tge25519.c - sick - sign and check files using ed25519
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tge25519.c (11221B)
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1 /*
2 * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
3 * Peter Schwabe, Bo-Yin Yang.
4 * Copied from supercop-20230530/crypto_sign/ed25519/ref/ge25519.c
5 */
6
7 #include "fe25519.h"
8 #include "sc25519.h"
9 #include "ge25519.h"
10
11 /*
12 * Arithmetic on the twisted Edwards curve -x^2 + y^2 = 1 + dx^2y^2
13 * with d = -(121665/121666) = 37095705934669439343138083508754565189542113879843219016388785533085940283555
14 * Base point: (15112221349535400772501151409588531511454012693041857206046113283949847762202,46316835694926478169428394003475163141307993866256225615783033603165251855960);
15 */
16
17 /* d */
18 static const fe25519 ge25519_ecd = {{0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75, 0xAB, 0xD8, 0x41, 0x41, 0x4D, 0x0A, 0x70, 0x00,
19 0x98, 0xE8, 0x79, 0x77, 0x79, 0x40, 0xC7, 0x8C, 0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52}};
20 /* 2*d */
21 static const fe25519 ge25519_ec2d = {{0x59, 0xF1, 0xB2, 0x26, 0x94, 0x9B, 0xD6, 0xEB, 0x56, 0xB1, 0x83, 0x82, 0x9A, 0x14, 0xE0, 0x00,
22 0x30, 0xD1, 0xF3, 0xEE, 0xF2, 0x80, 0x8E, 0x19, 0xE7, 0xFC, 0xDF, 0x56, 0xDC, 0xD9, 0x06, 0x24}};
23 /* sqrt(-1) */
24 static const fe25519 ge25519_sqrtm1 = {{0xB0, 0xA0, 0x0E, 0x4A, 0x27, 0x1B, 0xEE, 0xC4, 0x78, 0xE4, 0x2F, 0xAD, 0x06, 0x18, 0x43, 0x2F,
25 0xA7, 0xD7, 0xFB, 0x3D, 0x99, 0x00, 0x4D, 0x2B, 0x0B, 0xDF, 0xC1, 0x4F, 0x80, 0x24, 0x83, 0x2B}};
26
27 #define ge25519_p3 ge25519
28
29 typedef struct
30 {
31 fe25519 x;
32 fe25519 z;
33 fe25519 y;
34 fe25519 t;
35 } ge25519_p1p1;
36
37 typedef struct
38 {
39 fe25519 x;
40 fe25519 y;
41 fe25519 z;
42 } ge25519_p2;
43
44 typedef struct
45 {
46 fe25519 x;
47 fe25519 y;
48 } ge25519_aff;
49
50
51 /* Packed coordinates of the base point */
52 const ge25519 ge25519_base = {{{0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9, 0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69,
53 0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0, 0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21}},
54 {{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
55 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}},
56 {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
57 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
58 {{0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D, 0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20,
59 0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66, 0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67}}};
60
61 /* Multiples of the base point in affine representation */
62 static const ge25519_aff ge25519_base_multiples_affine[425] = {
63 #include "ge25519_base.data"
64 };
65
66 static void p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p)
67 {
68 fe25519_mul(&r->x, &p->x, &p->t);
69 fe25519_mul(&r->y, &p->y, &p->z);
70 fe25519_mul(&r->z, &p->z, &p->t);
71 }
72
73 static void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p)
74 {
75 p1p1_to_p2((ge25519_p2 *)r, p);
76 fe25519_mul(&r->t, &p->x, &p->y);
77 }
78
79 static void ge25519_mixadd2(ge25519_p3 *r, const ge25519_aff *q)
80 {
81 fe25519 a,b,t1,t2,c,d,e,f,g,h,qt;
82 fe25519_mul(&qt, &q->x, &q->y);
83 fe25519_sub(&a, &r->y, &r->x); /* A = (Y1-X1)*(Y2-X2) */
84 fe25519_add(&b, &r->y, &r->x); /* B = (Y1+X1)*(Y2+X2) */
85 fe25519_sub(&t1, &q->y, &q->x);
86 fe25519_add(&t2, &q->y, &q->x);
87 fe25519_mul(&a, &a, &t1);
88 fe25519_mul(&b, &b, &t2);
89 fe25519_sub(&e, &b, &a); /* E = B-A */
90 fe25519_add(&h, &b, &a); /* H = B+A */
91 fe25519_mul(&c, &r->t, &qt); /* C = T1*k*T2 */
92 fe25519_mul(&c, &c, &ge25519_ec2d);
93 fe25519_add(&d, &r->z, &r->z); /* D = Z1*2 */
94 fe25519_sub(&f, &d, &c); /* F = D-C */
95 fe25519_add(&g, &d, &c); /* G = D+C */
96 fe25519_mul(&r->x, &e, &f);
97 fe25519_mul(&r->y, &h, &g);
98 fe25519_mul(&r->z, &g, &f);
99 fe25519_mul(&r->t, &e, &h);
100 }
101
102 static void add_p1p1(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_p3 *q)
103 {
104 fe25519 a, b, c, d, t;
105
106 fe25519_sub(&a, &p->y, &p->x); /* A = (Y1-X1)*(Y2-X2) */
107 fe25519_sub(&t, &q->y, &q->x);
108 fe25519_mul(&a, &a, &t);
109 fe25519_add(&b, &p->x, &p->y); /* B = (Y1+X1)*(Y2+X2) */
110 fe25519_add(&t, &q->x, &q->y);
111 fe25519_mul(&b, &b, &t);
112 fe25519_mul(&c, &p->t, &q->t); /* C = T1*k*T2 */
113 fe25519_mul(&c, &c, &ge25519_ec2d);
114 fe25519_mul(&d, &p->z, &q->z); /* D = Z1*2*Z2 */
115 fe25519_add(&d, &d, &d);
116 fe25519_sub(&r->x, &b, &a); /* E = B-A */
117 fe25519_sub(&r->t, &d, &c); /* F = D-C */
118 fe25519_add(&r->z, &d, &c); /* G = D+C */
119 fe25519_add(&r->y, &b, &a); /* H = B+A */
120 }
121
122 /* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */
123 static void dbl_p1p1(ge25519_p1p1 *r, const ge25519_p2 *p)
124 {
125 fe25519 a,b,c,d;
126 fe25519_square(&a, &p->x);
127 fe25519_square(&b, &p->y);
128 fe25519_square(&c, &p->z);
129 fe25519_add(&c, &c, &c);
130 fe25519_neg(&d, &a);
131
132 fe25519_add(&r->x, &p->x, &p->y);
133 fe25519_square(&r->x, &r->x);
134 fe25519_sub(&r->x, &r->x, &a);
135 fe25519_sub(&r->x, &r->x, &b);
136 fe25519_add(&r->z, &d, &b);
137 fe25519_sub(&r->t, &r->z, &c);
138 fe25519_sub(&r->y, &d, &b);
139 }
140
141 /* Constant-time version of: if(b) r = p */
142 static void cmov_aff(ge25519_aff *r, const ge25519_aff *p, unsigned char b)
143 {
144 fe25519_cmov(&r->x, &p->x, b);
145 fe25519_cmov(&r->y, &p->y, b);
146 }
147
148 static unsigned char equal(signed char b,signed char c)
149 {
150 unsigned char ub = b;
151 unsigned char uc = c;
152 unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
153 crypto_uint32 y = x; /* 0: yes; 1..255: no */
154 y -= 1; /* 4294967295: yes; 0..254: no */
155 y >>= 31; /* 1: yes; 0: no */
156 return y;
157 }
158
159 static unsigned char negative(signed char b)
160 {
161 unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
162 x >>= 63; /* 1: yes; 0: no */
163 return x;
164 }
165
166 static void choose_t(ge25519_aff *t, unsigned long long pos, signed char b)
167 {
168 /* constant time */
169 fe25519 v;
170 *t = ge25519_base_multiples_affine[5*pos+0];
171 cmov_aff(t, &ge25519_base_multiples_affine[5*pos+1],equal(b,1) | equal(b,-1));
172 cmov_aff(t, &ge25519_base_multiples_affine[5*pos+2],equal(b,2) | equal(b,-2));
173 cmov_aff(t, &ge25519_base_multiples_affine[5*pos+3],equal(b,3) | equal(b,-3));
174 cmov_aff(t, &ge25519_base_multiples_affine[5*pos+4],equal(b,-4));
175 fe25519_neg(&v, &t->x);
176 fe25519_cmov(&t->x, &v, negative(b));
177 }
178
179 static void setneutral(ge25519 *r)
180 {
181 fe25519_setzero(&r->x);
182 fe25519_setone(&r->y);
183 fe25519_setone(&r->z);
184 fe25519_setzero(&r->t);
185 }
186
187 /* ********************************************************************
188 * EXPORTED FUNCTIONS
189 ******************************************************************** */
190
191 /* return 0 on success, -1 otherwise */
192 int ge25519_unpackneg_vartime(ge25519_p3 *r, const unsigned char p[32])
193 {
194 unsigned char par;
195 fe25519 t, chk, num, den, den2, den4, den6;
196 fe25519_setone(&r->z);
197 par = p[31] >> 7;
198 fe25519_unpack(&r->y, p);
199 fe25519_square(&num, &r->y); /* x = y^2 */
200 fe25519_mul(&den, &num, &ge25519_ecd); /* den = dy^2 */
201 fe25519_sub(&num, &num, &r->z); /* x = y^2-1 */
202 fe25519_add(&den, &r->z, &den); /* den = dy^2+1 */
203
204 /* Computation of sqrt(num/den) */
205 /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
206 fe25519_square(&den2, &den);
207 fe25519_square(&den4, &den2);
208 fe25519_mul(&den6, &den4, &den2);
209 fe25519_mul(&t, &den6, &num);
210 fe25519_mul(&t, &t, &den);
211
212 fe25519_pow2523(&t, &t);
213 /* 2. computation of r->x = t * num * den^3 */
214 fe25519_mul(&t, &t, &num);
215 fe25519_mul(&t, &t, &den);
216 fe25519_mul(&t, &t, &den);
217 fe25519_mul(&r->x, &t, &den);
218
219 /* 3. Check whether sqrt computation gave correct result, multiply by sqrt(-1) if not: */
220 fe25519_square(&chk, &r->x);
221 fe25519_mul(&chk, &chk, &den);
222 if (!fe25519_iseq_vartime(&chk, &num))
223 fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1);
224
225 /* 4. Now we have one of the two square roots, except if input was not a square */
226 fe25519_square(&chk, &r->x);
227 fe25519_mul(&chk, &chk, &den);
228 if (!fe25519_iseq_vartime(&chk, &num))
229 return -1;
230
231 /* 5. Choose the desired square root according to parity: */
232 if(fe25519_getparity(&r->x) != (1-par))
233 fe25519_neg(&r->x, &r->x);
234
235 fe25519_mul(&r->t, &r->x, &r->y);
236 return 0;
237 }
238
239 void ge25519_pack(unsigned char r[32], const ge25519_p3 *p)
240 {
241 fe25519 tx, ty, zi;
242 fe25519_invert(&zi, &p->z);
243 fe25519_mul(&tx, &p->x, &zi);
244 fe25519_mul(&ty, &p->y, &zi);
245 fe25519_pack(r, &ty);
246 r[31] ^= fe25519_getparity(&tx) << 7;
247 }
248
249 int ge25519_isneutral_vartime(const ge25519_p3 *p)
250 {
251 int ret = 1;
252 if(!fe25519_iszero(&p->x)) ret = 0;
253 if(!fe25519_iseq_vartime(&p->y, &p->z)) ret = 0;
254 return ret;
255 }
256
257 /* computes [s1]p1 + [s2]p2 */
258 void ge25519_double_scalarmult_vartime(ge25519_p3 *r, const ge25519_p3 *p1, const sc25519 *s1, const ge25519_p3 *p2, const sc25519 *s2)
259 {
260 ge25519_p1p1 tp1p1;
261 ge25519_p3 pre[16];
262 unsigned char b[127];
263 int i;
264
265 /* precomputation s2 s1 */
266 setneutral(pre); /* 00 00 */
267 pre[1] = *p1; /* 00 01 */
268 dbl_p1p1(&tp1p1,(ge25519_p2 *)p1); p1p1_to_p3( &pre[2], &tp1p1); /* 00 10 */
269 add_p1p1(&tp1p1,&pre[1], &pre[2]); p1p1_to_p3( &pre[3], &tp1p1); /* 00 11 */
270 pre[4] = *p2; /* 01 00 */
271 add_p1p1(&tp1p1,&pre[1], &pre[4]); p1p1_to_p3( &pre[5], &tp1p1); /* 01 01 */
272 add_p1p1(&tp1p1,&pre[2], &pre[4]); p1p1_to_p3( &pre[6], &tp1p1); /* 01 10 */
273 add_p1p1(&tp1p1,&pre[3], &pre[4]); p1p1_to_p3( &pre[7], &tp1p1); /* 01 11 */
274 dbl_p1p1(&tp1p1,(ge25519_p2 *)p2); p1p1_to_p3( &pre[8], &tp1p1); /* 10 00 */
275 add_p1p1(&tp1p1,&pre[1], &pre[8]); p1p1_to_p3( &pre[9], &tp1p1); /* 10 01 */
276 dbl_p1p1(&tp1p1,(ge25519_p2 *)&pre[5]); p1p1_to_p3(&pre[10], &tp1p1); /* 10 10 */
277 add_p1p1(&tp1p1,&pre[3], &pre[8]); p1p1_to_p3(&pre[11], &tp1p1); /* 10 11 */
278 add_p1p1(&tp1p1,&pre[4], &pre[8]); p1p1_to_p3(&pre[12], &tp1p1); /* 11 00 */
279 add_p1p1(&tp1p1,&pre[1],&pre[12]); p1p1_to_p3(&pre[13], &tp1p1); /* 11 01 */
280 add_p1p1(&tp1p1,&pre[2],&pre[12]); p1p1_to_p3(&pre[14], &tp1p1); /* 11 10 */
281 add_p1p1(&tp1p1,&pre[3],&pre[12]); p1p1_to_p3(&pre[15], &tp1p1); /* 11 11 */
282
283 sc25519_2interleave2(b,s1,s2);
284
285 /* scalar multiplication */
286 *r = pre[b[126]];
287 for(i=125;i>=0;i--)
288 {
289 dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
290 p1p1_to_p2((ge25519_p2 *) r, &tp1p1);
291 dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
292 if(b[i]!=0)
293 {
294 p1p1_to_p3(r, &tp1p1);
295 add_p1p1(&tp1p1, r, &pre[b[i]]);
296 }
297 if(i != 0) p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
298 else p1p1_to_p3(r, &tp1p1);
299 }
300 }
301
302 void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s)
303 {
304 signed char b[85];
305 int i;
306 ge25519_aff t;
307 sc25519_window3(b,s);
308
309 choose_t((ge25519_aff *)r, 0, b[0]);
310 fe25519_setone(&r->z);
311 fe25519_mul(&r->t, &r->x, &r->y);
312 for(i=1;i<85;i++)
313 {
314 choose_t(&t, (unsigned long long) i, b[i]);
315 ge25519_mixadd2(r, &t);
316 }
317 }