v
Зеркало из https://github.com/vlang/v
1module edwards25519
2
3import math.bits
4import math.unsigned
5import encoding.binary
6import crypto.internal.subtle
7
8// embedded unsigned.Uint128
9struct Uint128 {
10unsigned.Uint128
11}
12
13// Element represents an element of the edwards25519 GF(2^255-19). Note that this
14// is not a cryptographically secure group, and should only be used to interact
15// with edwards25519.Point coordinates.
16//
17// This type works similarly to math/big.Int, and all arguments and receivers
18// are allowed to alias.
19//
20// The zero value is a valid zero element.
21pub struct Element {
22mut:
23// An element t represents the integer
24// t.l0 + t.l1*2^51 + t.l2*2^102 + t.l3*2^153 + t.l4*2^204
25//
26// Between operations, all limbs are expected to be lower than 2^52.
27l0 u64
28l1 u64
29l2 u64
30l3 u64
31l4 u64
32}
33
34const mask_low_51_bits = u64((1 << 51) - 1)
35const fe_zero = Element{
36l0: 0
37l1: 0
38l2: 0
39l3: 0
40l4: 0
41}
42const fe_one = Element{
43l0: 1
44l1: 0
45l2: 0
46l3: 0
47l4: 0
48}
49// sqrt_m1 is 2^((p-1)/4), which squared is equal to -1 by Euler's Criterion.
50const sqrt_m1 = Element{
51l0: 1718705420411056
52l1: 234908883556509
53l2: 2233514472574048
54l3: 2117202627021982
55l4: 765476049583133
56}
57
58// mul_64 returns a * b.
59fn mul_64(a u64, b u64) Uint128 {
60hi, lo := bits.mul_64(a, b)
61return Uint128{
62lo: lo
63hi: hi
64}
65}
66
67// add_mul_64 returns v + a * b.
68fn add_mul_64(v Uint128, a u64, b u64) Uint128 {
69mut hi, lo := bits.mul_64(a, b)
70low, carry := bits.add_64(lo, v.lo, 0)
71hi, _ = bits.add_64(hi, v.hi, carry)
72return Uint128{
73lo: low
74hi: hi
75}
76}
77
78// shift_right_by_51 returns a >> 51. a is assumed to be at most 115 bits.
79fn shift_right_by_51(a Uint128) u64 {
80return (a.hi << (64 - 51)) | (a.lo >> 51)
81}
82
83fn fe_mul_generic(a Element, b Element) Element {
84a0 := a.l0
85a1 := a.l1
86a2 := a.l2
87a3 := a.l3
88a4 := a.l4
89
90b0 := b.l0
91b1 := b.l1
92b2 := b.l2
93b3 := b.l3
94b4 := b.l4
95
96// Limb multiplication works like pen-and-paper columnar multiplication, but
97// with 51-bit limbs instead of digits.
98//
99// a4 a3 a2 a1 a0 x
100// b4 b3 b2 b1 b0 =
101// ------------------------
102// a4b0 a3b0 a2b0 a1b0 a0b0 +
103// a4b1 a3b1 a2b1 a1b1 a0b1 +
104// a4b2 a3b2 a2b2 a1b2 a0b2 +
105// a4b3 a3b3 a2b3 a1b3 a0b3 +
106// a4b4 a3b4 a2b4 a1b4 a0b4 =
107// ----------------------------------------------
108// r8 r7 r6 r5 r4 r3 r2 r1 r0
109//
110// We can then use the reduction identity (a * 2²⁵⁵ + b = a * 19 + b) to
111// reduce the limbs that would overflow 255 bits. r5 * 2²⁵⁵ becomes 19 * r5,
112// r6 * 2³⁰⁶ becomes 19 * r6 * 2⁵¹, etc.
113//
114// Reduction can be carried out simultaneously to multiplication. For
115// example, we do not compute r5: whenever the result of a multiplication
116// belongs to r5, like a1b4, we multiply it by 19 and add the result to r0.
117//
118// a4b0 a3b0 a2b0 a1b0 a0b0 +
119// a3b1 a2b1 a1b1 a0b1 19×a4b1 +
120// a2b2 a1b2 a0b2 19×a4b2 19×a3b2 +
121// a1b3 a0b3 19×a4b3 19×a3b3 19×a2b3 +
122// a0b4 19×a4b4 19×a3b4 19×a2b4 19×a1b4 =
123// --------------------------------------
124// r4 r3 r2 r1 r0
125//
126// Finally we add up the columns into wide, overlapping limbs.
127
128a1_19 := a1 * 19
129a2_19 := a2 * 19
130a3_19 := a3 * 19
131a4_19 := a4 * 19
132
133// r0 = a0×b0 + 19×(a1×b4 + a2×b3 + a3×b2 + a4×b1)
134mut r0 := mul_64(a0, b0)
135r0 = add_mul_64(r0, a1_19, b4)
136r0 = add_mul_64(r0, a2_19, b3)
137r0 = add_mul_64(r0, a3_19, b2)
138r0 = add_mul_64(r0, a4_19, b1)
139
140// r1 = a0×b1 + a1×b0 + 19×(a2×b4 + a3×b3 + a4×b2)
141mut r1 := mul_64(a0, b1)
142r1 = add_mul_64(r1, a1, b0)
143r1 = add_mul_64(r1, a2_19, b4)
144r1 = add_mul_64(r1, a3_19, b3)
145r1 = add_mul_64(r1, a4_19, b2)
146
147// r2 = a0×b2 + a1×b1 + a2×b0 + 19×(a3×b4 + a4×b3)
148mut r2 := mul_64(a0, b2)
149r2 = add_mul_64(r2, a1, b1)
150r2 = add_mul_64(r2, a2, b0)
151r2 = add_mul_64(r2, a3_19, b4)
152r2 = add_mul_64(r2, a4_19, b3)
153
154// r3 = a0×b3 + a1×b2 + a2×b1 + a3×b0 + 19×a4×b4
155mut r3 := mul_64(a0, b3)
156r3 = add_mul_64(r3, a1, b2)
157r3 = add_mul_64(r3, a2, b1)
158r3 = add_mul_64(r3, a3, b0)
159r3 = add_mul_64(r3, a4_19, b4)
160
161// r4 = a0×b4 + a1×b3 + a2×b2 + a3×b1 + a4×b0
162mut r4 := mul_64(a0, b4)
163r4 = add_mul_64(r4, a1, b3)
164r4 = add_mul_64(r4, a2, b2)
165r4 = add_mul_64(r4, a3, b1)
166r4 = add_mul_64(r4, a4, b0)
167
168// After the multiplication, we need to reduce (carry) the five coefficients
169// to obtain a result with limbs that are at most slightly larger than 2⁵¹,
170// to respect the Element invariant.
171//
172// Overall, the reduction works the same as carryPropagate, except with
173// wider inputs: we take the carry for each coefficient by shifting it right
174// by 51, and add it to the limb above it. The top carry is multiplied by 19
175// according to the reduction identity and added to the lowest limb.
176//
177// The largest coefficient (r0) will be at most 111 bits, which guarantees
178// that all carries are at most 111 - 51 = 60 bits, which fits in a u64.
179//
180// r0 = a0×b0 + 19×(a1×b4 + a2×b3 + a3×b2 + a4×b1)
181// r0 < 2⁵²×2⁵² + 19×(2⁵²×2⁵² + 2⁵²×2⁵² + 2⁵²×2⁵² + 2⁵²×2⁵²)
182// r0 < (1 + 19 × 4) × 2⁵² × 2⁵²
183// r0 < 2⁷ × 2⁵² × 2⁵²
184// r0 < 2¹¹¹
185//
186// Moreover, the top coefficient (r4) is at most 107 bits, so c4 is at most
187// 56 bits, and c4 * 19 is at most 61 bits, which again fits in a u64 and
188// allows us to easily apply the reduction identity.
189//
190// r4 = a0×b4 + a1×b3 + a2×b2 + a3×b1 + a4×b0
191// r4 < 5 × 2⁵² × 2⁵²
192// r4 < 2¹⁰⁷
193//
194
195c0 := shift_right_by_51(r0)
196c1 := shift_right_by_51(r1)
197c2 := shift_right_by_51(r2)
198c3 := shift_right_by_51(r3)
199c4 := shift_right_by_51(r4)
200
201rr0 := r0.lo & mask_low_51_bits + c4 * 19
202rr1 := r1.lo & mask_low_51_bits + c0
203rr2 := r2.lo & mask_low_51_bits + c1
204rr3 := r3.lo & mask_low_51_bits + c2
205rr4 := r4.lo & mask_low_51_bits + c3
206
207// Now all coefficients fit into 64-bit registers but are still too large to
208// be passed around as a Element. We therefore do one last carry chain,
209// where the carries will be small enough to fit in the wiggle room above 2⁵¹.
210mut v := Element{
211l0: rr0
212l1: rr1
213l2: rr2
214l3: rr3
215l4: rr4
216}
217// v.carryPropagate()
218// using `carry_propagate_generic()` instead
219v = v.carry_propagate_generic()
220return v
221}
222
223// carry_propagate_generic brings the limbs below 52 bits by applying the reduction
224// identity (a * 2²⁵⁵ + b = a * 19 + b) to the l4 carry.
225fn (mut v Element) carry_propagate_generic() Element {
226c0 := v.l0 >> 51
227c1 := v.l1 >> 51
228c2 := v.l2 >> 51
229c3 := v.l3 >> 51
230c4 := v.l4 >> 51
231
232v.l0 = v.l0 & mask_low_51_bits + c4 * 19
233v.l1 = v.l1 & mask_low_51_bits + c0
234v.l2 = v.l2 & mask_low_51_bits + c1
235v.l3 = v.l3 & mask_low_51_bits + c2
236v.l4 = v.l4 & mask_low_51_bits + c3
237return v
238}
239
240fn fe_square_generic(a Element) Element {
241l0 := a.l0
242l1 := a.l1
243l2 := a.l2
244l3 := a.l3
245l4 := a.l4
246
247// Squaring works precisely like multiplication above, but thanks to its
248// symmetry we get to group a few terms together.
249//
250// l4 l3 l2 l1 l0 x
251// l4 l3 l2 l1 l0 =
252// ------------------------
253// l4l0 l3l0 l2l0 l1l0 l0l0 +
254// l4l1 l3l1 l2l1 l1l1 l0l1 +
255// l4l2 l3l2 l2l2 l1l2 l0l2 +
256// l4l3 l3l3 l2l3 l1l3 l0l3 +
257// l4l4 l3l4 l2l4 l1l4 l0l4 =
258// ----------------------------------------------
259// r8 r7 r6 r5 r4 r3 r2 r1 r0
260//
261// l4l0 l3l0 l2l0 l1l0 l0l0 +
262// l3l1 l2l1 l1l1 l0l1 19×l4l1 +
263// l2l2 l1l2 l0l2 19×l4l2 19×l3l2 +
264// l1l3 l0l3 19×l4l3 19×l3l3 19×l2l3 +
265// l0l4 19×l4l4 19×l3l4 19×l2l4 19×l1l4 =
266// --------------------------------------
267// r4 r3 r2 r1 r0
268//
269// With precomputed 2×, 19×, and 2×19× terms, we can compute each limb with
270// only three mul_64 and four Add64, instead of five and eight.
271
272l0_2 := l0 * 2
273l1_2 := l1 * 2
274
275l1_38 := l1 * 38
276l2_38 := l2 * 38
277l3_38 := l3 * 38
278
279l3_19 := l3 * 19
280l4_19 := l4 * 19
281
282// r0 = l0×l0 + 19×(l1×l4 + l2×l3 + l3×l2 + l4×l1) = l0×l0 + 19×2×(l1×l4 + l2×l3)
283mut r0 := mul_64(l0, l0)
284r0 = add_mul_64(r0, l1_38, l4)
285r0 = add_mul_64(r0, l2_38, l3)
286
287// r1 = l0×l1 + l1×l0 + 19×(l2×l4 + l3×l3 + l4×l2) = 2×l0×l1 + 19×2×l2×l4 + 19×l3×l3
288mut r1 := mul_64(l0_2, l1)
289r1 = add_mul_64(r1, l2_38, l4)
290r1 = add_mul_64(r1, l3_19, l3)
291
292// r2 = l0×l2 + l1×l1 + l2×l0 + 19×(l3×l4 + l4×l3) = 2×l0×l2 + l1×l1 + 19×2×l3×l4
293mut r2 := mul_64(l0_2, l2)
294r2 = add_mul_64(r2, l1, l1)
295r2 = add_mul_64(r2, l3_38, l4)
296
297// r3 = l0×l3 + l1×l2 + l2×l1 + l3×l0 + 19×l4×l4 = 2×l0×l3 + 2×l1×l2 + 19×l4×l4
298mut r3 := mul_64(l0_2, l3)
299r3 = add_mul_64(r3, l1_2, l2)
300r3 = add_mul_64(r3, l4_19, l4)
301
302// r4 = l0×l4 + l1×l3 + l2×l2 + l3×l1 + l4×l0 = 2×l0×l4 + 2×l1×l3 + l2×l2
303mut r4 := mul_64(l0_2, l4)
304r4 = add_mul_64(r4, l1_2, l3)
305r4 = add_mul_64(r4, l2, l2)
306
307c0 := shift_right_by_51(r0)
308c1 := shift_right_by_51(r1)
309c2 := shift_right_by_51(r2)
310c3 := shift_right_by_51(r3)
311c4 := shift_right_by_51(r4)
312
313rr0 := r0.lo & mask_low_51_bits + c4 * 19
314rr1 := r1.lo & mask_low_51_bits + c0
315rr2 := r2.lo & mask_low_51_bits + c1
316rr3 := r3.lo & mask_low_51_bits + c2
317rr4 := r4.lo & mask_low_51_bits + c3
318
319mut v := Element{
320l0: rr0
321l1: rr1
322l2: rr2
323l3: rr3
324l4: rr4
325}
326v = v.carry_propagate_generic()
327return v
328}
329
330// zero sets v = 0, and returns v.
331pub fn (mut v Element) zero() Element {
332v = fe_zero
333return v
334}
335
336// one sets v = 1, and returns v.
337pub fn (mut v Element) one() Element {
338v = fe_one
339return v
340}
341
342// reduce reduces v modulo 2^255 - 19 and returns it.
343pub fn (mut v Element) reduce() Element {
344v = v.carry_propagate_generic()
345
346// After the light reduction we now have a edwards25519 element representation
347// v < 2^255 + 2^13 * 19, but need v < 2^255 - 19.
348
349// If v >= 2^255 - 19, then v + 19 >= 2^255, which would overflow 2^255 - 1,
350// generating a carry. That is, c will be 0 if v < 2^255 - 19, and 1 otherwise.
351mut c := (v.l0 + 19) >> 51
352c = (v.l1 + c) >> 51
353c = (v.l2 + c) >> 51
354c = (v.l3 + c) >> 51
355c = (v.l4 + c) >> 51
356
357// If v < 2^255 - 19 and c = 0, this will be a no-op. Otherwise, it's
358// effectively applying the reduction identity to the carry.
359v.l0 += 19 * c
360
361v.l1 += v.l0 >> 51
362v.l0 = v.l0 & mask_low_51_bits
363v.l2 += v.l1 >> 51
364v.l1 = v.l1 & mask_low_51_bits
365v.l3 += v.l2 >> 51
366v.l2 = v.l2 & mask_low_51_bits
367v.l4 += v.l3 >> 51
368v.l3 = v.l3 & mask_low_51_bits
369// no additional carry
370v.l4 = v.l4 & mask_low_51_bits
371
372return v
373}
374
375// add sets v = a + b, and returns v.
376pub fn (mut v Element) add(a Element, b Element) Element {
377v.l0 = a.l0 + b.l0
378v.l1 = a.l1 + b.l1
379v.l2 = a.l2 + b.l2
380v.l3 = a.l3 + b.l3
381v.l4 = a.l4 + b.l4
382// Using the generic implementation here is actually faster than the
383// assembly. Probably because the body of this function is so simple that
384// the compiler can figure out better optimizations by inlining the carry
385// propagation.
386return v.carry_propagate_generic()
387}
388
389// subtract sets v = a - b, and returns v.
390pub fn (mut v Element) subtract(a Element, b Element) Element {
391// We first add 2 * p, to guarantee the subtraction won't underflow, and
392// then subtract b (which can be up to 2^255 + 2^13 * 19).
393v.l0 = (a.l0 + 0xFFFFFFFFFFFDA) - b.l0
394v.l1 = (a.l1 + 0xFFFFFFFFFFFFE) - b.l1
395v.l2 = (a.l2 + 0xFFFFFFFFFFFFE) - b.l2
396v.l3 = (a.l3 + 0xFFFFFFFFFFFFE) - b.l3
397v.l4 = (a.l4 + 0xFFFFFFFFFFFFE) - b.l4
398return v.carry_propagate_generic()
399}
400
401// negate sets v = -a, and returns v.
402pub fn (mut v Element) negate(a Element) Element {
403return v.subtract(fe_zero, a)
404}
405
406// invert sets v = 1/z mod p, and returns v.
407//
408// If z == 0, invert returns v = 0.
409pub fn (mut v Element) invert(z Element) Element {
410// Inversion is implemented as exponentiation with exponent p − 2. It uses the
411// same sequence of 255 squarings and 11 multiplications as [Curve25519].
412mut z2 := Element{}
413mut z9 := Element{}
414mut z11 := Element{}
415mut z2_5_0 := Element{}
416mut z2_10_0 := Element{}
417mut z2_20_0 := Element{}
418mut z2_50_0 := Element{}
419mut z2_100_0 := Element{}
420mut t := Element{}
421
422z2.square(z) // 2
423t.square(z2) // 4
424t.square(t) // 8
425z9.multiply(t, z) // 9
426z11.multiply(z9, z2) // 11
427t.square(z11) // 22
428z2_5_0.multiply(t, z9) // 31 = 2^5 - 2^0
429
430t.square(z2_5_0) // 2^6 - 2^1
431for i := 0; i < 4; i++ {
432t.square(t) // 2^10 - 2^5
433}
434z2_10_0.multiply(t, z2_5_0) // 2^10 - 2^0
435
436t.square(z2_10_0) // 2^11 - 2^1
437for i := 0; i < 9; i++ {
438t.square(t) // 2^20 - 2^10
439}
440z2_20_0.multiply(t, z2_10_0) // 2^20 - 2^0
441
442t.square(z2_20_0) // 2^21 - 2^1
443for i := 0; i < 19; i++ {
444t.square(t) // 2^40 - 2^20
445}
446t.multiply(t, z2_20_0) // 2^40 - 2^0
447
448t.square(t) // 2^41 - 2^1
449for i := 0; i < 9; i++ {
450t.square(t) // 2^50 - 2^10
451}
452z2_50_0.multiply(t, z2_10_0) // 2^50 - 2^0
453
454t.square(z2_50_0) // 2^51 - 2^1
455for i := 0; i < 49; i++ {
456t.square(t) // 2^100 - 2^50
457}
458z2_100_0.multiply(t, z2_50_0) // 2^100 - 2^0
459
460t.square(z2_100_0) // 2^101 - 2^1
461for i := 0; i < 99; i++ {
462t.square(t) // 2^200 - 2^100
463}
464t.multiply(t, z2_100_0) // 2^200 - 2^0
465
466t.square(t) // 2^201 - 2^1
467for i := 0; i < 49; i++ {
468t.square(t) // 2^250 - 2^50
469}
470t.multiply(t, z2_50_0) // 2^250 - 2^0
471
472t.square(t) // 2^251 - 2^1
473t.square(t) // 2^252 - 2^2
474t.square(t) // 2^253 - 2^3
475t.square(t) // 2^254 - 2^4
476t.square(t) // 2^255 - 2^5
477
478return v.multiply(t, z11) // 2^255 - 21
479}
480
481// square sets v = x * x, and returns v.
482pub fn (mut v Element) square(x Element) Element {
483v = fe_square_generic(x)
484return v
485}
486
487// multiply sets v = x * y, and returns v.
488pub fn (mut v Element) multiply(x Element, y Element) Element {
489v = fe_mul_generic(x, y)
490return v
491}
492
493// mul_51 returns lo + hi * 2⁵¹ = a * b.
494fn mul_51(a u64, b u32) (u64, u64) {
495mh, ml := bits.mul_64(a, u64(b))
496lo := ml & mask_low_51_bits
497hi := (mh << 13) | (ml >> 51)
498return lo, hi
499}
500
501// pow_22523 set v = x^((p-5)/8), and returns v. (p-5)/8 is 2^252-3.
502pub fn (mut v Element) pow_22523(x Element) Element {
503mut t0, mut t1, mut t2 := Element{}, Element{}, Element{}
504
505t0.square(x) // x^2
506t1.square(t0) // x^4
507t1.square(t1) // x^8
508t1.multiply(x, t1) // x^9
509t0.multiply(t0, t1) // x^11
510t0.square(t0) // x^22
511t0.multiply(t1, t0) // x^31
512t1.square(t0) // x^62
513for i := 1; i < 5; i++ { // x^992
514t1.square(t1)
515}
516t0.multiply(t1, t0) // x^1023 -> 1023 = 2^10 - 1
517t1.square(t0) // 2^11 - 2
518for i := 1; i < 10; i++ { // 2^20 - 2^10
519t1.square(t1)
520}
521t1.multiply(t1, t0) // 2^20 - 1
522t2.square(t1) // 2^21 - 2
523for i := 1; i < 20; i++ { // 2^40 - 2^20
524t2.square(t2)
525}
526t1.multiply(t2, t1) // 2^40 - 1
527t1.square(t1) // 2^41 - 2
528for i := 1; i < 10; i++ { // 2^50 - 2^10
529t1.square(t1)
530}
531t0.multiply(t1, t0) // 2^50 - 1
532t1.square(t0) // 2^51 - 2
533for i := 1; i < 50; i++ { // 2^100 - 2^50
534t1.square(t1)
535}
536t1.multiply(t1, t0) // 2^100 - 1
537t2.square(t1) // 2^101 - 2
538for i := 1; i < 100; i++ { // 2^200 - 2^100
539t2.square(t2)
540}
541t1.multiply(t2, t1) // 2^200 - 1
542t1.square(t1) // 2^201 - 2
543for i := 1; i < 50; i++ { // 2^250 - 2^50
544t1.square(t1)
545}
546t0.multiply(t1, t0) // 2^250 - 1
547t0.square(t0) // 2^251 - 2
548t0.square(t0) // 2^252 - 4
549return v.multiply(t0, x) // 2^252 - 3 -> x^(2^252-3)
550}
551
552// sqrt_ratio sets r to the non-negative square root of the ratio of u and v.
553//
554// If u/v is square, sqrt_ratio returns r and 1. If u/v is not square, sqrt_ratio
555// sets r according to Section 4.3 of draft-irtf-cfrg-ristretto255-decaf448-00,
556// and returns r and 0.
557pub fn (mut r Element) sqrt_ratio(u Element, v Element) (Element, int) {
558mut a, mut b := Element{}, Element{}
559
560// r = (u * v3) * (u * v7)^((p-5)/8)
561v2 := a.square(v)
562uv3 := b.multiply(u, b.multiply(v2, v))
563uv7 := a.multiply(uv3, a.square(v2))
564r.multiply(uv3, r.pow_22523(uv7))
565
566mut check := a.multiply(v, a.square(r)) // check = v * r^2
567
568mut uneg := b.negate(u)
569correct_sign_sqrt := check.equal(u)
570flipped_sign_sqrt := check.equal(uneg)
571flipped_sign_sqrt_i := check.equal(uneg.multiply(uneg, sqrt_m1))
572
573rprime := b.multiply(r, sqrt_m1) // r_prime = SQRT_M1 * r
574// r = CT_selected(r_prime IF flipped_sign_sqrt | flipped_sign_sqrt_i ELSE r)
575r.selected(rprime, r, flipped_sign_sqrt | flipped_sign_sqrt_i)
576
577r.absolute(r) // Choose the nonnegative square root.
578return r, correct_sign_sqrt | flipped_sign_sqrt
579}
580
581// mask_64_bits returns 0xffffffff if cond is 1, and 0 otherwise.
582fn mask_64_bits(cond int) u64 {
583// in go, `^` operates on bit mean NOT, flip bit
584// in v, its a ~ bitwise NOT
585return ~(u64(cond) - 1)
586}
587
588// selected sets v to a if cond == 1, and to b if cond == 0.
589pub fn (mut v Element) selected(a Element, b Element, cond int) Element {
590// see above notes
591m := mask_64_bits(cond)
592v.l0 = (m & a.l0) | (~m & b.l0)
593v.l1 = (m & a.l1) | (~m & b.l1)
594v.l2 = (m & a.l2) | (~m & b.l2)
595v.l3 = (m & a.l3) | (~m & b.l3)
596v.l4 = (m & a.l4) | (~m & b.l4)
597return v
598}
599
600// is_negative returns 1 if v is negative, and 0 otherwise.
601pub fn (mut v Element) is_negative() int {
602return int(v.bytes()[0] & 1)
603}
604
605// absolute sets v to |u|, and returns v.
606pub fn (mut v Element) absolute(u Element) Element {
607mut e := Element{}
608mut uk := u
609return v.selected(e.negate(uk), uk, uk.is_negative())
610}
611
612// set sets v = a, and returns v.
613pub fn (mut v Element) set(a Element) Element {
614v = a
615return v
616}
617
618// set_bytes sets v to x, where x is a 32-byte little-endian encoding. If x is
619// not of the right length, SetUniformBytes returns an error, and the
620// receiver is unchanged.
621//
622// Consistent with RFC 7748, the most significant bit (the high bit of the
623// last byte) is ignored, and non-canonical values (2^255-19 through 2^255-1)
624// are accepted. Note that this is laxer than specified by RFC 8032.
625pub fn (mut v Element) set_bytes(x []u8) !Element {
626if x.len != 32 {
627return error('edwards25519: invalid edwards25519 element input size')
628}
629
630// Bits 0:51 (bytes 0:8, bits 0:64, shift 0, mask 51).
631v.l0 = binary.little_endian_u64(x[0..8])
632v.l0 &= mask_low_51_bits
633// Bits 51:102 (bytes 6:14, bits 48:112, shift 3, mask 51).
634v.l1 = binary.little_endian_u64(x[6..14]) >> 3
635v.l1 &= mask_low_51_bits
636// Bits 102:153 (bytes 12:20, bits 96:160, shift 6, mask 51).
637v.l2 = binary.little_endian_u64(x[12..20]) >> 6
638v.l2 &= mask_low_51_bits
639// Bits 153:204 (bytes 19:27, bits 152:216, shift 1, mask 51).
640v.l3 = binary.little_endian_u64(x[19..27]) >> 1
641v.l3 &= mask_low_51_bits
642// Bits 204:251 (bytes 24:32, bits 192:256, shift 12, mask 51).
643// Note: not bytes 25:33, shift 4, to avoid overread.
644v.l4 = binary.little_endian_u64(x[24..32]) >> 12
645v.l4 &= mask_low_51_bits
646
647return v
648}
649
650// bytes returns the canonical 32-byte little-endian encoding of v.
651pub fn (mut v Element) bytes() []u8 {
652// This function is outlined to make the allocations inline in the caller
653// rather than happen on the heap.
654// out := v.bytes_generic()
655return v.bytes_generic()
656}
657
658fn (mut v Element) bytes_generic() []u8 {
659mut out := []u8{len: 32}
660
661v = v.reduce()
662
663mut buf := []u8{len: 8}
664idxs := [v.l0, v.l1, v.l2, v.l3, v.l4]
665for i, l in idxs {
666bits_offset := i * 51
667binary.little_endian_put_u64(mut buf, l << u32(bits_offset % 8))
668for j, bb in buf {
669off := bits_offset / 8 + j
670if off >= out.len {
671break
672}
673out[off] |= bb
674}
675}
676
677return out
678}
679
680// equal returns 1 if v and u are equal, and 0 otherwise.
681pub fn (mut v Element) equal(ue Element) int {
682mut u := ue
683sa := u.bytes()
684sv := v.bytes()
685return subtle.constant_time_compare(sa, sv)
686}
687
688// swap swaps v and u if cond == 1 or leaves them unchanged if cond == 0, and returns v.
689pub fn (mut v Element) swap(mut u Element, cond int) {
690// mut u := ue
691m := mask_64_bits(cond)
692mut t := m & (v.l0 ^ u.l0)
693v.l0 ^= t
694u.l0 ^= t
695t = m & (v.l1 ^ u.l1)
696v.l1 ^= t
697u.l1 ^= t
698t = m & (v.l2 ^ u.l2)
699v.l2 ^= t
700u.l2 ^= t
701t = m & (v.l3 ^ u.l3)
702v.l3 ^= t
703u.l3 ^= t
704t = m & (v.l4 ^ u.l4)
705v.l4 ^= t
706u.l4 ^= t
707}
708
709// mult_32 sets v = x * y, and returns v.
710pub fn (mut v Element) mult_32(x Element, y u32) Element {
711x0lo, x0hi := mul_51(x.l0, y)
712x1lo, x1hi := mul_51(x.l1, y)
713x2lo, x2hi := mul_51(x.l2, y)
714x3lo, x3hi := mul_51(x.l3, y)
715x4lo, x4hi := mul_51(x.l4, y)
716v.l0 = x0lo + 19 * x4hi // carried over per the reduction identity
717v.l1 = x1lo + x0hi
718v.l2 = x2lo + x1hi
719v.l3 = x3lo + x2hi
720v.l4 = x4lo + x3hi
721// The hi portions are going to be only 32 bits, plus any previous excess,
722// so we can skip the carry propagation.
723return v
724}
725
726fn swap_endianness(mut buf []u8) []u8 {
727for i := 0; i < buf.len / 2; i++ {
728buf[i], buf[buf.len - i - 1] = buf[buf.len - i - 1], buf[i]
729}
730return buf
731}
732