1 /* $OpenBSD: smult_curve25519_ref.c,v 1.2 2013/11/02 22:02:14 markus Exp $ */
2 /*
3 version 20081011
4 Matthew Dempsky
5 Public domain.
6 Derived 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
12 int crypto_scalarmult_curve25519(unsigned char *, const unsigned char *, const unsigned char *);
13
add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])14 static 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
sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])23 static 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
squeeze(unsigned int a[32])37 static 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
49 static 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
freeze(unsigned int a[32])53 static 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
mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])65 static 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
mult121665(unsigned int out[32],const unsigned int a[32])80 static 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
square(unsigned int out[32],const unsigned int a[32])93 static 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
select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b)113 static 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
mainloop(unsigned int work[64],const unsigned char e[32])127 static 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
recip(unsigned int out[32],const unsigned int z[32])183 static 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
crypto_scalarmult_curve25519(unsigned char * q,const unsigned char * n,const unsigned char * p)250 int 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