1/* $OpenBSD: smult_curve25519_ref.c,v 1.2 2013/11/02 22:02:14 markus Exp $ */
2/*
3version 20081011
4Matthew Dempsky
5Public domain.
6Derived from public domain code by D. J. Bernstein.
7*/
8
9int crypto_scalarmult_curve25519(unsigned char *, const unsigned char *, const unsigned char *);
10
11static void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
12{
13  unsigned int j;
14  unsigned int u;
15  u = 0;
16  for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; }
17  u += a[31] + b[31]; out[31] = u;
18}
19
20static void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
21{
22  unsigned int j;
23  unsigned int u;
24  u = 218;
25  for (j = 0;j < 31;++j) {
26    u += a[j] + 65280 - b[j];
27    out[j] = u & 255;
28    u >>= 8;
29  }
30  u += a[31] - b[31];
31  out[31] = u;
32}
33
34static void squeeze(unsigned int a[32])
35{
36  unsigned int j;
37  unsigned int u;
38  u = 0;
39  for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
40  u += a[31]; a[31] = u & 127;
41  u = 19 * (u >> 7);
42  for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
43  u += a[31]; a[31] = u;
44}
45
46static const unsigned int minusp[32] = {
47 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128
48} ;
49
50static void freeze(unsigned int a[32])
51{
52  unsigned int aorig[32];
53  unsigned int j;
54  unsigned int negative;
55
56  for (j = 0;j < 32;++j) aorig[j] = a[j];
57  add(a,a,minusp);
58  negative = -((a[31] >> 7) & 1);
59  for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]);
60}
61
62static void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
63{
64  unsigned int i;
65  unsigned int j;
66  unsigned int u;
67
68  for (i = 0;i < 32;++i) {
69    u = 0;
70    for (j = 0;j <= i;++j) u += a[j] * b[i - j];
71    for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j];
72    out[i] = u;
73  }
74  squeeze(out);
75}
76
77static void mult121665(unsigned int out[32],const unsigned int a[32])
78{
79  unsigned int j;
80  unsigned int u;
81
82  u = 0;
83  for (j = 0;j < 31;++j) { u += 121665 * a[j]; out[j] = u & 255; u >>= 8; }
84  u += 121665 * a[31]; out[31] = u & 127;
85  u = 19 * (u >> 7);
86  for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; }
87  u += out[j]; out[j] = u;
88}
89
90static void square(unsigned int out[32],const unsigned int a[32])
91{
92  unsigned int i;
93  unsigned int j;
94  unsigned int u;
95
96  for (i = 0;i < 32;++i) {
97    u = 0;
98    for (j = 0;j < i - j;++j) u += a[j] * a[i - j];
99    for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j];
100    u *= 2;
101    if ((i & 1) == 0) {
102      u += a[i / 2] * a[i / 2];
103      u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
104    }
105    out[i] = u;
106  }
107  squeeze(out);
108}
109
110static void select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b)
111{
112  unsigned int j;
113  unsigned int t;
114  unsigned int bminus1;
115
116  bminus1 = b - 1;
117  for (j = 0;j < 64;++j) {
118    t = bminus1 & (r[j] ^ s[j]);
119    p[j] = s[j] ^ t;
120    q[j] = r[j] ^ t;
121  }
122}
123
124static void mainloop(unsigned int work[64],const unsigned char e[32])
125{
126  unsigned int xzm1[64];
127  unsigned int xzm[64];
128  unsigned int xzmb[64];
129  unsigned int xzm1b[64];
130  unsigned int xznb[64];
131  unsigned int xzn1b[64];
132  unsigned int a0[64];
133  unsigned int a1[64];
134  unsigned int b0[64];
135  unsigned int b1[64];
136  unsigned int c1[64];
137  unsigned int r[32];
138  unsigned int s[32];
139  unsigned int t[32];
140  unsigned int u[32];
141  unsigned int j;
142  unsigned int b;
143  int pos;
144
145  for (j = 0;j < 32;++j) xzm1[j] = work[j];
146  xzm1[32] = 1;
147  for (j = 33;j < 64;++j) xzm1[j] = 0;
148
149  xzm[0] = 1;
150  for (j = 1;j < 64;++j) xzm[j] = 0;
151
152  for (pos = 254;pos >= 0;--pos) {
153    b = e[pos / 8] >> (pos & 7);
154    b &= 1;
155    select(xzmb,xzm1b,xzm,xzm1,b);
156    add(a0,xzmb,xzmb + 32);
157    sub(a0 + 32,xzmb,xzmb + 32);
158    add(a1,xzm1b,xzm1b + 32);
159    sub(a1 + 32,xzm1b,xzm1b + 32);
160    square(b0,a0);
161    square(b0 + 32,a0 + 32);
162    mult(b1,a1,a0 + 32);
163    mult(b1 + 32,a1 + 32,a0);
164    add(c1,b1,b1 + 32);
165    sub(c1 + 32,b1,b1 + 32);
166    square(r,c1 + 32);
167    sub(s,b0,b0 + 32);
168    mult121665(t,s);
169    add(u,t,b0);
170    mult(xznb,b0,b0 + 32);
171    mult(xznb + 32,s,u);
172    square(xzn1b,c1);
173    mult(xzn1b + 32,r,work);
174    select(xzm,xzm1,xznb,xzn1b,b);
175  }
176
177  for (j = 0;j < 64;++j) work[j] = xzm[j];
178}
179
180static void recip(unsigned int out[32],const unsigned int z[32])
181{
182  unsigned int z2[32];
183  unsigned int z9[32];
184  unsigned int z11[32];
185  unsigned int z2_5_0[32];
186  unsigned int z2_10_0[32];
187  unsigned int z2_20_0[32];
188  unsigned int z2_50_0[32];
189  unsigned int z2_100_0[32];
190  unsigned int t0[32];
191  unsigned int t1[32];
192  int i;
193
194  /* 2 */ square(z2,z);
195  /* 4 */ square(t1,z2);
196  /* 8 */ square(t0,t1);
197  /* 9 */ mult(z9,t0,z);
198  /* 11 */ mult(z11,z9,z2);
199  /* 22 */ square(t0,z11);
200  /* 2^5 - 2^0 = 31 */ mult(z2_5_0,t0,z9);
201
202  /* 2^6 - 2^1 */ square(t0,z2_5_0);
203  /* 2^7 - 2^2 */ square(t1,t0);
204  /* 2^8 - 2^3 */ square(t0,t1);
205  /* 2^9 - 2^4 */ square(t1,t0);
206  /* 2^10 - 2^5 */ square(t0,t1);
207  /* 2^10 - 2^0 */ mult(z2_10_0,t0,z2_5_0);
208
209  /* 2^11 - 2^1 */ square(t0,z2_10_0);
210  /* 2^12 - 2^2 */ square(t1,t0);
211  /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t0,t1); square(t1,t0); }
212  /* 2^20 - 2^0 */ mult(z2_20_0,t1,z2_10_0);
213
214  /* 2^21 - 2^1 */ square(t0,z2_20_0);
215  /* 2^22 - 2^2 */ square(t1,t0);
216  /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { square(t0,t1); square(t1,t0); }
217  /* 2^40 - 2^0 */ mult(t0,t1,z2_20_0);
218
219  /* 2^41 - 2^1 */ square(t1,t0);
220  /* 2^42 - 2^2 */ square(t0,t1);
221  /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t1,t0); square(t0,t1); }
222  /* 2^50 - 2^0 */ mult(z2_50_0,t0,z2_10_0);
223
224  /* 2^51 - 2^1 */ square(t0,z2_50_0);
225  /* 2^52 - 2^2 */ square(t1,t0);
226  /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
227  /* 2^100 - 2^0 */ mult(z2_100_0,t1,z2_50_0);
228
229  /* 2^101 - 2^1 */ square(t1,z2_100_0);
230  /* 2^102 - 2^2 */ square(t0,t1);
231  /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { square(t1,t0); square(t0,t1); }
232  /* 2^200 - 2^0 */ mult(t1,t0,z2_100_0);
233
234  /* 2^201 - 2^1 */ square(t0,t1);
235  /* 2^202 - 2^2 */ square(t1,t0);
236  /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
237  /* 2^250 - 2^0 */ mult(t0,t1,z2_50_0);
238
239  /* 2^251 - 2^1 */ square(t1,t0);
240  /* 2^252 - 2^2 */ square(t0,t1);
241  /* 2^253 - 2^3 */ square(t1,t0);
242  /* 2^254 - 2^4 */ square(t0,t1);
243  /* 2^255 - 2^5 */ square(t1,t0);
244  /* 2^255 - 21 */ mult(out,t1,z11);
245}
246
247int crypto_scalarmult_curve25519(unsigned char *q,
248  const unsigned char *n,
249  const unsigned char *p)
250{
251  unsigned int work[96];
252  unsigned char e[32];
253  unsigned int i;
254  for (i = 0;i < 32;++i) e[i] = n[i];
255  e[0] &= 248;
256  e[31] &= 127;
257  e[31] |= 64;
258  for (i = 0;i < 32;++i) work[i] = p[i];
259  mainloop(work,e);
260  recip(work + 32,work + 32);
261  mult(work + 64,work,work + 32);
262  freeze(work + 64);
263  for (i = 0;i < 32;++i) q[i] = work[64 + i];
264  return 0;
265}
266