1 /*
2 * Copyright 2017-2021 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright 2015-2016 Cryptography Research, Inc.
4 *
5 * Licensed under the Apache License 2.0 (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
9 *
10 * Originally written by Mike Hamburg
11 */
12 #include <openssl/crypto.h>
13
14 #include "word.h"
15 #include "point_448.h"
16
17 static const c448_word_t MONTGOMERY_FACTOR = (c448_word_t) 0x3bd440fae918bc5ULL;
18 static const curve448_scalar_t sc_p = {
19 {
20 {
21 SC_LIMB(0x2378c292ab5844f3ULL), SC_LIMB(0x216cc2728dc58f55ULL),
22 SC_LIMB(0xc44edb49aed63690ULL), SC_LIMB(0xffffffff7cca23e9ULL),
23 SC_LIMB(0xffffffffffffffffULL), SC_LIMB(0xffffffffffffffffULL),
24 SC_LIMB(0x3fffffffffffffffULL)
25 }
26 }
27 }, sc_r2 = {
28 {
29 {
30
31 SC_LIMB(0xe3539257049b9b60ULL), SC_LIMB(0x7af32c4bc1b195d9ULL),
32 SC_LIMB(0x0d66de2388ea1859ULL), SC_LIMB(0xae17cf725ee4d838ULL),
33 SC_LIMB(0x1a9cc14ba3c47c44ULL), SC_LIMB(0x2052bcb7e4d070afULL),
34 SC_LIMB(0x3402a939f823b729ULL)
35 }
36 }
37 };
38
39 #define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
40
41 const curve448_scalar_t ossl_curve448_scalar_one = {{{1}}};
42 const curve448_scalar_t ossl_curve448_scalar_zero = {{{0}}};
43
44 /*
45 * {extra,accum} - sub +? p
46 * Must have extra <= 1
47 */
sc_subx(curve448_scalar_t out,const c448_word_t accum[C448_SCALAR_LIMBS],const curve448_scalar_t sub,const curve448_scalar_t p,c448_word_t extra)48 static void sc_subx(curve448_scalar_t out,
49 const c448_word_t accum[C448_SCALAR_LIMBS],
50 const curve448_scalar_t sub,
51 const curve448_scalar_t p, c448_word_t extra)
52 {
53 c448_dsword_t chain = 0;
54 unsigned int i;
55 c448_word_t borrow;
56
57 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
58 chain = (chain + accum[i]) - sub->limb[i];
59 out->limb[i] = (c448_word_t)chain;
60 chain >>= WBITS;
61 }
62 borrow = (c448_word_t)chain + extra; /* = 0 or -1 */
63
64 chain = 0;
65 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
66 chain = (chain + out->limb[i]) + (p->limb[i] & borrow);
67 out->limb[i] = (c448_word_t)chain;
68 chain >>= WBITS;
69 }
70 }
71
sc_montmul(curve448_scalar_t out,const curve448_scalar_t a,const curve448_scalar_t b)72 static void sc_montmul(curve448_scalar_t out, const curve448_scalar_t a,
73 const curve448_scalar_t b)
74 {
75 unsigned int i, j;
76 c448_word_t accum[C448_SCALAR_LIMBS + 1] = { 0 };
77 c448_word_t hi_carry = 0;
78
79 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
80 c448_word_t mand = a->limb[i];
81 const c448_word_t *mier = b->limb;
82
83 c448_dword_t chain = 0;
84 for (j = 0; j < C448_SCALAR_LIMBS; j++) {
85 chain += ((c448_dword_t) mand) * mier[j] + accum[j];
86 accum[j] = (c448_word_t)chain;
87 chain >>= WBITS;
88 }
89 accum[j] = (c448_word_t)chain;
90
91 mand = accum[0] * MONTGOMERY_FACTOR;
92 chain = 0;
93 mier = sc_p->limb;
94 for (j = 0; j < C448_SCALAR_LIMBS; j++) {
95 chain += (c448_dword_t) mand *mier[j] + accum[j];
96 if (j)
97 accum[j - 1] = (c448_word_t)chain;
98 chain >>= WBITS;
99 }
100 chain += accum[j];
101 chain += hi_carry;
102 accum[j - 1] = (c448_word_t)chain;
103 hi_carry = chain >> WBITS;
104 }
105
106 sc_subx(out, accum, sc_p, sc_p, hi_carry);
107 }
108
ossl_curve448_scalar_mul(curve448_scalar_t out,const curve448_scalar_t a,const curve448_scalar_t b)109 void ossl_curve448_scalar_mul(curve448_scalar_t out, const curve448_scalar_t a,
110 const curve448_scalar_t b)
111 {
112 sc_montmul(out, a, b);
113 sc_montmul(out, out, sc_r2);
114 }
115
116 void
ossl_curve448_scalar_sub(curve448_scalar_t out,const curve448_scalar_t a,const curve448_scalar_t b)117 ossl_curve448_scalar_sub(curve448_scalar_t out, const curve448_scalar_t a,
118 const curve448_scalar_t b)
119 {
120 sc_subx(out, a->limb, b, sc_p, 0);
121 }
122
123 void
ossl_curve448_scalar_add(curve448_scalar_t out,const curve448_scalar_t a,const curve448_scalar_t b)124 ossl_curve448_scalar_add(curve448_scalar_t out, const curve448_scalar_t a,
125 const curve448_scalar_t b)
126 {
127 c448_dword_t chain = 0;
128 unsigned int i;
129
130 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
131 chain = (chain + a->limb[i]) + b->limb[i];
132 out->limb[i] = (c448_word_t)chain;
133 chain >>= WBITS;
134 }
135 sc_subx(out, out->limb, sc_p, sc_p, (c448_word_t)chain);
136 }
137
scalar_decode_short(curve448_scalar_t s,const unsigned char * ser,size_t nbytes)138 static ossl_inline void scalar_decode_short(curve448_scalar_t s,
139 const unsigned char *ser,
140 size_t nbytes)
141 {
142 size_t i, j, k = 0;
143
144 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
145 c448_word_t out = 0;
146
147 for (j = 0; j < sizeof(c448_word_t) && k < nbytes; j++, k++)
148 out |= ((c448_word_t) ser[k]) << (8 * j);
149 s->limb[i] = out;
150 }
151 }
152
153 c448_error_t
ossl_curve448_scalar_decode(curve448_scalar_t s,const unsigned char ser[C448_SCALAR_BYTES])154 ossl_curve448_scalar_decode(curve448_scalar_t s,
155 const unsigned char ser[C448_SCALAR_BYTES])
156 {
157 unsigned int i;
158 c448_dsword_t accum = 0;
159
160 scalar_decode_short(s, ser, C448_SCALAR_BYTES);
161 for (i = 0; i < C448_SCALAR_LIMBS; i++)
162 accum = (accum + s->limb[i] - sc_p->limb[i]) >> WBITS;
163 /* Here accum == 0 or -1 */
164
165 ossl_curve448_scalar_mul(s, s, ossl_curve448_scalar_one); /* ham-handed reduce */
166
167 return c448_succeed_if(~word_is_zero((uint32_t)accum));
168 }
169
ossl_curve448_scalar_destroy(curve448_scalar_t scalar)170 void ossl_curve448_scalar_destroy(curve448_scalar_t scalar)
171 {
172 OPENSSL_cleanse(scalar, sizeof(curve448_scalar_t));
173 }
174
175 void
ossl_curve448_scalar_decode_long(curve448_scalar_t s,const unsigned char * ser,size_t ser_len)176 ossl_curve448_scalar_decode_long(curve448_scalar_t s,
177 const unsigned char *ser, size_t ser_len)
178 {
179 size_t i;
180 curve448_scalar_t t1, t2;
181
182 if (ser_len == 0) {
183 curve448_scalar_copy(s, ossl_curve448_scalar_zero);
184 return;
185 }
186
187 i = ser_len - (ser_len % C448_SCALAR_BYTES);
188 if (i == ser_len)
189 i -= C448_SCALAR_BYTES;
190
191 scalar_decode_short(t1, &ser[i], ser_len - i);
192
193 if (ser_len == sizeof(curve448_scalar_t)) {
194 assert(i == 0);
195 /* ham-handed reduce */
196 ossl_curve448_scalar_mul(s, t1, ossl_curve448_scalar_one);
197 ossl_curve448_scalar_destroy(t1);
198 return;
199 }
200
201 while (i) {
202 i -= C448_SCALAR_BYTES;
203 sc_montmul(t1, t1, sc_r2);
204 (void)ossl_curve448_scalar_decode(t2, ser + i);
205 ossl_curve448_scalar_add(t1, t1, t2);
206 }
207
208 curve448_scalar_copy(s, t1);
209 ossl_curve448_scalar_destroy(t1);
210 ossl_curve448_scalar_destroy(t2);
211 }
212
213 void
ossl_curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],const curve448_scalar_t s)214 ossl_curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
215 const curve448_scalar_t s)
216 {
217 unsigned int i, j, k = 0;
218
219 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
220 for (j = 0; j < sizeof(c448_word_t); j++, k++)
221 ser[k] = s->limb[i] >> (8 * j);
222 }
223 }
224
225 void
ossl_curve448_scalar_halve(curve448_scalar_t out,const curve448_scalar_t a)226 ossl_curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a)
227 {
228 c448_word_t mask = 0 - (a->limb[0] & 1);
229 c448_dword_t chain = 0;
230 unsigned int i;
231
232 for (i = 0; i < C448_SCALAR_LIMBS; i++) {
233 chain = (chain + a->limb[i]) + (sc_p->limb[i] & mask);
234 out->limb[i] = (c448_word_t)chain;
235 chain >>= C448_WORD_BITS;
236 }
237 for (i = 0; i < C448_SCALAR_LIMBS - 1; i++)
238 out->limb[i] = out->limb[i] >> 1 | out->limb[i + 1] << (WBITS - 1);
239 out->limb[i] = out->limb[i] >> 1 | (c448_word_t)(chain << (WBITS - 1));
240 }
241