Annotation of src/usr.bin/ssh/smult_curve25519_ref.c, Revision 1.2
1.2 ! markus 1: /* $OpenBSD: myproposal.h,v 1.33 2013/11/02 21:59:15 markus Exp $ */
1.1 markus 2: /*
3: version 20081011
4: Matthew Dempsky
5: Public domain.
6: Derived from public domain code by D. J. Bernstein.
7: */
8:
9: int crypto_scalarmult_curve25519(unsigned char *, const unsigned char *, const unsigned char *);
10:
11: static 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:
20: static 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:
34: static 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:
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
48: } ;
49:
50: static 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:
62: static 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:
77: static 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:
90: static 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:
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)
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:
124: static 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:
180: static 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:
247: int 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: }
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