_limb_t)ce & MAX_SIGNED_LIMB; ce >>= SIGNED_LIMB_SIZE;
330 : : }
331 : : /* Compute limb SIGNED_LIMBS-1 of t*[d,e]+modulus*[md,me], and store it in output limb SIGNED_LIMBS-2. */
332 : 1123143 : di = d.limbs[SIGNED_LIMBS - 1];
333 : 1123143 : ei = e.limbs[SIGNED_LIMBS - 1];
334 : 1123143 : cd += (signed_double_limb_t)u * di + (signed_double_limb_t)v * ei;
335 : 1123143 : ce += (signed_double_limb_t)q * di + (signed_double_limb_t)r * ei;
336 : 1123143 : cd += (signed_double_limb_t)md << FINAL_LIMB_MODULUS_BITS;
337 : 1123143 : ce += (signed_double_limb_t)me << FINAL_LIMB_MODULUS_BITS;
338 : 1123143 : d.limbs[SIGNED_LIMBS - 2] = (signed_limb_t)cd & MAX_SIGNED_LIMB; cd >>= SIGNED_LIMB_SIZE;
339 : 1123143 : e.limbs[SIGNED_LIMBS - 2] = (signed_limb_t)ce & MAX_SIGNED_LIMB; ce >>= SIGNED_LIMB_SIZE;
340 : : /* What remains goes into output limb SINGED_LIMBS-1 */
341 : 1123143 : d.limbs[SIGNED_LIMBS - 1] = (signed_limb_t)cd;
342 : 1123143 : e.limbs[SIGNED_LIMBS - 1] = (signed_limb_t)ce;
343 : 1123143 : }
344 : :
345 : : /** Apply matrix t/2^SIGNED_LIMB_SIZE to vector (f,g).
346 : : *
347 : : * The matrix t must be chosen such that t*(f,g) results in multiples of 2^SIGNED_LIMB_SIZE.
348 : : * This is the case for matrices computed by ComputeDivstepMatrix().
349 : : */
350 : 1123143 : inline void UpdateFG(Num3072Signed& f, Num3072Signed& g, const SignedMatrix& t, int len)
351 : : {
352 : 1123143 : const signed_limb_t u = t.u, v=t.v, q=t.q, r=t.r;
353 : :
354 : 1123143 : signed_limb_t fi, gi;
355 : 1123143 : signed_double_limb_t cf, cg;
356 : : /* Start computing t*[f,g]. */
357 : 1123143 : fi = f.limbs[0];
358 : 1123143 : gi = g.limbs[0];
359 : 1123143 : cf = (signed_double_limb_t)u * fi + (signed_double_limb_t)v * gi;
360 : 1123143 : cg = (signed_double_limb_t)q * fi + (signed_double_limb_t)r * gi;
361 : : /* Verify that the bottom SIGNED_LIMB_BITS bits of the result are zero, and then throw them away. */
362 : 1123143 : Assume((cf & MAX_SIGNED_LIMB) == 0);
363 : 1123143 : Assume((cg & MAX_SIGNED_LIMB) == 0);
364 : 1123143 : cf >>= SIGNED_LIMB_SIZE;
365 : 1123143 : cg >>= SIGNED_LIMB_SIZE;
366 : : /* Now iteratively compute limb i=1..SIGNED_LIMBS-1 of t*[f,g], and store them in output limb i-1 (shifting
367 : : * down by SIGNED_LIMB_BITS bits). */
368 [ + + ]: 41409787 : for (int i = 1; i < len; ++i) {
369 : 40286644 : fi = f.limbs[i];
370 : 40286644 : gi = g.limbs[i];
371 : 40286644 : cf += (signed_double_limb_t)u * fi + (signed_double_limb_t)v * gi;
372 : 40286644 : cg += (signed_double_limb_t)q * fi + (signed_double_limb_t)r * gi;
373 : 40286644 : f.limbs[i - 1] = (signed_limb_t)cf & MAX_SIGNED_LIMB; cf >>= SIGNED_LIMB_SIZE;
374 : 40286644 : g.limbs[i - 1] = (signed_limb_t)cg & MAX_SIGNED_LIMB; cg >>= SIGNED_LIMB_SIZE;
375 : : }
376 : : /* What remains is limb SIGNED_LIMBS of t*[f,g]; store it as output limb SIGNED_LIMBS-1. */
377 : 1123143 : f.limbs[len - 1] = (signed_limb_t)cf;
378 : 1123143 : g.limbs[len - 1] = (signed_limb_t)cg;
379 : :
380 : 1123143 : }
381 : : } // namespace
382 : :
383 : 11219 : Num3072 Num3072::GetInverse() const
384 : : {
385 : : // Compute a modular inverse based on a variant of the safegcd algorithm:
386 : : // - Paper: https://gcd.cr.yp.to/papers.html
387 : : // - Inspired by this code in libsecp256k1:
388 : : // https://github.com/bitcoin-core/secp256k1/blob/master/src/modinv32_impl.h
389 : : // - Explanation of the algorithm:
390 : : // https://github.com/bitcoin-core/secp256k1/blob/master/doc/safegcd_implementation.md
391 : :
392 : : // Local variables d, e, f, g:
393 : : // - f and g are the variables whose gcd we compute (despite knowing the answer is 1):
394 : : // - f is always odd, and initialized as modulus
395 : : // - g is initialized as *this (called x in what follows)
396 : : // - d and e are the numbers for which at every step it is the case that:
397 : : // - f = d * x mod modulus; d is initialized as 0
398 : : // - g = e * x mod modulus; e is initialized as 1
399 : 11219 : Num3072Signed d, e, f, g;
400 : 11219 : e.limbs[0] = 1;
401 : : // F is initialized as modulus, which in signed limb representation can be expressed
402 : : // simply as 2^3072 + -MAX_PRIME_DIFF.
403 : 11219 : f.limbs[0] = -MAX_PRIME_DIFF;
404 : 11219 : f.limbs[FINAL_LIMB_POSITION] = ((limb_t)1) << FINAL_LIMB_MODULUS_BITS;
405 : 11219 : g.FromNum3072(*this);
406 : 11219 : int len = SIGNED_LIMBS; //!< The number of significant limbs in f and g
407 : 11219 : signed_limb_t eta = -1; //!< State to track knowledge about ratio of f and g
408 : : // Perform divsteps on [f,g] until g=0 is reached, keeping (d,e) synchronized with them.
409 : 1123143 : while (true) {
410 : : // Compute transformation matrix t that represents the next SIGNED_LIMB_SIZE divsteps
411 : : // to apply. This can be computed from just the bottom limb of f and g, and eta.
412 : 1123143 : SignedMatrix t;
413 : 1123143 : eta = ComputeDivstepMatrix(eta, f.limbs[0], g.limbs[0], t);
414 : : // Apply that transformation matrix to the full [f,g] vector.
415 : 1123143 : UpdateFG(f, g, t, len);
416 : : // Apply that transformation matrix to the full [d,e] vector (mod modulus).
417 : 1123143 : UpdateDE(d, e, t);
418 : :
419 : : // Check if g is zero.
420 [ + + ]: 1123143 : if (g.limbs[0] == 0) {
421 : : signed_limb_t cond = 0;
422 [ + + ]: 26080019 : for (int j = 1; j < len; ++j) {
423 : 25547424 : cond |= g.limbs[j];
424 : : }
425 : : // If so, we're done.
426 [ + + ]: 532595 : if (cond == 0) break;
427 : : }
428 : :
429 : : // Check if the top limbs of both f and g are both 0 or -1.
430 : 1111924 : signed_limb_t fn = f.limbs[len - 1], gn = g.limbs[len - 1];
431 : 1111924 : signed_limb_t cond = ((signed_limb_t)len - 2) >> (LIMB_SIZE - 1);
432 : 1111924 : cond |= fn ^ (fn >> (LIMB_SIZE - 1));
433 : 1111924 : cond |= gn ^ (gn >> (LIMB_SIZE - 1));
434 [ + + ]: 1111924 : if (cond == 0) {
435 : : // If so, drop the top limb, shrinking the size of f and g, by
436 : : // propagating the sign to the previous limb.
437 : 549731 : f.limbs[len - 2] |= (limb_t)f.limbs[len - 1] << SIGNED_LIMB_SIZE;
438 : 549731 : g.limbs[len - 2] |= (limb_t)g.limbs[len - 1] << SIGNED_LIMB_SIZE;
439 : 549731 : --len;
440 : : }
441 : : }
442 : : // At some point, [f,g] will have been rewritten into [f',0], such that gcd(f,g) = gcd(f',0).
443 : : // This is proven in the paper. As f started out being modulus, a prime number, we know that
444 : : // gcd is 1, and thus f' is 1 or -1.
445 : 11219 : Assume((f.limbs[0] & MAX_SIGNED_LIMB) == 1 || (f.limbs[0] & MAX_SIGNED_LIMB) == MAX_SIGNED_LIMB);
446 : : // As we've maintained the invariant that f = d * x mod modulus, we get d/f mod modulus is the
447 : : // modular inverse of x we're looking for. As f is 1 or -1, it is also true that d/f = d*f.
448 : : // Normalize d to prepare it for output, while negating it if f is negative.
449 : 11219 : d.Normalize(f.limbs[len - 1] >> (LIMB_SIZE - 1));
450 : 11219 : Num3072 ret;
451 : 11219 : d.ToNum3072(ret);
452 : 11219 : return ret;
453 : : }
454 : :
455 : 24609 : void Num3072::Multiply(const Num3072& a)
456 : : {
457 : 24609 : limb_t c0 = 0, c1 = 0, c2 = 0;
458 : 24609 : Num3072 tmp;
459 : :
460 : : /* Compute limbs 0..N-2 of this*a into tmp, including one reduction. */
461 [ + + ]: 1181232 : for (int j = 0; j < LIMBS - 1; ++j) {
462 : 1156623 : limb_t d0 = 0, d1 = 0, d2 = 0;
463 : 1156623 : mul(d0, d1, this->limbs[1 + j], a.limbs[LIMBS + j - (1 + j)]);
464 [ + + ]: 27758952 : for (int i = 2 + j; i < LIMBS; ++i) muladd3(d0, d1, d2, this->limbs[i], a.limbs[LIMBS + j - i]);
465 : 1156623 : mulnadd3(c0, c1, c2, d0, d1, d2, MAX_PRIME_DIFF);
466 [ + + ]: 28915575 : for (int i = 0; i < j + 1; ++i) muladd3(c0, c1, c2, this->limbs[i], a.limbs[j - i]);
467 : 1156623 : extract3(c0, c1, c2, tmp.limbs[j]);
468 : : }
469 : :
470 : : /* Compute limb N-1 of a*b into tmp. */
471 [ + - ]: 24609 : assert(c2 == 0);
472 [ + + ]: 1205841 : for (int i = 0; i < LIMBS; ++i) muladd3(c0, c1, c2, this->limbs[i], a.limbs[LIMBS - 1 - i]);
473 : 24609 : extract3(c0, c1, c2, tmp.limbs[LIMBS - 1]);
474 : :
475 : : /* Perform a second reduction. */
476 : 24609 : muln2(c0, c1, MAX_PRIME_DIFF);
477 [ + + ]: 1205841 : for (int j = 0; j < LIMBS; ++j) {
478 : 1181232 : addnextract2(c0, c1, tmp.limbs[j], this->limbs[j]);
479 : : }
480 : :
481 [ - + ]: 24609 : assert(c1 == 0);
482 [ - + ]: 24609 : assert(c0 == 0 || c0 == 1);
483 : :
484 : : /* Perform up to two more reductions if the internal state has already
485 : : * overflown the MAX of Num3072 or if it is larger than the modulus or
486 : : * if both are the case.
487 : : * */
488 [ + + ]: 24609 : if (this->IsOverflow()) this->FullReduce();
489 [ - + ]: 24609 : if (c0) this->FullReduce();
490 : 24609 : }
491 : :
492 : 58860 : void Num3072::SetToOne()
493 : : {
494 : 58860 : this->limbs[0] = 1;
495 [ + + ]: 2825280 : for (int i = 1; i < LIMBS; ++i) this->limbs[i] = 0;
496 : 58860 : }
497 : :
498 : 11219 : void Num3072::Divide(const Num3072& a)
499 : : {
500 [ + + ]: 11219 : if (this->IsOverflow()) this->FullReduce();
501 : :
502 : 11219 : Num3072 inv{};
503 [ - + ]: 11219 : if (a.IsOverflow()) {
504 : 0 : Num3072 b = a;
505 : 0 : b.FullReduce();
506 : 0 : inv = b.GetInverse();
507 : : } else {
508 : 11219 : inv = a.GetInverse();
509 : : }
510 : :
511 : 11219 : this->Multiply(inv);
512 [ - + ]: 11219 : if (this->IsOverflow()) this->FullReduce();
513 : 11219 : }
514 : :
515 : 13170 : Num3072::Num3072(const unsigned char (&data)[BYTE_SIZE]) {
516 [ + + ]: 645330 : for (int i = 0; i < LIMBS; ++i) {
517 : 632160 : if (sizeof(limb_t) == 4) {
518 : : this->limbs[i] = ReadLE32(data + 4 * i);
519 : 632160 : } else if (sizeof(limb_t) == 8) {
520 : 632160 : this->limbs[i] = ReadLE64(data + 8 * i);
521 : : }
522 : : }
523 : 13170 : }
524 : :
525 : 11219 : void Num3072::ToBytes(unsigned char (&out)[BYTE_SIZE]) {
526 [ + + ]: 549731 : for (int i = 0; i < LIMBS; ++i) {
527 : 538512 : if (sizeof(limb_t) == 4) {
528 : : WriteLE32(out + i * 4, this->limbs[i]);
529 : 538512 : } else if (sizeof(limb_t) == 8) {
530 : 538512 : WriteLE64(out + i * 8, this->limbs[i]);
531 : : }
532 : : }
533 : 11219 : }
534 : :
535 : 13170 : Num3072 MuHash3072::ToNum3072(Span<const unsigned char> in) {
536 : 13170 : unsigned char tmp[Num3072::BYTE_SIZE];
537 : :
538 : 13170 : uint256 hashed_in{(HashWriter{} << in).GetSHA256()};
539 : 13170 : static_assert(sizeof(tmp) % ChaCha20Aligned::BLOCKLEN == 0);
540 : 13170 : ChaCha20Aligned{MakeByteSpan(hashed_in)}.Keystream(MakeWritableByteSpan(tmp));
541 : 13170 : Num3072 out{tmp};
542 : :
543 : 13170 : return out;
544 : : }
545 : :
546 : 186 : MuHash3072::MuHash3072(Span<const unsigned char> in) noexcept
547 : : {
548 : 186 : m_numerator = ToNum3072(in);
549 : 186 : }
550 : :
551 : 11219 : void MuHash3072::Finalize(uint256& out) noexcept
552 : : {
553 : 11219 : m_numerator.Divide(m_denominator);
554 : 11219 : m_denominator.SetToOne(); // Needed to keep the MuHash object valid
555 : :
556 : 11219 : unsigned char data[Num3072::BYTE_SIZE];
557 : 11219 : m_numerator.ToBytes(data);
558 : :
559 : 11219 : out = (HashWriter{} << data).GetSHA256();
560 : 11219 : }
561 : :
562 : 112 : MuHash3072& MuHash3072::operator*=(const MuHash3072& mul) noexcept
563 : : {
564 : 112 : m_numerator.Multiply(mul.m_numerator);
565 : 112 : m_denominator.Multiply(mul.m_denominator);
566 : 112 : return *this;
567 : : }
568 : :
569 : 91 : MuHash3072& MuHash3072::operator/=(const MuHash3072& div) noexcept
570 : : {
571 : 91 : m_numerator.Multiply(div.m_denominator);
572 : 91 : m_denominator.Multiply(div.m_numerator);
573 : 91 : return *this;
574 : : }
575 : :
576 : 12667 : MuHash3072& MuHash3072::Insert(Span<const unsigned char> in) noexcept {
577 : 12667 : m_numerator.Multiply(ToNum3072(in));
578 : 12667 : return *this;
579 : : }
580 : :
581 : 317 : MuHash3072& MuHash3072::Remove(Span<const unsigned char> in) noexcept {
582 : 317 : m_denominator.Multiply(ToNum3072(in));
583 : 317 : return *this;
584 : : }
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