aboutsummaryrefslogblamecommitdiffstats
path: root/curve25519-u128.c
blob: b51d18a944d7db20d8a3129ed8e1ddeb8b6f813c (plain) (tree)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420



































































































































































































































































































































































































































                                                                                                                                      
/* SPDX-License-Identifier: GPL-2.0
 *
 * Copyright (C) 2008 Google Inc. All Rights Reserved.
 * Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
 *
 * Original author: Adam Langley <agl@imperialviolet.org>
 */

#include <linux/kernel.h>
#include <linux/string.h>

enum { CURVE25519_POINT_SIZE = 32 };

typedef u64 limb;
typedef limb felem[5];
typedef __uint128_t u128;

static __always_inline void normalize_secret(u8 secret[CURVE25519_POINT_SIZE])
{
	secret[0] &= 248;
	secret[31] &= 127;
	secret[31] |= 64;
}

/* Sum two numbers: output += in */
static __always_inline void fsum(limb *output, const limb *in)
{
	output[0] += in[0];
	output[1] += in[1];
	output[2] += in[2];
	output[3] += in[3];
	output[4] += in[4];
}

/* Find the difference of two numbers: output = in - output
 * (note the order of the arguments!)
 *
 * Assumes that out[i] < 2**52
 * On return, out[i] < 2**55
 */
static __always_inline void fdifference_backwards(felem out, const felem in)
{
	/* 152 is 19 << 3 */
	static const limb two54m152 = (((limb)1) << 54) - 152;
	static const limb two54m8 = (((limb)1) << 54) - 8;

	out[0] = in[0] + two54m152 - out[0];
	out[1] = in[1] + two54m8 - out[1];
	out[2] = in[2] + two54m8 - out[2];
	out[3] = in[3] + two54m8 - out[3];
	out[4] = in[4] + two54m8 - out[4];
}

/* Multiply a number by a scalar: output = in * scalar */
static __always_inline void fscalar_product(felem output, const felem in, const limb scalar)
{
	u128 a;

	a = ((u128) in[0]) * scalar;
	output[0] = ((limb)a) & 0x7ffffffffffffUL;

	a = ((u128) in[1]) * scalar + ((limb) (a >> 51));
	output[1] = ((limb)a) & 0x7ffffffffffffUL;

	a = ((u128) in[2]) * scalar + ((limb) (a >> 51));
	output[2] = ((limb)a) & 0x7ffffffffffffUL;

	a = ((u128) in[3]) * scalar + ((limb) (a >> 51));
	output[3] = ((limb)a) & 0x7ffffffffffffUL;

	a = ((u128) in[4]) * scalar + ((limb) (a >> 51));
	output[4] = ((limb)a) & 0x7ffffffffffffUL;

	output[0] += (a >> 51) * 19;
}

/* Multiply two numbers: output = in2 * in
 *
 * output must be distinct to both inputs. The inputs are reduced coefficient
 * form, the output is not.
 *
 * Assumes that in[i] < 2**55 and likewise for in2.
 * On return, output[i] < 2**52
 */
static __always_inline void fmul(felem output, const felem in2, const felem in)
{
	u128 t[5];
	limb r0, r1, r2, r3, r4, s0, s1, s2, s3, s4, c;

	r0 = in[0];
	r1 = in[1];
	r2 = in[2];
	r3 = in[3];
	r4 = in[4];

	s0 = in2[0];
	s1 = in2[1];
	s2 = in2[2];
	s3 = in2[3];
	s4 = in2[4];

	t[0]  =  ((u128) r0) * s0;
	t[1]  =  ((u128) r0) * s1 + ((u128) r1) * s0;
	t[2]  =  ((u128) r0) * s2 + ((u128) r2) * s0 + ((u128) r1) * s1;
	t[3]  =  ((u128) r0) * s3 + ((u128) r3) * s0 + ((u128) r1) * s2 + ((u128) r2) * s1;
	t[4]  =  ((u128) r0) * s4 + ((u128) r4) * s0 + ((u128) r3) * s1 + ((u128) r1) * s3 + ((u128) r2) * s2;

	r4 *= 19;
	r1 *= 19;
	r2 *= 19;
	r3 *= 19;

	t[0] += ((u128) r4) * s1 + ((u128) r1) * s4 + ((u128) r2) * s3 + ((u128) r3) * s2;
	t[1] += ((u128) r4) * s2 + ((u128) r2) * s4 + ((u128) r3) * s3;
	t[2] += ((u128) r4) * s3 + ((u128) r3) * s4;
	t[3] += ((u128) r4) * s4;

			r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
	t[1] += c;      r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
	t[2] += c;      r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
	t[3] += c;      r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
	t[4] += c;      r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
	r0 +=   c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
	r1 +=   c;      c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
	r2 +=   c;

	output[0] = r0;
	output[1] = r1;
	output[2] = r2;
	output[3] = r3;
	output[4] = r4;
}

static __always_inline void fsquare_times(felem output, const felem in, limb count)
{
	u128 t[5];
	limb r0, r1, r2, r3, r4, c;
	limb d0, d1, d2, d4, d419;

	r0 = in[0];
	r1 = in[1];
	r2 = in[2];
	r3 = in[3];
	r4 = in[4];

	do {
		d0 = r0 * 2;
		d1 = r1 * 2;
		d2 = r2 * 2 * 19;
		d419 = r4 * 19;
		d4 = d419 * 2;

		t[0] = ((u128) r0) * r0 + ((u128) d4) * r1 + (((u128) d2) * (r3     ));
		t[1] = ((u128) d0) * r1 + ((u128) d4) * r2 + (((u128) r3) * (r3 * 19));
		t[2] = ((u128) d0) * r2 + ((u128) r1) * r1 + (((u128) d4) * (r3     ));
		t[3] = ((u128) d0) * r3 + ((u128) d1) * r2 + (((u128) r4) * (d419   ));
		t[4] = ((u128) d0) * r4 + ((u128) d1) * r3 + (((u128) r2) * (r2     ));

				r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
		t[1] += c;      r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
		t[2] += c;      r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
		t[3] += c;      r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
		t[4] += c;      r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
		r0 +=   c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
		r1 +=   c;      c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
		r2 +=   c;
	} while (--count);

	output[0] = r0;
	output[1] = r1;
	output[2] = r2;
	output[3] = r3;
	output[4] = r4;
}

/* Load a little-endian 64-bit number  */
static inline limb load_limb(const u8 *in)
{
	return le64_to_cpu(*(__le64 *)in);
}

static inline void store_limb(u8 *out, limb in)
{
	*(__le64 *)out = cpu_to_le64(in);
}

/* Take a little-endian, 32-byte number and expand it into polynomial form */
static inline void fexpand(limb *output, const u8 *in)
{
	output[0] = load_limb(in) & 0x7ffffffffffffUL;
	output[1] = (load_limb(in + 6) >> 3) & 0x7ffffffffffffUL;
	output[2] = (load_limb(in + 12) >> 6) & 0x7ffffffffffffUL;
	output[3] = (load_limb(in + 19) >> 1) & 0x7ffffffffffffUL;
	output[4] = (load_limb(in + 24) >> 12) & 0x7ffffffffffffUL;
}

/* Take a fully reduced polynomial form number and contract it into a
 * little-endian, 32-byte array
 */
static void fcontract(u8 *output, const felem input)
{
	u128 t[5];

	t[0] = input[0];
	t[1] = input[1];
	t[2] = input[2];
	t[3] = input[3];
	t[4] = input[4];

	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
	t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;

	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
	t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;

	/* now t is between 0 and 2^255-1, properly carried. */
	/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */

	t[0] += 19;

	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
	t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;

	/* now between 19 and 2^255-1 in both cases, and offset by 19. */

	t[0] += 0x8000000000000UL - 19;
	t[1] += 0x8000000000000UL - 1;
	t[2] += 0x8000000000000UL - 1;
	t[3] += 0x8000000000000UL - 1;
	t[4] += 0x8000000000000UL - 1;

	/* now between 2^255 and 2^256-20, and offset by 2^255. */

	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
	t[4] &= 0x7ffffffffffffUL;

	store_limb(output,    t[0] | (t[1] << 51));
	store_limb(output+8,  (t[1] >> 13) | (t[2] << 38));
	store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
	store_limb(output+24, (t[3] >> 39) | (t[4] << 12));
}

/* Input: Q, Q', Q-Q'
 * Output: 2Q, Q+Q'
 *
 *   x2 z3: long form
 *   x3 z3: long form
 *   x z: short form, destroyed
 *   xprime zprime: short form, destroyed
 *   qmqp: short form, preserved
 */
static void fmonty(limb *x2, limb *z2, /* output 2Q */
			 limb *x3, limb *z3, /* output Q + Q' */
			 limb *x, limb *z,   /* input Q */
			 limb *xprime, limb *zprime, /* input Q' */

			 const limb *qmqp /* input Q - Q' */)
{
	limb origx[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5], zzzprime[5];

	memcpy(origx, x, 5 * sizeof(limb));
	fsum(x, z);
	fdifference_backwards(z, origx);  // does x - z

	memcpy(origxprime, xprime, sizeof(limb) * 5);
	fsum(xprime, zprime);
	fdifference_backwards(zprime, origxprime);
	fmul(xxprime, xprime, z);
	fmul(zzprime, x, zprime);
	memcpy(origxprime, xxprime, sizeof(limb) * 5);
	fsum(xxprime, zzprime);
	fdifference_backwards(zzprime, origxprime);
	fsquare_times(x3, xxprime, 1);
	fsquare_times(zzzprime, zzprime, 1);
	fmul(z3, zzzprime, qmqp);

	fsquare_times(xx, x, 1);
	fsquare_times(zz, z, 1);
	fmul(x2, xx, zz);
	fdifference_backwards(zz, xx);  // does zz = xx - zz
	fscalar_product(zzz, zz, 121665);
	fsum(zzz, xx);
	fmul(z2, zz, zzz);
}

/* Maybe swap the contents of two limb arrays (@a and @b), each @len elements
 * long. Perform the swap iff @swap is non-zero.
 *
 * This function performs the swap without leaking any side-channel
 * information.
 */
static void swap_conditional(limb a[5], limb b[5], limb iswap)
{
	unsigned int i;
	const limb swap = -iswap;

	for (i = 0; i < 5; ++i) {
		const limb x = swap & (a[i] ^ b[i]);

		a[i] ^= x;
		b[i] ^= x;
	}
}

/* Calculates nQ where Q is the x-coordinate of a point on the curve
 *
 *   resultx/resultz: the x coordinate of the resulting curve point (short form)
 *   n: a little endian, 32-byte number
 *   q: a point of the curve (short form)
 */
static void cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q)
{
	limb a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
	limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
	limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
	limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;

	unsigned int i, j;

	memcpy(nqpqx, q, sizeof(limb) * 5);

	for (i = 0; i < 32; ++i) {
		u8 byte = n[31 - i];

		for (j = 0; j < 8; ++j) {
			const limb bit = byte >> 7;

			swap_conditional(nqx, nqpqx, bit);
			swap_conditional(nqz, nqpqz, bit);
			fmonty(nqx2, nqz2,
						 nqpqx2, nqpqz2,
						 nqx, nqz,
						 nqpqx, nqpqz,
						 q);
			swap_conditional(nqx2, nqpqx2, bit);
			swap_conditional(nqz2, nqpqz2, bit);

			t = nqx;
			nqx = nqx2;
			nqx2 = t;
			t = nqz;
			nqz = nqz2;
			nqz2 = t;
			t = nqpqx;
			nqpqx = nqpqx2;
			nqpqx2 = t;
			t = nqpqz;
			nqpqz = nqpqz2;
			nqpqz2 = t;

			byte <<= 1;
		}
	}

	memcpy(resultx, nqx, sizeof(limb) * 5);
	memcpy(resultz, nqz, sizeof(limb) * 5);
}

static void crecip(felem out, const felem z)
{
	felem a, t0, b, c;

	/* 2 */ fsquare_times(a, z, 1); // a = 2
	/* 8 */ fsquare_times(t0, a, 2);
	/* 9 */ fmul(b, t0, z); // b = 9
	/* 11 */ fmul(a, b, a); // a = 11
	/* 22 */ fsquare_times(t0, a, 1);
	/* 2^5 - 2^0 = 31 */ fmul(b, t0, b);
	/* 2^10 - 2^5 */ fsquare_times(t0, b, 5);
	/* 2^10 - 2^0 */ fmul(b, t0, b);
	/* 2^20 - 2^10 */ fsquare_times(t0, b, 10);
	/* 2^20 - 2^0 */ fmul(c, t0, b);
	/* 2^40 - 2^20 */ fsquare_times(t0, c, 20);
	/* 2^40 - 2^0 */ fmul(t0, t0, c);
	/* 2^50 - 2^10 */ fsquare_times(t0, t0, 10);
	/* 2^50 - 2^0 */ fmul(b, t0, b);
	/* 2^100 - 2^50 */ fsquare_times(t0, b, 50);
	/* 2^100 - 2^0 */ fmul(c, t0, b);
	/* 2^200 - 2^100 */ fsquare_times(t0, c, 100);
	/* 2^200 - 2^0 */ fmul(t0, t0, c);
	/* 2^250 - 2^50 */ fsquare_times(t0, t0, 50);
	/* 2^250 - 2^0 */ fmul(t0, t0, b);
	/* 2^255 - 2^5 */ fsquare_times(t0, t0, 5);
	/* 2^255 - 21 */ fmul(out, t0, a);
}

bool curve25519(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
{
	limb bp[5], x[5], z[5], zmone[5];
	u8 e[32];

	memcpy(e, secret, 32);
	normalize_secret(e);

	fexpand(bp, basepoint);
	cmult(x, z, e, bp);
	crecip(zmone, z);
	fmul(z, x, zmone);
	fcontract(mypublic, z);

	memzero_explicit(e, sizeof(e));
	memzero_explicit(bp, sizeof(bp));
	memzero_explicit(x, sizeof(x));
	memzero_explicit(z, sizeof(z));
	memzero_explicit(zmone, sizeof(zmone));

	return true;
}