1 /* $OpenBSD: smult_curve25519_ref.c,v 1.2 2013/11/02 22:02:14 markus Exp $ */
6 Derived from public domain code by D. J. Bernstein.
9 int crypto_scalarmult_curve25519(unsigned char *, const unsigned char *, const unsigned char *);
11 static void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
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;
20 static void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
25 for (j = 0;j < 31;++j) {
26 u += a[j] + 65280 - b[j];
34 static void squeeze(unsigned int a[32])
39 for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
40 u += a[31]; a[31] = u & 127;
42 for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
43 u += a[31]; a[31] = u;
46 static 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
50 static void freeze(unsigned int a[32])
52 unsigned int aorig[32];
54 unsigned int negative;
56 for (j = 0;j < 32;++j) aorig[j] = a[j];
58 negative = -((a[31] >> 7) & 1);
59 for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]);
62 static void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
68 for (i = 0;i < 32;++i) {
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];
77 static void mult121665(unsigned int out[32],const unsigned int a[32])
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;
86 for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; }
87 u += out[j]; out[j] = u;
90 static void square(unsigned int out[32],const unsigned int a[32])
96 for (i = 0;i < 32;++i) {
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];
102 u += a[i / 2] * a[i / 2];
103 u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
110 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 unsigned int bminus1;
117 for (j = 0;j < 64;++j) {
118 t = bminus1 & (r[j] ^ s[j]);
124 static void mainloop(unsigned int work[64],const unsigned char e[32])
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];
145 for (j = 0;j < 32;++j) xzm1[j] = work[j];
147 for (j = 33;j < 64;++j) xzm1[j] = 0;
150 for (j = 1;j < 64;++j) xzm[j] = 0;
152 for (pos = 254;pos >= 0;--pos) {
153 b = e[pos / 8] >> (pos & 7);
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);
161 square(b0 + 32,a0 + 32);
163 mult(b1 + 32,a1 + 32,a0);
165 sub(c1 + 32,b1,b1 + 32);
170 mult(xznb,b0,b0 + 32);
173 mult(xzn1b + 32,r,work);
174 select(xzm,xzm1,xznb,xzn1b,b);
177 for (j = 0;j < 64;++j) work[j] = xzm[j];
180 static void recip(unsigned int out[32],const unsigned int z[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];
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);
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);
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);
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);
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);
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);
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);
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);
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);
247 int crypto_scalarmult_curve25519(unsigned char *q,
248 const unsigned char *n,
249 const unsigned char *p)
251 unsigned int work[96];
254 for (i = 0;i < 32;++i) e[i] = n[i];
258 for (i = 0;i < 32;++i) work[i] = p[i];
260 recip(work + 32,work + 32);
261 mult(work + 64,work,work + 32);
263 for (i = 0;i < 32;++i) q[i] = work[64 + i];