1/* $OpenBSD: sc25519.c,v 1.1 2014/07/22 00:41:19 deraadt Exp $ */
2
3/*
4 * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
5 * Peter Schwabe, Bo-Yin Yang.
6 * Copied from supercop-20130419/crypto_sign/ed25519/ref/sc25519.c
7 */
8
9#include "sc25519.h"
10
11/*Arithmetic modulo the group order m = 2^252 +  27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989 */
12
13static const crypto_uint32 m[32] = {0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, 0xDE, 0xF9, 0xDE, 0x14,
14                                    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10};
15
16static const crypto_uint32 mu[33] = {0x1B, 0x13, 0x2C, 0x0A, 0xA3, 0xE5, 0x9C, 0xED, 0xA7, 0x29, 0x63, 0x08, 0x5D, 0x21, 0x06, 0x21,
17                                     0xEB, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0F};
18
19static crypto_uint32 lt(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
20{
21  unsigned int x = a;
22  x -= (unsigned int) b; /* 0..65535: no; 4294901761..4294967295: yes */
23  x >>= 31; /* 0: no; 1: yes */
24  return x;
25}
26
27/* Reduce coefficients of r before calling reduce_add_sub */
28static void reduce_add_sub(sc25519 *r)
29{
30  crypto_uint32 pb = 0;
31  crypto_uint32 b;
32  crypto_uint32 mask;
33  int i;
34  unsigned char t[32];
35
36  for(i=0;i<32;i++)
37  {
38    pb += m[i];
39    b = lt(r->v[i],pb);
40    t[i] = r->v[i]-pb+(b<<8);
41    pb = b;
42  }
43  mask = b - 1;
44  for(i=0;i<32;i++)
45    r->v[i] ^= mask & (r->v[i] ^ t[i]);
46}
47
48/* Reduce coefficients of x before calling barrett_reduce */
49static void barrett_reduce(sc25519 *r, const crypto_uint32 x[64])
50{
51  /* See HAC, Alg. 14.42 */
52  int i,j;
53  crypto_uint32 q2[66];
54  crypto_uint32 *q3 = q2 + 33;
55  crypto_uint32 r1[33];
56  crypto_uint32 r2[33];
57  crypto_uint32 carry;
58  crypto_uint32 pb = 0;
59  crypto_uint32 b;
60
61  for (i = 0;i < 66;++i) q2[i] = 0;
62  for (i = 0;i < 33;++i) r2[i] = 0;
63
64  for(i=0;i<33;i++)
65    for(j=0;j<33;j++)
66      if(i+j >= 31) q2[i+j] += mu[i]*x[j+31];
67  carry = q2[31] >> 8;
68  q2[32] += carry;
69  carry = q2[32] >> 8;
70  q2[33] += carry;
71
72  for(i=0;i<33;i++)r1[i] = x[i];
73  for(i=0;i<32;i++)
74    for(j=0;j<33;j++)
75      if(i+j < 33) r2[i+j] += m[i]*q3[j];
76
77  for(i=0;i<32;i++)
78  {
79    carry = r2[i] >> 8;
80    r2[i+1] += carry;
81    r2[i] &= 0xff;
82  }
83
84  for(i=0;i<32;i++)
85  {
86    pb += r2[i];
87    b = lt(r1[i],pb);
88    r->v[i] = r1[i]-pb+(b<<8);
89    pb = b;
90  }
91
92  /* XXX: Can it really happen that r<0?, See HAC, Alg 14.42, Step 3
93   * If so: Handle  it here!
94   */
95
96  reduce_add_sub(r);
97  reduce_add_sub(r);
98}
99
100void sc25519_from32bytes(sc25519 *r, const unsigned char x[32])
101{
102  int i;
103  crypto_uint32 t[64];
104  for(i=0;i<32;i++) t[i] = x[i];
105  for(i=32;i<64;++i) t[i] = 0;
106  barrett_reduce(r, t);
107}
108
109void shortsc25519_from16bytes(shortsc25519 *r, const unsigned char x[16])
110{
111  int i;
112  for(i=0;i<16;i++) r->v[i] = x[i];
113}
114
115void sc25519_from64bytes(sc25519 *r, const unsigned char x[64])
116{
117  int i;
118  crypto_uint32 t[64];
119  for(i=0;i<64;i++) t[i] = x[i];
120  barrett_reduce(r, t);
121}
122
123void sc25519_from_shortsc(sc25519 *r, const shortsc25519 *x)
124{
125  int i;
126  for(i=0;i<16;i++)
127    r->v[i] = x->v[i];
128  for(i=0;i<16;i++)
129    r->v[16+i] = 0;
130}
131
132void sc25519_to32bytes(unsigned char r[32], const sc25519 *x)
133{
134  int i;
135  for(i=0;i<32;i++) r[i] = x->v[i];
136}
137
138int sc25519_iszero_vartime(const sc25519 *x)
139{
140  int i;
141  for(i=0;i<32;i++)
142    if(x->v[i] != 0) return 0;
143  return 1;
144}
145
146int sc25519_isshort_vartime(const sc25519 *x)
147{
148  int i;
149  for(i=31;i>15;i--)
150    if(x->v[i] != 0) return 0;
151  return 1;
152}
153
154int sc25519_lt_vartime(const sc25519 *x, const sc25519 *y)
155{
156  int i;
157  for(i=31;i>=0;i--)
158  {
159    if(x->v[i] < y->v[i]) return 1;
160    if(x->v[i] > y->v[i]) return 0;
161  }
162  return 0;
163}
164
165void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y)
166{
167  int i, carry;
168  for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i];
169  for(i=0;i<31;i++)
170  {
171    carry = r->v[i] >> 8;
172    r->v[i+1] += carry;
173    r->v[i] &= 0xff;
174  }
175  reduce_add_sub(r);
176}
177
178void sc25519_sub_nored(sc25519 *r, const sc25519 *x, const sc25519 *y)
179{
180  crypto_uint32 b = 0;
181  crypto_uint32 t;
182  int i;
183  for(i=0;i<32;i++)
184  {
185    t = x->v[i] - y->v[i] - b;
186    r->v[i] = t & 255;
187    b = (t >> 8) & 1;
188  }
189}
190
191void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y)
192{
193  int i,j,carry;
194  crypto_uint32 t[64];
195  for(i=0;i<64;i++)t[i] = 0;
196
197  for(i=0;i<32;i++)
198    for(j=0;j<32;j++)
199      t[i+j] += x->v[i] * y->v[j];
200
201  /* Reduce coefficients */
202  for(i=0;i<63;i++)
203  {
204    carry = t[i] >> 8;
205    t[i+1] += carry;
206    t[i] &= 0xff;
207  }
208
209  barrett_reduce(r, t);
210}
211
212void sc25519_mul_shortsc(sc25519 *r, const sc25519 *x, const shortsc25519 *y)
213{
214  sc25519 t;
215  sc25519_from_shortsc(&t, y);
216  sc25519_mul(r, x, &t);
217}
218
219void sc25519_window3(signed char r[85], const sc25519 *s)
220{
221  char carry;
222  int i;
223  for(i=0;i<10;i++)
224  {
225    r[8*i+0]  =  s->v[3*i+0]       & 7;
226    r[8*i+1]  = (s->v[3*i+0] >> 3) & 7;
227    r[8*i+2]  = (s->v[3*i+0] >> 6) & 7;
228    r[8*i+2] ^= (s->v[3*i+1] << 2) & 7;
229    r[8*i+3]  = (s->v[3*i+1] >> 1) & 7;
230    r[8*i+4]  = (s->v[3*i+1] >> 4) & 7;
231    r[8*i+5]  = (s->v[3*i+1] >> 7) & 7;
232    r[8*i+5] ^= (s->v[3*i+2] << 1) & 7;
233    r[8*i+6]  = (s->v[3*i+2] >> 2) & 7;
234    r[8*i+7]  = (s->v[3*i+2] >> 5) & 7;
235  }
236  r[8*i+0]  =  s->v[3*i+0]       & 7;
237  r[8*i+1]  = (s->v[3*i+0] >> 3) & 7;
238  r[8*i+2]  = (s->v[3*i+0] >> 6) & 7;
239  r[8*i+2] ^= (s->v[3*i+1] << 2) & 7;
240  r[8*i+3]  = (s->v[3*i+1] >> 1) & 7;
241  r[8*i+4]  = (s->v[3*i+1] >> 4) & 7;
242
243  /* Making it signed */
244  carry = 0;
245  for(i=0;i<84;i++)
246  {
247    r[i] += carry;
248    r[i+1] += r[i] >> 3;
249    r[i] &= 7;
250    carry = r[i] >> 2;
251    r[i] -= carry<<3;
252  }
253  r[84] += carry;
254}
255
256void sc25519_window5(signed char r[51], const sc25519 *s)
257{
258  char carry;
259  int i;
260  for(i=0;i<6;i++)
261  {
262    r[8*i+0]  =  s->v[5*i+0]       & 31;
263    r[8*i+1]  = (s->v[5*i+0] >> 5) & 31;
264    r[8*i+1] ^= (s->v[5*i+1] << 3) & 31;
265    r[8*i+2]  = (s->v[5*i+1] >> 2) & 31;
266    r[8*i+3]  = (s->v[5*i+1] >> 7) & 31;
267    r[8*i+3] ^= (s->v[5*i+2] << 1) & 31;
268    r[8*i+4]  = (s->v[5*i+2] >> 4) & 31;
269    r[8*i+4] ^= (s->v[5*i+3] << 4) & 31;
270    r[8*i+5]  = (s->v[5*i+3] >> 1) & 31;
271    r[8*i+6]  = (s->v[5*i+3] >> 6) & 31;
272    r[8*i+6] ^= (s->v[5*i+4] << 2) & 31;
273    r[8*i+7]  = (s->v[5*i+4] >> 3) & 31;
274  }
275  r[8*i+0]  =  s->v[5*i+0]       & 31;
276  r[8*i+1]  = (s->v[5*i+0] >> 5) & 31;
277  r[8*i+1] ^= (s->v[5*i+1] << 3) & 31;
278  r[8*i+2]  = (s->v[5*i+1] >> 2) & 31;
279
280  /* Making it signed */
281  carry = 0;
282  for(i=0;i<50;i++)
283  {
284    r[i] += carry;
285    r[i+1] += r[i] >> 5;
286    r[i] &= 31;
287    carry = r[i] >> 4;
288    r[i] -= carry<<5;
289  }
290  r[50] += carry;
291}
292
293void sc25519_2interleave2(unsigned char r[127], const sc25519 *s1, const sc25519 *s2)
294{
295  int i;
296  for(i=0;i<31;i++)
297  {
298    r[4*i]   = ( s1->v[i]       & 3) ^ (( s2->v[i]       & 3) << 2);
299    r[4*i+1] = ((s1->v[i] >> 2) & 3) ^ (((s2->v[i] >> 2) & 3) << 2);
300    r[4*i+2] = ((s1->v[i] >> 4) & 3) ^ (((s2->v[i] >> 4) & 3) << 2);
301    r[4*i+3] = ((s1->v[i] >> 6) & 3) ^ (((s2->v[i] >> 6) & 3) << 2);
302  }
303  r[124] = ( s1->v[31]       & 3) ^ (( s2->v[31]       & 3) << 2);
304  r[125] = ((s1->v[31] >> 2) & 3) ^ (((s2->v[31] >> 2) & 3) << 2);
305  r[126] = ((s1->v[31] >> 4) & 3) ^ (((s2->v[31] >> 4) & 3) << 2);
306}
307