1 // Copyright 2013 The Go Authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style
3 // license that can be found in the LICENSE file.
5 // We have an implementation in amd64 assembly so this code is only run on
6 // non-amd64 platforms. The amd64 assembly does not support gccgo.
7 // +build !amd64 gccgo appengine
15 // This code is a port of the public domain, "ref10" implementation of
16 // curve25519 from SUPERCOP 20130419 by D. J. Bernstein.
18 // fieldElement represents an element of the field GF(2^255 - 19). An element
19 // t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
20 // t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
22 type fieldElement [10]int32
24 func feZero(fe *fieldElement) {
30 func feOne(fe *fieldElement) {
35 func feAdd(dst, a, b *fieldElement) {
41 func feSub(dst, a, b *fieldElement) {
47 func feCopy(dst, src *fieldElement) {
53 // feCSwap replaces (f,g) with (g,f) if b == 1; replaces (f,g) with (f,g) if b == 0.
55 // Preconditions: b in {0,1}.
56 func feCSwap(f, g *fieldElement, b int32) {
59 t := b & (f[i] ^ g[i])
65 // load3 reads a 24-bit, little-endian value from in.
66 func load3(in []byte) int64 {
69 r |= int64(in[1]) << 8
70 r |= int64(in[2]) << 16
74 // load4 reads a 32-bit, little-endian value from in.
75 func load4(in []byte) int64 {
76 return int64(binary.LittleEndian.Uint32(in))
79 func feFromBytes(dst *fieldElement, src *[32]byte) {
81 h1 := load3(src[4:]) << 6
82 h2 := load3(src[7:]) << 5
83 h3 := load3(src[10:]) << 3
84 h4 := load3(src[13:]) << 2
86 h6 := load3(src[20:]) << 7
87 h7 := load3(src[23:]) << 5
88 h8 := load3(src[26:]) << 4
89 h9 := (load3(src[29:]) & 0x7fffff) << 2
92 carry[9] = (h9 + 1<<24) >> 25
95 carry[1] = (h1 + 1<<24) >> 25
98 carry[3] = (h3 + 1<<24) >> 25
101 carry[5] = (h5 + 1<<24) >> 25
104 carry[7] = (h7 + 1<<24) >> 25
108 carry[0] = (h0 + 1<<25) >> 26
111 carry[2] = (h2 + 1<<25) >> 26
114 carry[4] = (h4 + 1<<25) >> 26
117 carry[6] = (h6 + 1<<25) >> 26
120 carry[8] = (h8 + 1<<25) >> 26
136 // feToBytes marshals h to s.
138 // |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
140 // Write p=2^255-19; q=floor(h/p).
141 // Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
144 // Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
145 // Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
147 // Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
151 // Have 0<=r<=p-1=2^255-20.
152 // Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
154 // Write x=r+19(2^-255)r+y.
155 // Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
157 // Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
158 // so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
159 func feToBytes(s *[32]byte, h *fieldElement) {
162 q := (19*h[9] + (1 << 24)) >> 25
174 // Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
176 // Goal: Output h-2^255 q, which is between 0 and 2^255-20.
178 carry[0] = h[0] >> 26
180 h[0] -= carry[0] << 26
181 carry[1] = h[1] >> 25
183 h[1] -= carry[1] << 25
184 carry[2] = h[2] >> 26
186 h[2] -= carry[2] << 26
187 carry[3] = h[3] >> 25
189 h[3] -= carry[3] << 25
190 carry[4] = h[4] >> 26
192 h[4] -= carry[4] << 26
193 carry[5] = h[5] >> 25
195 h[5] -= carry[5] << 25
196 carry[6] = h[6] >> 26
198 h[6] -= carry[6] << 26
199 carry[7] = h[7] >> 25
201 h[7] -= carry[7] << 25
202 carry[8] = h[8] >> 26
204 h[8] -= carry[8] << 26
205 carry[9] = h[9] >> 25
206 h[9] -= carry[9] << 25
209 // Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
210 // Have h[0]+...+2^230 h[9] between 0 and 2^255-1;
211 // evidently 2^255 h10-2^255 q = 0.
212 // Goal: Output h[0]+...+2^230 h[9].
214 s[0] = byte(h[0] >> 0)
215 s[1] = byte(h[0] >> 8)
216 s[2] = byte(h[0] >> 16)
217 s[3] = byte((h[0] >> 24) | (h[1] << 2))
218 s[4] = byte(h[1] >> 6)
219 s[5] = byte(h[1] >> 14)
220 s[6] = byte((h[1] >> 22) | (h[2] << 3))
221 s[7] = byte(h[2] >> 5)
222 s[8] = byte(h[2] >> 13)
223 s[9] = byte((h[2] >> 21) | (h[3] << 5))
224 s[10] = byte(h[3] >> 3)
225 s[11] = byte(h[3] >> 11)
226 s[12] = byte((h[3] >> 19) | (h[4] << 6))
227 s[13] = byte(h[4] >> 2)
228 s[14] = byte(h[4] >> 10)
229 s[15] = byte(h[4] >> 18)
230 s[16] = byte(h[5] >> 0)
231 s[17] = byte(h[5] >> 8)
232 s[18] = byte(h[5] >> 16)
233 s[19] = byte((h[5] >> 24) | (h[6] << 1))
234 s[20] = byte(h[6] >> 7)
235 s[21] = byte(h[6] >> 15)
236 s[22] = byte((h[6] >> 23) | (h[7] << 3))
237 s[23] = byte(h[7] >> 5)
238 s[24] = byte(h[7] >> 13)
239 s[25] = byte((h[7] >> 21) | (h[8] << 4))
240 s[26] = byte(h[8] >> 4)
241 s[27] = byte(h[8] >> 12)
242 s[28] = byte((h[8] >> 20) | (h[9] << 6))
243 s[29] = byte(h[9] >> 2)
244 s[30] = byte(h[9] >> 10)
245 s[31] = byte(h[9] >> 18)
248 // feMul calculates h = f * g
249 // Can overlap h with f or g.
252 // |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
253 // |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
256 // |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
258 // Notes on implementation strategy:
260 // Using schoolbook multiplication.
261 // Karatsuba would save a little in some cost models.
263 // Most multiplications by 2 and 19 are 32-bit precomputations;
264 // cheaper than 64-bit postcomputations.
266 // There is one remaining multiplication by 19 in the carry chain;
267 // one *19 precomputation can be merged into this,
268 // but the resulting data flow is considerably less clean.
270 // There are 12 carries below.
271 // 10 of them are 2-way parallelizable and vectorizable.
272 // Can get away with 11 carries, but then data flow is much deeper.
274 // With tighter constraints on inputs can squeeze carries into int32.
275 func feMul(h, f, g *fieldElement) {
296 g1_19 := 19 * g1 // 1.4*2^29
297 g2_19 := 19 * g2 // 1.4*2^30; still ok
310 f0g0 := int64(f0) * int64(g0)
311 f0g1 := int64(f0) * int64(g1)
312 f0g2 := int64(f0) * int64(g2)
313 f0g3 := int64(f0) * int64(g3)
314 f0g4 := int64(f0) * int64(g4)
315 f0g5 := int64(f0) * int64(g5)
316 f0g6 := int64(f0) * int64(g6)
317 f0g7 := int64(f0) * int64(g7)
318 f0g8 := int64(f0) * int64(g8)
319 f0g9 := int64(f0) * int64(g9)
320 f1g0 := int64(f1) * int64(g0)
321 f1g1_2 := int64(f1_2) * int64(g1)
322 f1g2 := int64(f1) * int64(g2)
323 f1g3_2 := int64(f1_2) * int64(g3)
324 f1g4 := int64(f1) * int64(g4)
325 f1g5_2 := int64(f1_2) * int64(g5)
326 f1g6 := int64(f1) * int64(g6)
327 f1g7_2 := int64(f1_2) * int64(g7)
328 f1g8 := int64(f1) * int64(g8)
329 f1g9_38 := int64(f1_2) * int64(g9_19)
330 f2g0 := int64(f2) * int64(g0)
331 f2g1 := int64(f2) * int64(g1)
332 f2g2 := int64(f2) * int64(g2)
333 f2g3 := int64(f2) * int64(g3)
334 f2g4 := int64(f2) * int64(g4)
335 f2g5 := int64(f2) * int64(g5)
336 f2g6 := int64(f2) * int64(g6)
337 f2g7 := int64(f2) * int64(g7)
338 f2g8_19 := int64(f2) * int64(g8_19)
339 f2g9_19 := int64(f2) * int64(g9_19)
340 f3g0 := int64(f3) * int64(g0)
341 f3g1_2 := int64(f3_2) * int64(g1)
342 f3g2 := int64(f3) * int64(g2)
343 f3g3_2 := int64(f3_2) * int64(g3)
344 f3g4 := int64(f3) * int64(g4)
345 f3g5_2 := int64(f3_2) * int64(g5)
346 f3g6 := int64(f3) * int64(g6)
347 f3g7_38 := int64(f3_2) * int64(g7_19)
348 f3g8_19 := int64(f3) * int64(g8_19)
349 f3g9_38 := int64(f3_2) * int64(g9_19)
350 f4g0 := int64(f4) * int64(g0)
351 f4g1 := int64(f4) * int64(g1)
352 f4g2 := int64(f4) * int64(g2)
353 f4g3 := int64(f4) * int64(g3)
354 f4g4 := int64(f4) * int64(g4)
355 f4g5 := int64(f4) * int64(g5)
356 f4g6_19 := int64(f4) * int64(g6_19)
357 f4g7_19 := int64(f4) * int64(g7_19)
358 f4g8_19 := int64(f4) * int64(g8_19)
359 f4g9_19 := int64(f4) * int64(g9_19)
360 f5g0 := int64(f5) * int64(g0)
361 f5g1_2 := int64(f5_2) * int64(g1)
362 f5g2 := int64(f5) * int64(g2)
363 f5g3_2 := int64(f5_2) * int64(g3)
364 f5g4 := int64(f5) * int64(g4)
365 f5g5_38 := int64(f5_2) * int64(g5_19)
366 f5g6_19 := int64(f5) * int64(g6_19)
367 f5g7_38 := int64(f5_2) * int64(g7_19)
368 f5g8_19 := int64(f5) * int64(g8_19)
369 f5g9_38 := int64(f5_2) * int64(g9_19)
370 f6g0 := int64(f6) * int64(g0)
371 f6g1 := int64(f6) * int64(g1)
372 f6g2 := int64(f6) * int64(g2)
373 f6g3 := int64(f6) * int64(g3)
374 f6g4_19 := int64(f6) * int64(g4_19)
375 f6g5_19 := int64(f6) * int64(g5_19)
376 f6g6_19 := int64(f6) * int64(g6_19)
377 f6g7_19 := int64(f6) * int64(g7_19)
378 f6g8_19 := int64(f6) * int64(g8_19)
379 f6g9_19 := int64(f6) * int64(g9_19)
380 f7g0 := int64(f7) * int64(g0)
381 f7g1_2 := int64(f7_2) * int64(g1)
382 f7g2 := int64(f7) * int64(g2)
383 f7g3_38 := int64(f7_2) * int64(g3_19)
384 f7g4_19 := int64(f7) * int64(g4_19)
385 f7g5_38 := int64(f7_2) * int64(g5_19)
386 f7g6_19 := int64(f7) * int64(g6_19)
387 f7g7_38 := int64(f7_2) * int64(g7_19)
388 f7g8_19 := int64(f7) * int64(g8_19)
389 f7g9_38 := int64(f7_2) * int64(g9_19)
390 f8g0 := int64(f8) * int64(g0)
391 f8g1 := int64(f8) * int64(g1)
392 f8g2_19 := int64(f8) * int64(g2_19)
393 f8g3_19 := int64(f8) * int64(g3_19)
394 f8g4_19 := int64(f8) * int64(g4_19)
395 f8g5_19 := int64(f8) * int64(g5_19)
396 f8g6_19 := int64(f8) * int64(g6_19)
397 f8g7_19 := int64(f8) * int64(g7_19)
398 f8g8_19 := int64(f8) * int64(g8_19)
399 f8g9_19 := int64(f8) * int64(g9_19)
400 f9g0 := int64(f9) * int64(g0)
401 f9g1_38 := int64(f9_2) * int64(g1_19)
402 f9g2_19 := int64(f9) * int64(g2_19)
403 f9g3_38 := int64(f9_2) * int64(g3_19)
404 f9g4_19 := int64(f9) * int64(g4_19)
405 f9g5_38 := int64(f9_2) * int64(g5_19)
406 f9g6_19 := int64(f9) * int64(g6_19)
407 f9g7_38 := int64(f9_2) * int64(g7_19)
408 f9g8_19 := int64(f9) * int64(g8_19)
409 f9g9_38 := int64(f9_2) * int64(g9_19)
410 h0 := f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38
411 h1 := f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19
412 h2 := f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38
413 h3 := f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19
414 h4 := f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38
415 h5 := f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19
416 h6 := f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38
417 h7 := f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19
418 h8 := f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38
419 h9 := f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0
422 // |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
423 // i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
424 // |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
425 // i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
427 carry[0] = (h0 + (1 << 25)) >> 26
430 carry[4] = (h4 + (1 << 25)) >> 26
438 carry[1] = (h1 + (1 << 24)) >> 25
441 carry[5] = (h5 + (1 << 24)) >> 25
444 // |h1| <= 2^24; from now on fits into int32
445 // |h5| <= 2^24; from now on fits into int32
449 carry[2] = (h2 + (1 << 25)) >> 26
452 carry[6] = (h6 + (1 << 25)) >> 26
455 // |h2| <= 2^25; from now on fits into int32 unchanged
456 // |h6| <= 2^25; from now on fits into int32 unchanged
460 carry[3] = (h3 + (1 << 24)) >> 25
463 carry[7] = (h7 + (1 << 24)) >> 25
466 // |h3| <= 2^24; from now on fits into int32 unchanged
467 // |h7| <= 2^24; from now on fits into int32 unchanged
471 carry[4] = (h4 + (1 << 25)) >> 26
474 carry[8] = (h8 + (1 << 25)) >> 26
477 // |h4| <= 2^25; from now on fits into int32 unchanged
478 // |h8| <= 2^25; from now on fits into int32 unchanged
482 carry[9] = (h9 + (1 << 24)) >> 25
485 // |h9| <= 2^24; from now on fits into int32 unchanged
488 carry[0] = (h0 + (1 << 25)) >> 26
491 // |h0| <= 2^25; from now on fits into int32 unchanged
506 // feSquare calculates h = f*f. Can overlap h with f.
509 // |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
512 // |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
513 func feSquare(h, f *fieldElement) {
532 f5_38 := 38 * f5 // 1.31*2^30
533 f6_19 := 19 * f6 // 1.31*2^30
534 f7_38 := 38 * f7 // 1.31*2^30
535 f8_19 := 19 * f8 // 1.31*2^30
536 f9_38 := 38 * f9 // 1.31*2^30
537 f0f0 := int64(f0) * int64(f0)
538 f0f1_2 := int64(f0_2) * int64(f1)
539 f0f2_2 := int64(f0_2) * int64(f2)
540 f0f3_2 := int64(f0_2) * int64(f3)
541 f0f4_2 := int64(f0_2) * int64(f4)
542 f0f5_2 := int64(f0_2) * int64(f5)
543 f0f6_2 := int64(f0_2) * int64(f6)
544 f0f7_2 := int64(f0_2) * int64(f7)
545 f0f8_2 := int64(f0_2) * int64(f8)
546 f0f9_2 := int64(f0_2) * int64(f9)
547 f1f1_2 := int64(f1_2) * int64(f1)
548 f1f2_2 := int64(f1_2) * int64(f2)
549 f1f3_4 := int64(f1_2) * int64(f3_2)
550 f1f4_2 := int64(f1_2) * int64(f4)
551 f1f5_4 := int64(f1_2) * int64(f5_2)
552 f1f6_2 := int64(f1_2) * int64(f6)
553 f1f7_4 := int64(f1_2) * int64(f7_2)
554 f1f8_2 := int64(f1_2) * int64(f8)
555 f1f9_76 := int64(f1_2) * int64(f9_38)
556 f2f2 := int64(f2) * int64(f2)
557 f2f3_2 := int64(f2_2) * int64(f3)
558 f2f4_2 := int64(f2_2) * int64(f4)
559 f2f5_2 := int64(f2_2) * int64(f5)
560 f2f6_2 := int64(f2_2) * int64(f6)
561 f2f7_2 := int64(f2_2) * int64(f7)
562 f2f8_38 := int64(f2_2) * int64(f8_19)
563 f2f9_38 := int64(f2) * int64(f9_38)
564 f3f3_2 := int64(f3_2) * int64(f3)
565 f3f4_2 := int64(f3_2) * int64(f4)
566 f3f5_4 := int64(f3_2) * int64(f5_2)
567 f3f6_2 := int64(f3_2) * int64(f6)
568 f3f7_76 := int64(f3_2) * int64(f7_38)
569 f3f8_38 := int64(f3_2) * int64(f8_19)
570 f3f9_76 := int64(f3_2) * int64(f9_38)
571 f4f4 := int64(f4) * int64(f4)
572 f4f5_2 := int64(f4_2) * int64(f5)
573 f4f6_38 := int64(f4_2) * int64(f6_19)
574 f4f7_38 := int64(f4) * int64(f7_38)
575 f4f8_38 := int64(f4_2) * int64(f8_19)
576 f4f9_38 := int64(f4) * int64(f9_38)
577 f5f5_38 := int64(f5) * int64(f5_38)
578 f5f6_38 := int64(f5_2) * int64(f6_19)
579 f5f7_76 := int64(f5_2) * int64(f7_38)
580 f5f8_38 := int64(f5_2) * int64(f8_19)
581 f5f9_76 := int64(f5_2) * int64(f9_38)
582 f6f6_19 := int64(f6) * int64(f6_19)
583 f6f7_38 := int64(f6) * int64(f7_38)
584 f6f8_38 := int64(f6_2) * int64(f8_19)
585 f6f9_38 := int64(f6) * int64(f9_38)
586 f7f7_38 := int64(f7) * int64(f7_38)
587 f7f8_38 := int64(f7_2) * int64(f8_19)
588 f7f9_76 := int64(f7_2) * int64(f9_38)
589 f8f8_19 := int64(f8) * int64(f8_19)
590 f8f9_38 := int64(f8) * int64(f9_38)
591 f9f9_38 := int64(f9) * int64(f9_38)
592 h0 := f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38
593 h1 := f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38
594 h2 := f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19
595 h3 := f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38
596 h4 := f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38
597 h5 := f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38
598 h6 := f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19
599 h7 := f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38
600 h8 := f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38
601 h9 := f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2
604 carry[0] = (h0 + (1 << 25)) >> 26
607 carry[4] = (h4 + (1 << 25)) >> 26
611 carry[1] = (h1 + (1 << 24)) >> 25
614 carry[5] = (h5 + (1 << 24)) >> 25
618 carry[2] = (h2 + (1 << 25)) >> 26
621 carry[6] = (h6 + (1 << 25)) >> 26
625 carry[3] = (h3 + (1 << 24)) >> 25
628 carry[7] = (h7 + (1 << 24)) >> 25
632 carry[4] = (h4 + (1 << 25)) >> 26
635 carry[8] = (h8 + (1 << 25)) >> 26
639 carry[9] = (h9 + (1 << 24)) >> 25
643 carry[0] = (h0 + (1 << 25)) >> 26
659 // feMul121666 calculates h = f * 121666. Can overlap h with f.
662 // |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
665 // |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
666 func feMul121666(h, f *fieldElement) {
667 h0 := int64(f[0]) * 121666
668 h1 := int64(f[1]) * 121666
669 h2 := int64(f[2]) * 121666
670 h3 := int64(f[3]) * 121666
671 h4 := int64(f[4]) * 121666
672 h5 := int64(f[5]) * 121666
673 h6 := int64(f[6]) * 121666
674 h7 := int64(f[7]) * 121666
675 h8 := int64(f[8]) * 121666
676 h9 := int64(f[9]) * 121666
679 carry[9] = (h9 + (1 << 24)) >> 25
682 carry[1] = (h1 + (1 << 24)) >> 25
685 carry[3] = (h3 + (1 << 24)) >> 25
688 carry[5] = (h5 + (1 << 24)) >> 25
691 carry[7] = (h7 + (1 << 24)) >> 25
695 carry[0] = (h0 + (1 << 25)) >> 26
698 carry[2] = (h2 + (1 << 25)) >> 26
701 carry[4] = (h4 + (1 << 25)) >> 26
704 carry[6] = (h6 + (1 << 25)) >> 26
707 carry[8] = (h8 + (1 << 25)) >> 26
723 // feInvert sets out = z^-1.
724 func feInvert(out, z *fieldElement) {
725 var t0, t1, t2, t3 fieldElement
729 for i = 1; i < 1; i++ {
733 for i = 1; i < 2; i++ {
739 for i = 1; i < 1; i++ {
744 for i = 1; i < 5; i++ {
749 for i = 1; i < 10; i++ {
754 for i = 1; i < 20; i++ {
759 for i = 1; i < 10; i++ {
764 for i = 1; i < 50; i++ {
769 for i = 1; i < 100; i++ {
774 for i = 1; i < 50; i++ {
779 for i = 1; i < 5; i++ {
785 func scalarMult(out, in, base *[32]byte) {
793 var x1, x2, z2, x3, z3, tmp0, tmp1 fieldElement
794 feFromBytes(&x1, base)
800 for pos := 254; pos >= 0; pos-- {
801 b := e[pos/8] >> uint(pos&7)
804 feCSwap(&x2, &x3, swap)
805 feCSwap(&z2, &z3, swap)
808 feSub(&tmp0, &x3, &z3)
809 feSub(&tmp1, &x2, &z2)
812 feMul(&z3, &tmp0, &x2)
813 feMul(&z2, &z2, &tmp1)
814 feSquare(&tmp0, &tmp1)
818 feMul(&x2, &tmp1, &tmp0)
819 feSub(&tmp1, &tmp1, &tmp0)
821 feMul121666(&z3, &tmp1)
823 feAdd(&tmp0, &tmp0, &z3)
825 feMul(&z2, &tmp1, &tmp0)
828 feCSwap(&x2, &x3, swap)
829 feCSwap(&z2, &z3, swap)