Coverage Report

Created: 2021-02-21 07:20

/src/botan/src/lib/pubkey/curve25519/donna.cpp
Line
Count
Source
1
/*
2
* Based on curve25519-donna-c64.c from github.com/agl/curve25519-donna
3
* revision 80ad9b9930c9baef5829dd2a235b6b7646d32a8e
4
*
5
* Further changes
6
* (C) 2014,2018 Jack Lloyd
7
*
8
* Botan is released under the Simplified BSD License (see license.txt)
9
*/
10
11
/* Copyright 2008, Google Inc.
12
* All rights reserved.
13
*
14
* Code released into the public domain.
15
*
16
* curve25519-donna: Curve25519 elliptic curve, public key function
17
*
18
* https://code.google.com/p/curve25519-donna/
19
*
20
* Adam Langley <agl@imperialviolet.org>
21
*
22
* Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
23
*
24
* More information about curve25519 can be found here
25
*   https://cr.yp.to/ecdh.html
26
*
27
* djb's sample implementation of curve25519 is written in a special assembly
28
* language called qhasm and uses the floating point registers.
29
*
30
* This is, almost, a clean room reimplementation from the curve25519 paper. It
31
* uses many of the tricks described therein. Only the crecip function is taken
32
* from the sample implementation.
33
*/
34
35
#include <botan/curve25519.h>
36
#include <botan/internal/mul128.h>
37
#include <botan/internal/ct_utils.h>
38
#include <botan/internal/donna128.h>
39
#include <botan/internal/loadstor.h>
40
41
namespace Botan {
42
43
namespace {
44
45
#if !defined(BOTAN_TARGET_HAS_NATIVE_UINT128)
46
typedef donna128 uint128_t;
47
#endif
48
49
/* Sum two numbers: output += in */
50
inline void fsum(uint64_t out[5], const uint64_t in[5])
51
612k
   {
52
612k
   out[0] += in[0];
53
612k
   out[1] += in[1];
54
612k
   out[2] += in[2];
55
612k
   out[3] += in[3];
56
612k
   out[4] += in[4];
57
612k
   }
58
59
/* Find the difference of two numbers: out = in - out
60
* (note the order of the arguments!)
61
*
62
* Assumes that out[i] < 2**52
63
* On return, out[i] < 2**55
64
*/
65
inline void fdifference_backwards(uint64_t out[5], const uint64_t in[5])
66
612k
   {
67
   /* 152 is 19 << 3 */
68
612k
   const uint64_t two54m152 = (static_cast<uint64_t>(1) << 54) - 152;
69
612k
   const uint64_t two54m8   = (static_cast<uint64_t>(1) << 54) - 8;
70
71
612k
   out[0] = in[0] + two54m152 - out[0];
72
612k
   out[1] = in[1] + two54m8 - out[1];
73
612k
   out[2] = in[2] + two54m8 - out[2];
74
612k
   out[3] = in[3] + two54m8 - out[3];
75
612k
   out[4] = in[4] + two54m8 - out[4];
76
612k
   }
77
78
inline void fadd_sub(uint64_t x[5],
79
                     uint64_t y[5])
80
459k
   {
81
   // TODO merge these and avoid the tmp array
82
459k
   uint64_t tmp[5];
83
459k
   copy_mem(tmp, y, 5);
84
459k
   fsum(y, x);
85
459k
   fdifference_backwards(x, tmp);  // does x - z
86
459k
   }
87
88
/* Multiply a number by a scalar: out = in * scalar */
89
inline void fscalar_product(uint64_t out[5], const uint64_t in[5], const uint64_t scalar)
90
153k
   {
91
153k
   uint128_t a = uint128_t(in[0]) * scalar;
92
153k
   out[0] = a & 0x7ffffffffffff;
93
94
153k
   a = uint128_t(in[1]) * scalar + carry_shift(a, 51);
95
153k
   out[1] = a & 0x7ffffffffffff;
96
97
153k
   a = uint128_t(in[2]) * scalar + carry_shift(a, 51);
98
153k
   out[2] = a & 0x7ffffffffffff;
99
100
153k
   a = uint128_t(in[3]) * scalar + carry_shift(a, 51);
101
153k
   out[3] = a & 0x7ffffffffffff;
102
103
153k
   a = uint128_t(in[4]) * scalar + carry_shift(a, 51);
104
153k
   out[4] = a & 0x7ffffffffffff;
105
106
153k
   out[0] += carry_shift(a, 51) * 19;
107
153k
   }
108
109
/* Multiply two numbers: out = in2 * in
110
*
111
* out must be distinct to both inputs. The inputs are reduced coefficient
112
* form, the output is not.
113
*
114
* Assumes that in[i] < 2**55 and likewise for in2.
115
* On return, out[i] < 2**52
116
*/
117
inline void fmul(uint64_t out[5], const uint64_t in[5], const uint64_t in2[5])
118
772k
   {
119
772k
   const uint128_t s0 = in2[0];
120
772k
   const uint128_t s1 = in2[1];
121
772k
   const uint128_t s2 = in2[2];
122
772k
   const uint128_t s3 = in2[3];
123
772k
   const uint128_t s4 = in2[4];
124
125
772k
   uint64_t r0 = in[0];
126
772k
   uint64_t r1 = in[1];
127
772k
   uint64_t r2 = in[2];
128
772k
   uint64_t r3 = in[3];
129
772k
   uint64_t r4 = in[4];
130
131
772k
   uint128_t t0 = r0 * s0;
132
772k
   uint128_t t1 = r0 * s1 + r1 * s0;
133
772k
   uint128_t t2 = r0 * s2 + r2 * s0 + r1 * s1;
134
772k
   uint128_t t3 = r0 * s3 + r3 * s0 + r1 * s2 + r2 * s1;
135
772k
   uint128_t t4 = r0 * s4 + r4 * s0 + r3 * s1 + r1 * s3 + r2 * s2;
136
137
772k
   r4 *= 19;
138
772k
   r1 *= 19;
139
772k
   r2 *= 19;
140
772k
   r3 *= 19;
141
142
772k
   t0 += r4 * s1 + r1 * s4 + r2 * s3 + r3 * s2;
143
772k
   t1 += r4 * s2 + r2 * s4 + r3 * s3;
144
772k
   t2 += r4 * s3 + r3 * s4;
145
772k
   t3 += r4 * s4;
146
147
772k
   r0 = t0 & 0x7ffffffffffff; t1 += carry_shift(t0, 51);
148
772k
   r1 = t1 & 0x7ffffffffffff; t2 += carry_shift(t1, 51);
149
772k
   r2 = t2 & 0x7ffffffffffff; t3 += carry_shift(t2, 51);
150
772k
   r3 = t3 & 0x7ffffffffffff; t4 += carry_shift(t3, 51);
151
772k
   r4 = t4 & 0x7ffffffffffff; uint64_t c = carry_shift(t4, 51);
152
153
772k
   r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
154
772k
   r1 += c;      c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
155
772k
   r2 += c;
156
157
772k
   out[0] = r0;
158
772k
   out[1] = r1;
159
772k
   out[2] = r2;
160
772k
   out[3] = r3;
161
772k
   out[4] = r4;
162
772k
   }
163
164
inline void fsquare(uint64_t out[5], const uint64_t in[5], size_t count = 1)
165
618k
   {
166
618k
   uint64_t r0 = in[0];
167
618k
   uint64_t r1 = in[1];
168
618k
   uint64_t r2 = in[2];
169
618k
   uint64_t r3 = in[3];
170
618k
   uint64_t r4 = in[4];
171
172
1.38M
   for(size_t i = 0; i != count; ++i)
173
764k
      {
174
764k
      const uint64_t d0 = r0 * 2;
175
764k
      const uint64_t d1 = r1 * 2;
176
764k
      const uint64_t d2 = r2 * 2 * 19;
177
764k
      const uint64_t d419 = r4 * 19;
178
764k
      const uint64_t d4 = d419 * 2;
179
180
764k
      uint128_t t0 = uint128_t(r0) * r0 + uint128_t(d4) * r1 + uint128_t(d2) * (r3     );
181
764k
      uint128_t t1 = uint128_t(d0) * r1 + uint128_t(d4) * r2 + uint128_t(r3) * (r3 * 19);
182
764k
      uint128_t t2 = uint128_t(d0) * r2 + uint128_t(r1) * r1 + uint128_t(d4) * (r3     );
183
764k
      uint128_t t3 = uint128_t(d0) * r3 + uint128_t(d1) * r2 + uint128_t(r4) * (d419   );
184
764k
      uint128_t t4 = uint128_t(d0) * r4 + uint128_t(d1) * r3 + uint128_t(r2) * (r2     );
185
186
764k
      r0 = t0 & 0x7ffffffffffff; t1 += carry_shift(t0, 51);
187
764k
      r1 = t1 & 0x7ffffffffffff; t2 += carry_shift(t1, 51);
188
764k
      r2 = t2 & 0x7ffffffffffff; t3 += carry_shift(t2, 51);
189
764k
      r3 = t3 & 0x7ffffffffffff; t4 += carry_shift(t3, 51);
190
764k
      r4 = t4 & 0x7ffffffffffff; uint64_t c = carry_shift(t4, 51);
191
192
764k
      r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
193
764k
      r1 += c;      c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
194
764k
      r2 += c;
195
764k
      }
196
197
618k
   out[0] = r0;
198
618k
   out[1] = r1;
199
618k
   out[2] = r2;
200
618k
   out[3] = r3;
201
618k
   out[4] = r4;
202
618k
   }
203
204
/* Take a little-endian, 32-byte number and expand it into polynomial form */
205
inline void fexpand(uint64_t *out, const uint8_t *in)
206
598
   {
207
598
   out[0] = load_le<uint64_t>(in, 0) & 0x7ffffffffffff;
208
598
   out[1] = (load_le<uint64_t>(in+6, 0) >> 3) & 0x7ffffffffffff;
209
598
   out[2] = (load_le<uint64_t>(in+12, 0) >> 6) & 0x7ffffffffffff;
210
598
   out[3] = (load_le<uint64_t>(in+19, 0) >> 1) & 0x7ffffffffffff;
211
598
   out[4] = (load_le<uint64_t>(in+24, 0) >> 12) & 0x7ffffffffffff;
212
598
   }
213
214
/* Take a fully reduced polynomial form number and contract it into a
215
* little-endian, 32-byte array
216
*/
217
inline void fcontract(uint8_t *out, const uint64_t input[5])
218
598
   {
219
598
   uint128_t t0 = input[0];
220
598
   uint128_t t1 = input[1];
221
598
   uint128_t t2 = input[2];
222
598
   uint128_t t3 = input[3];
223
598
   uint128_t t4 = input[4];
224
225
1.79k
   for(size_t i = 0; i != 2; ++i)
226
1.19k
      {
227
1.19k
      t1 += t0 >> 51;        t0 &= 0x7ffffffffffff;
228
1.19k
      t2 += t1 >> 51;        t1 &= 0x7ffffffffffff;
229
1.19k
      t3 += t2 >> 51;        t2 &= 0x7ffffffffffff;
230
1.19k
      t4 += t3 >> 51;        t3 &= 0x7ffffffffffff;
231
1.19k
      t0 += (t4 >> 51) * 19; t4 &= 0x7ffffffffffff;
232
1.19k
      }
233
234
   /* now t is between 0 and 2^255-1, properly carried. */
235
   /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
236
237
598
   t0 += 19;
238
239
598
   t1 += t0 >> 51; t0 &= 0x7ffffffffffff;
240
598
   t2 += t1 >> 51; t1 &= 0x7ffffffffffff;
241
598
   t3 += t2 >> 51; t2 &= 0x7ffffffffffff;
242
598
   t4 += t3 >> 51; t3 &= 0x7ffffffffffff;
243
598
   t0 += (t4 >> 51) * 19; t4 &= 0x7ffffffffffff;
244
245
   /* now between 19 and 2^255-1 in both cases, and offset by 19. */
246
247
598
   t0 += 0x8000000000000 - 19;
248
598
   t1 += 0x8000000000000 - 1;
249
598
   t2 += 0x8000000000000 - 1;
250
598
   t3 += 0x8000000000000 - 1;
251
598
   t4 += 0x8000000000000 - 1;
252
253
   /* now between 2^255 and 2^256-20, and offset by 2^255. */
254
255
598
   t1 += t0 >> 51; t0 &= 0x7ffffffffffff;
256
598
   t2 += t1 >> 51; t1 &= 0x7ffffffffffff;
257
598
   t3 += t2 >> 51; t2 &= 0x7ffffffffffff;
258
598
   t4 += t3 >> 51; t3 &= 0x7ffffffffffff;
259
598
   t4 &= 0x7ffffffffffff;
260
261
598
   store_le(out,
262
598
            combine_lower(t0,  0, t1, 51),
263
598
            combine_lower(t1, 13, t2, 38),
264
598
            combine_lower(t2, 26, t3, 25),
265
598
            combine_lower(t3, 39, t4, 12));
266
598
   }
267
268
/* Input: Q, Q', Q-Q'
269
* Out: 2Q, Q+Q'
270
*
271
*   result.two_q (2*Q): long form
272
*   result.q_plus_q_dash (Q + Q): long form
273
*   in_q: short form, destroyed
274
*   in_q_dash: short form, destroyed
275
*   in_q_minus_q_dash: short form, preserved
276
*/
277
void fmonty(uint64_t result_two_q_x[5],
278
            uint64_t result_two_q_z[5],
279
            uint64_t result_q_plus_q_dash_x[5],
280
            uint64_t result_q_plus_q_dash_z[5],
281
            uint64_t in_q_x[5],
282
            uint64_t in_q_z[5],
283
            uint64_t in_q_dash_x[5],
284
            uint64_t in_q_dash_z[5],
285
            const uint64_t q_minus_q_dash[5])
286
153k
   {
287
153k
   uint64_t zzz[5];
288
153k
   uint64_t xx[5];
289
153k
   uint64_t zz[5];
290
153k
   uint64_t xxprime[5];
291
153k
   uint64_t zzprime[5];
292
153k
   uint64_t zzzprime[5];
293
294
153k
   fadd_sub(in_q_z, in_q_x);
295
153k
   fadd_sub(in_q_dash_z, in_q_dash_x);
296
297
153k
   fmul(xxprime, in_q_dash_x, in_q_z);
298
153k
   fmul(zzprime, in_q_dash_z, in_q_x);
299
300
153k
   fadd_sub(zzprime, xxprime);
301
302
153k
   fsquare(result_q_plus_q_dash_x, xxprime);
303
153k
   fsquare(zzzprime, zzprime);
304
153k
   fmul(result_q_plus_q_dash_z, zzzprime, q_minus_q_dash);
305
306
153k
   fsquare(xx, in_q_x);
307
153k
   fsquare(zz, in_q_z);
308
153k
   fmul(result_two_q_x, xx, zz);
309
310
153k
   fdifference_backwards(zz, xx);  // does zz = xx - zz
311
153k
   fscalar_product(zzz, zz, 121665);
312
153k
   fsum(zzz, xx);
313
314
153k
   fmul(result_two_q_z, zz, zzz);
315
153k
   }
316
317
/*
318
* Maybe swap the contents of two uint64_t arrays (@a and @b),
319
* Param @iswap is assumed to be either 0 or 1
320
*
321
* This function performs the swap without leaking any side-channel
322
* information.
323
*/
324
inline void swap_conditional(uint64_t a[5], uint64_t b[5],
325
                             uint64_t c[5], uint64_t d[5],
326
                             uint64_t iswap)
327
172k
   {
328
172k
   const uint64_t swap = 0 - iswap;
329
330
1.03M
   for(size_t i = 0; i < 5; ++i)
331
861k
      {
332
861k
      const uint64_t x0 = swap & (a[i] ^ b[i]);
333
861k
      const uint64_t x1 = swap & (c[i] ^ d[i]);
334
861k
      a[i] ^= x0;
335
861k
      b[i] ^= x0;
336
861k
      c[i] ^= x1;
337
861k
      d[i] ^= x1;
338
861k
      }
339
172k
   }
340
341
/* Calculates nQ where Q is the x-coordinate of a point on the curve
342
*
343
*   resultx/resultz: the x/z coordinate of the resulting curve point (short form)
344
*   n: a little endian, 32-byte number
345
*   q: a point of the curve (short form)
346
*/
347
void cmult(uint64_t resultx[5], uint64_t resultz[5], const uint8_t n[32], const uint64_t q[5])
348
598
   {
349
598
   uint64_t a[5] = {0}; // nqpqx
350
598
   uint64_t b[5] = {1}; // npqpz
351
598
   uint64_t c[5] = {1}; // nqx
352
598
   uint64_t d[5] = {0}; // nqz
353
598
   uint64_t e[5] = {0}; // npqqx2
354
598
   uint64_t f[5] = {1}; // npqqz2
355
598
   uint64_t g[5] = {0}; // nqx2
356
598
   uint64_t h[5] = {1}; // nqz2
357
358
598
   copy_mem(a, q, 5);
359
360
19.7k
   for(size_t i = 0; i < 32; ++i)
361
19.1k
      {
362
19.1k
      const uint64_t bit0 = (n[31 - i] >> 7) & 1;
363
19.1k
      const uint64_t bit1 = (n[31 - i] >> 6) & 1;
364
19.1k
      const uint64_t bit2 = (n[31 - i] >> 5) & 1;
365
19.1k
      const uint64_t bit3 = (n[31 - i] >> 4) & 1;
366
19.1k
      const uint64_t bit4 = (n[31 - i] >> 3) & 1;
367
19.1k
      const uint64_t bit5 = (n[31 - i] >> 2) & 1;
368
19.1k
      const uint64_t bit6 = (n[31 - i] >> 1) & 1;
369
19.1k
      const uint64_t bit7 = (n[31 - i] >> 0) & 1;
370
371
19.1k
      swap_conditional(c, a, d, b, bit0);
372
19.1k
      fmonty(g, h, e, f, c, d, a, b, q);
373
374
19.1k
      swap_conditional(g, e, h, f, bit0 ^ bit1);
375
19.1k
      fmonty(c, d, a, b, g, h, e, f, q);
376
377
19.1k
      swap_conditional(c, a, d, b, bit1 ^ bit2);
378
19.1k
      fmonty(g, h, e, f, c, d, a, b, q);
379
380
19.1k
      swap_conditional(g, e, h, f, bit2 ^ bit3);
381
19.1k
      fmonty(c, d, a, b, g, h, e, f, q);
382
383
19.1k
      swap_conditional(c, a, d, b, bit3 ^ bit4);
384
19.1k
      fmonty(g, h, e, f, c, d, a, b, q);
385
386
19.1k
      swap_conditional(g, e, h, f, bit4 ^ bit5);
387
19.1k
      fmonty(c, d, a, b, g, h, e, f, q);
388
389
19.1k
      swap_conditional(c, a, d, b, bit5 ^ bit6);
390
19.1k
      fmonty(g, h, e, f, c, d, a, b, q);
391
392
19.1k
      swap_conditional(g, e, h, f, bit6 ^ bit7);
393
19.1k
      fmonty(c, d, a, b, g, h, e, f, q);
394
395
19.1k
      swap_conditional(c, a, d, b, bit7);
396
19.1k
      }
397
398
598
   copy_mem(resultx, c, 5);
399
598
   copy_mem(resultz, d, 5);
400
598
   }
401
402
403
// -----------------------------------------------------------------------------
404
// Shamelessly copied from djb's code, tightened a little
405
// -----------------------------------------------------------------------------
406
void crecip(uint64_t out[5], const uint64_t z[5])
407
598
   {
408
598
   uint64_t a[5];
409
598
   uint64_t b[5];
410
598
   uint64_t c[5];
411
598
   uint64_t t0[5];
412
413
598
   fsquare(a, z);       // 2
414
598
   fsquare(t0, a, 2);   // 8
415
598
   fmul(b, t0, z);      // 9
416
598
   fmul(a, b, a);       // 11
417
598
   fsquare(t0, a);      // 22
418
598
   fmul(b, t0, b);      // 2^5 - 2^0 = 31
419
598
   fsquare(t0, b, 5);   // 2^10 - 2^5
420
598
   fmul(b, t0, b);      // 2^10 - 2^0
421
598
   fsquare(t0, b, 10);  // 2^20 - 2^10
422
598
   fmul(c, t0, b);      // 2^20 - 2^0
423
598
   fsquare(t0, c, 20);  // 2^40 - 2^20
424
598
   fmul(t0, t0, c);     // 2^40 - 2^0
425
598
   fsquare(t0, t0, 10); // 2^50 - 2^10
426
598
   fmul(b, t0, b);      // 2^50 - 2^0
427
598
   fsquare(t0, b, 50);  // 2^100 - 2^50
428
598
   fmul(c, t0, b);      // 2^100 - 2^0
429
598
   fsquare(t0, c, 100); // 2^200 - 2^100
430
598
   fmul(t0, t0, c);     // 2^200 - 2^0
431
598
   fsquare(t0, t0, 50); // 2^250 - 2^50
432
598
   fmul(t0, t0, b);     // 2^250 - 2^0
433
598
   fsquare(t0, t0, 5);  // 2^255 - 2^5
434
598
   fmul(out, t0, a);    // 2^255 - 21
435
598
   }
436
437
}
438
439
void
440
curve25519_donna(uint8_t mypublic[32], const uint8_t secret[32], const uint8_t basepoint[32])
441
598
   {
442
598
   CT::poison(secret, 32);
443
598
   CT::poison(basepoint, 32);
444
445
598
   uint64_t bp[5], x[5], z[5], zmone[5];
446
598
   uint8_t e[32];
447
448
598
   copy_mem(e, secret, 32);
449
598
   e[ 0] &= 248;
450
598
   e[31] &= 127;
451
598
   e[31] |= 64;
452
453
598
   fexpand(bp, basepoint);
454
598
   cmult(x, z, e, bp);
455
598
   crecip(zmone, z);
456
598
   fmul(z, x, zmone);
457
598
   fcontract(mypublic, z);
458
459
598
   CT::unpoison(secret, 32);
460
598
   CT::unpoison(basepoint, 32);
461
598
   CT::unpoison(mypublic, 32);
462
598
   }
463
464
}