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
9#include "includes.h"
10__RCSID("$NetBSD: smult_curve25519_ref.c,v 1.5 2017/04/18 18:41:46 christos Exp $");
11
12int crypto_scalarmult_curve25519(unsigned char *, const unsigned char *, const unsigned char *);
13
14static void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
15{
16  unsigned int j;
17  unsigned int u;
18  u = 0;
19  for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; }
20  u += a[31] + b[31]; out[31] = u;
21}
22
23static void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
24{
25  unsigned int j;
26  unsigned int u;
27  u = 218;
28  for (j = 0;j < 31;++j) {
29    u += a[j] + 65280 - b[j];
30    out[j] = u & 255;
31    u >>= 8;
32  }
33  u += a[31] - b[31];
34  out[31] = u;
35}
36
37static void squeeze(unsigned int a[32])
38{
39  unsigned int j;
40  unsigned int u;
41  u = 0;
42  for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
43  u += a[31]; a[31] = u & 127;
44  u = 19 * (u >> 7);
45  for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
46  u += a[31]; a[31] = u;
47}
48
49static const unsigned int minusp[32] = {
50 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
51} ;
52
53static void freeze(unsigned int a[32])
54{
55  unsigned int aorig[32];
56  unsigned int j;
57  unsigned int negative;
58
59  for (j = 0;j < 32;++j) aorig[j] = a[j];
60  add(a,a,minusp);
61  negative = -((a[31] >> 7) & 1);
62  for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]);
63}
64
65static void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
66{
67  unsigned int i;
68  unsigned int j;
69  unsigned int u;
70
71  for (i = 0;i < 32;++i) {
72    u = 0;
73    for (j = 0;j <= i;++j) u += a[j] * b[i - j];
74    for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j];
75    out[i] = u;
76  }
77  squeeze(out);
78}
79
80static void mult121665(unsigned int out[32],const unsigned int a[32])
81{
82  unsigned int j;
83  unsigned int u;
84
85  u = 0;
86  for (j = 0;j < 31;++j) { u += 121665 * a[j]; out[j] = u & 255; u >>= 8; }
87  u += 121665 * a[31]; out[31] = u & 127;
88  u = 19 * (u >> 7);
89  for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; }
90  u += out[j]; out[j] = u;
91}
92
93static void square(unsigned int out[32],const unsigned int a[32])
94{
95  unsigned int i;
96  unsigned int j;
97  unsigned int u;
98
99  for (i = 0;i < 32;++i) {
100    u = 0;
101    for (j = 0;j < i - j;++j) u += a[j] * a[i - j];
102    for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j];
103    u *= 2;
104    if ((i & 1) == 0) {
105      u += a[i / 2] * a[i / 2];
106      u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
107    }
108    out[i] = u;
109  }
110  squeeze(out);
111}
112
113static void select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b)
114{
115  unsigned int j;
116  unsigned int t;
117  unsigned int bminus1;
118
119  bminus1 = b - 1;
120  for (j = 0;j < 64;++j) {
121    t = bminus1 & (r[j] ^ s[j]);
122    p[j] = s[j] ^ t;
123    q[j] = r[j] ^ t;
124  }
125}
126
127static void mainloop(unsigned int work[64],const unsigned char e[32])
128{
129  unsigned int xzm1[64];
130  unsigned int xzm[64];
131  unsigned int xzmb[64];
132  unsigned int xzm1b[64];
133  unsigned int xznb[64];
134  unsigned int xzn1b[64];
135  unsigned int a0[64];
136  unsigned int a1[64];
137  unsigned int b0[64];
138  unsigned int b1[64];
139  unsigned int c1[64];
140  unsigned int r[32];
141  unsigned int s[32];
142  unsigned int t[32];
143  unsigned int u[32];
144  unsigned int j;
145  unsigned int b;
146  int pos;
147
148  for (j = 0;j < 32;++j) xzm1[j] = work[j];
149  xzm1[32] = 1;
150  for (j = 33;j < 64;++j) xzm1[j] = 0;
151
152  xzm[0] = 1;
153  for (j = 1;j < 64;++j) xzm[j] = 0;
154
155  for (pos = 254;pos >= 0;--pos) {
156    b = e[pos / 8] >> (pos & 7);
157    b &= 1;
158    select(xzmb,xzm1b,xzm,xzm1,b);
159    add(a0,xzmb,xzmb + 32);
160    sub(a0 + 32,xzmb,xzmb + 32);
161    add(a1,xzm1b,xzm1b + 32);
162    sub(a1 + 32,xzm1b,xzm1b + 32);
163    square(b0,a0);
164    square(b0 + 32,a0 + 32);
165    mult(b1,a1,a0 + 32);
166    mult(b1 + 32,a1 + 32,a0);
167    add(c1,b1,b1 + 32);
168    sub(c1 + 32,b1,b1 + 32);
169    square(r,c1 + 32);
170    sub(s,b0,b0 + 32);
171    mult121665(t,s);
172    add(u,t,b0);
173    mult(xznb,b0,b0 + 32);
174    mult(xznb + 32,s,u);
175    square(xzn1b,c1);
176    mult(xzn1b + 32,r,work);
177    select(xzm,xzm1,xznb,xzn1b,b);
178  }
179
180  for (j = 0;j < 64;++j) work[j] = xzm[j];
181}
182
183static void recip(unsigned int out[32],const unsigned int z[32])
184{
185  unsigned int z2[32];
186  unsigned int z9[32];
187  unsigned int z11[32];
188  unsigned int z2_5_0[32];
189  unsigned int z2_10_0[32];
190  unsigned int z2_20_0[32];
191  unsigned int z2_50_0[32];
192  unsigned int z2_100_0[32];
193  unsigned int t0[32];
194  unsigned int t1[32];
195  int i;
196
197  /* 2 */ square(z2,z);
198  /* 4 */ square(t1,z2);
199  /* 8 */ square(t0,t1);
200  /* 9 */ mult(z9,t0,z);
201  /* 11 */ mult(z11,z9,z2);
202  /* 22 */ square(t0,z11);
203  /* 2^5 - 2^0 = 31 */ mult(z2_5_0,t0,z9);
204
205  /* 2^6 - 2^1 */ square(t0,z2_5_0);
206  /* 2^7 - 2^2 */ square(t1,t0);
207  /* 2^8 - 2^3 */ square(t0,t1);
208  /* 2^9 - 2^4 */ square(t1,t0);
209  /* 2^10 - 2^5 */ square(t0,t1);
210  /* 2^10 - 2^0 */ mult(z2_10_0,t0,z2_5_0);
211
212  /* 2^11 - 2^1 */ square(t0,z2_10_0);
213  /* 2^12 - 2^2 */ square(t1,t0);
214  /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t0,t1); square(t1,t0); }
215  /* 2^20 - 2^0 */ mult(z2_20_0,t1,z2_10_0);
216
217  /* 2^21 - 2^1 */ square(t0,z2_20_0);
218  /* 2^22 - 2^2 */ square(t1,t0);
219  /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { square(t0,t1); square(t1,t0); }
220  /* 2^40 - 2^0 */ mult(t0,t1,z2_20_0);
221
222  /* 2^41 - 2^1 */ square(t1,t0);
223  /* 2^42 - 2^2 */ square(t0,t1);
224  /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t1,t0); square(t0,t1); }
225  /* 2^50 - 2^0 */ mult(z2_50_0,t0,z2_10_0);
226
227  /* 2^51 - 2^1 */ square(t0,z2_50_0);
228  /* 2^52 - 2^2 */ square(t1,t0);
229  /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
230  /* 2^100 - 2^0 */ mult(z2_100_0,t1,z2_50_0);
231
232  /* 2^101 - 2^1 */ square(t1,z2_100_0);
233  /* 2^102 - 2^2 */ square(t0,t1);
234  /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { square(t1,t0); square(t0,t1); }
235  /* 2^200 - 2^0 */ mult(t1,t0,z2_100_0);
236
237  /* 2^201 - 2^1 */ square(t0,t1);
238  /* 2^202 - 2^2 */ square(t1,t0);
239  /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
240  /* 2^250 - 2^0 */ mult(t0,t1,z2_50_0);
241
242  /* 2^251 - 2^1 */ square(t1,t0);
243  /* 2^252 - 2^2 */ square(t0,t1);
244  /* 2^253 - 2^3 */ square(t1,t0);
245  /* 2^254 - 2^4 */ square(t0,t1);
246  /* 2^255 - 2^5 */ square(t1,t0);
247  /* 2^255 - 21 */ mult(out,t1,z11);
248}
249
250int crypto_scalarmult_curve25519(unsigned char *q,
251  const unsigned char *n,
252  const unsigned char *p)
253{
254  unsigned int work[96];
255  unsigned char e[32];
256  unsigned int i;
257  for (i = 0;i < 32;++i) e[i] = n[i];
258  e[0] &= 248;
259  e[31] &= 127;
260  e[31] |= 64;
261  for (i = 0;i < 32;++i) work[i] = p[i];
262  mainloop(work,e);
263  recip(work + 32,work + 32);
264  mult(work + 64,work,work + 32);
265  freeze(work + 64);
266  for (i = 0;i < 32;++i) q[i] = work[64 + i];
267  return 0;
268}
269