forked from tuneinsight/lattigo
-
Notifications
You must be signed in to change notification settings - Fork 0
/
ringqp.go
618 lines (522 loc) · 14.7 KB
/
ringqp.go
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
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
// Package ringqp is implements a wrapper for both the ringQ and ringP.
package ringqp
import (
"github.com/fedejinich/lattigo/v5/ring"
"github.com/fedejinich/lattigo/v5/utils"
)
// Poly represents a polynomial in the ring of polynomial modulo Q*P.
// This type is simply the union type between two ring.Poly, each one
// containing the modulus Q and P coefficients of that polynomial.
// The modulus Q represent the ciphertext modulus and the modulus P
// the special primes for the RNS decomposition during homomorphic
// operations involving keys.
type Poly struct {
Q, P *ring.Poly
}
// LevelQ returns the level of the polynomial modulo Q.
// Returns -1 if the modulus Q is absent.
func (p *Poly) LevelQ() int {
if p.Q != nil {
return p.Q.Level()
}
return -1
}
// LevelP returns the level of the polynomial modulo P.
// Returns -1 if the modulus P is absent.
func (p *Poly) LevelP() int {
if p.P != nil {
return p.P.Level()
}
return -1
}
// Equals returns true if the receiver Poly is equal to the provided other Poly.
// This method checks for equality of its two sub-polynomials.
func (p *Poly) Equals(other Poly) (v bool) {
if p == &other {
return true
}
v = true
if p.Q != nil {
v = p.Q.Equals(other.Q)
}
if p.P != nil {
v = v && p.P.Equals(other.P)
}
return v
}
// Copy copies the coefficients of other on the target polynomial.
// This method simply calls the Copy method for each of its sub-polynomials.
func (p *Poly) Copy(other Poly) {
if p.Q != nil {
copy(p.Q.Buff, other.Q.Buff)
}
if p.P != nil {
copy(p.P.Buff, other.P.Buff)
}
}
// CopyLvl copies the values of p1 on p2.
// The operation is performed at levelQ for the ringQ and levelP for the ringP.
func CopyLvl(levelQ, levelP int, p1, p2 Poly) {
if p1.Q != nil && p2.Q != nil {
ring.CopyLvl(levelQ, p1.Q, p2.Q)
}
if p1.P != nil && p2.P != nil {
ring.CopyLvl(levelP, p1.P, p2.P)
}
}
// CopyNew creates an exact copy of the target polynomial.
func (p *Poly) CopyNew() Poly {
if p == nil {
return Poly{}
}
var Q, P *ring.Poly
if p.Q != nil {
Q = p.Q.CopyNew()
}
if p.P != nil {
P = p.P.CopyNew()
}
return Poly{Q, P}
}
// Ring is a structure that implements the operation in the ring R_QP.
// This type is simply a union type between the two Ring types representing
// R_Q and R_P.
type Ring struct {
RingQ, RingP *ring.Ring
}
// AtLevel returns a shallow copy of the target ring configured to
// carry on operations at the specified levels.
func (r *Ring) AtLevel(levelQ, levelP int) *Ring {
var ringQ, ringP *ring.Ring
if levelQ > -1 && r.RingQ != nil {
ringQ = r.RingQ.AtLevel(levelQ)
}
if levelP > -1 && r.RingP != nil {
ringP = r.RingP.AtLevel(levelP)
}
return &Ring{
RingQ: ringQ,
RingP: ringP,
}
}
// LevelQ returns the level at which the target
// ring operates for the modulus Q.
func (r *Ring) LevelQ() int {
if r.RingQ != nil {
return r.RingQ.Level()
}
return -1
}
// LevelP returns the level at which the target
// ring operates for the modulus P.
func (r *Ring) LevelP() int {
if r.RingP != nil {
return r.RingP.Level()
}
return -1
}
// NewPoly creates a new polynomial with all coefficients set to 0.
func (r *Ring) NewPoly() Poly {
var Q, P *ring.Poly
if r.RingQ != nil {
Q = r.RingQ.NewPoly()
}
if r.RingP != nil {
P = r.RingP.NewPoly()
}
return Poly{Q, P}
}
// Add adds p1 to p2 coefficient-wise and writes the result on p3.
func (r *Ring) Add(p1, p2, p3 Poly) {
if r.RingQ != nil {
r.RingQ.Add(p1.Q, p2.Q, p3.Q)
}
if r.RingP != nil {
r.RingP.Add(p1.P, p2.P, p3.P)
}
}
// AddLazy adds p1 to p2 coefficient-wise and writes the result on p3 without modular reduction.
func (r *Ring) AddLazy(p1, p2, p3 Poly) {
if r.RingQ != nil {
r.RingQ.AddLazy(p1.Q, p2.Q, p3.Q)
}
if r.RingP != nil {
r.RingP.AddLazy(p1.P, p2.P, p3.P)
}
}
// Sub subtracts p2 to p1 coefficient-wise and writes the result on p3.
func (r *Ring) Sub(p1, p2, p3 Poly) {
if r.RingQ != nil {
r.RingQ.Sub(p1.Q, p2.Q, p3.Q)
}
if r.RingP != nil {
r.RingP.Sub(p1.P, p2.P, p3.P)
}
}
// Neg negates p1 coefficient-wise and writes the result on p2.
func (r *Ring) Neg(p1, p2 Poly) {
if r.RingQ != nil {
r.RingQ.Neg(p1.Q, p2.Q)
}
if r.RingP != nil {
r.RingP.Neg(p1.P, p2.P)
}
}
// NewRNSScalar creates a new Scalar value (i.e., a degree-0 polynomial) in the RingQP.
func (r *Ring) NewRNSScalar() ring.RNSScalar {
modlen := r.RingQ.ModuliChainLength()
if r.RingP != nil {
modlen += r.RingP.ModuliChainLength()
}
return make(ring.RNSScalar, modlen)
}
// NewRNSScalarFromUInt64 creates a new Scalar in the RingQP initialized with value v.
func (r *Ring) NewRNSScalarFromUInt64(v uint64) ring.RNSScalar {
var scalarQ, scalarP []uint64
if r.RingQ != nil {
scalarQ = r.RingQ.NewRNSScalarFromUInt64(v)
}
if r.RingP != nil {
scalarP = r.RingP.NewRNSScalarFromUInt64(v)
}
return append(scalarQ, scalarP...)
}
// SubRNSScalar subtracts s2 to s1 and stores the result in sout.
func (r *Ring) SubRNSScalar(s1, s2, sout ring.RNSScalar) {
qlen := r.RingQ.ModuliChainLength()
if r.RingQ != nil {
r.RingQ.SubRNSScalar(s1[:qlen], s2[:qlen], sout[:qlen])
}
if r.RingP != nil {
r.RingP.SubRNSScalar(s1[qlen:], s2[qlen:], sout[qlen:])
}
}
// MulRNSScalar multiplies s1 and s2 and stores the result in sout.
func (r *Ring) MulRNSScalar(s1, s2, sout ring.RNSScalar) {
qlen := r.RingQ.ModuliChainLength()
if r.RingQ != nil {
r.RingQ.MulRNSScalar(s1[:qlen], s2[:qlen], sout[:qlen])
}
if r.RingP != nil {
r.RingP.MulRNSScalar(s1[qlen:], s2[qlen:], sout[qlen:])
}
}
// EvalPolyScalar evaluate the polynomial pol at pt and writes the result in p3
func (r *Ring) EvalPolyScalar(pol []Poly, pt uint64, p3 Poly) {
polQ, polP := make([]*ring.Poly, len(pol)), make([]*ring.Poly, len(pol))
for i, coeff := range pol {
polQ[i] = coeff.Q
polP[i] = coeff.P
}
r.RingQ.EvalPolyScalar(polQ, pt, p3.Q)
if r.RingP != nil {
r.RingP.EvalPolyScalar(polP, pt, p3.P)
}
}
// MulScalar multiplies p1 by scalar and returns the result in p2.
func (r *Ring) MulScalar(p1 Poly, scalar uint64, p2 Poly) {
if r.RingQ != nil {
r.RingQ.MulScalar(p1.Q, scalar, p2.Q)
}
if r.RingP != nil {
r.RingP.MulScalar(p1.P, scalar, p2.P)
}
}
// NTT computes the NTT of p1 and returns the result on p2.
func (r *Ring) NTT(p1, p2 Poly) {
if r.RingQ != nil {
r.RingQ.NTT(p1.Q, p2.Q)
}
if r.RingP != nil {
r.RingP.NTT(p1.P, p2.P)
}
}
// INTT computes the inverse-NTT of p1 and returns the result on p2.
func (r *Ring) INTT(p1, p2 Poly) {
if r.RingQ != nil {
r.RingQ.INTT(p1.Q, p2.Q)
}
if r.RingP != nil {
r.RingP.INTT(p1.P, p2.P)
}
}
// NTTLazy computes the NTT of p1 and returns the result on p2.
// Output values are in the range [0, 2q-1].
func (r *Ring) NTTLazy(p1, p2 Poly) {
if r.RingQ != nil {
r.RingQ.NTTLazy(p1.Q, p2.Q)
}
if r.RingP != nil {
r.RingP.NTTLazy(p1.P, p2.P)
}
}
// MForm switches p1 to the Montgomery domain and writes the result on p2.
func (r *Ring) MForm(p1, p2 Poly) {
if r.RingQ != nil {
r.RingQ.MForm(p1.Q, p2.Q)
}
if r.RingP != nil {
r.RingP.MForm(p1.P, p2.P)
}
}
// IMForm switches back p1 from the Montgomery domain to the conventional domain and writes the result on p2.
func (r *Ring) IMForm(p1, p2 Poly) {
if r.RingQ != nil {
r.RingQ.IMForm(p1.Q, p2.Q)
}
if r.RingP != nil {
r.RingP.IMForm(p1.P, p2.P)
}
}
// MulCoeffsMontgomery multiplies p1 by p2 coefficient-wise with a Montgomery modular reduction.
func (r *Ring) MulCoeffsMontgomery(p1, p2, p3 Poly) {
if r.RingQ != nil {
r.RingQ.MulCoeffsMontgomery(p1.Q, p2.Q, p3.Q)
}
if r.RingP != nil {
r.RingP.MulCoeffsMontgomery(p1.P, p2.P, p3.P)
}
}
// MulCoeffsMontgomeryLazy multiplies p1 by p2 coefficient-wise with a constant-time Montgomery modular reduction.
// Result is within [0, 2q-1].
func (r *Ring) MulCoeffsMontgomeryLazy(p1, p2, p3 Poly) {
if r.RingQ != nil {
r.RingQ.MulCoeffsMontgomeryLazy(p1.Q, p2.Q, p3.Q)
}
if r.RingP != nil {
r.RingP.MulCoeffsMontgomeryLazy(p1.P, p2.P, p3.P)
}
}
// MulCoeffsMontgomeryLazyThenAddLazy multiplies p1 by p2 coefficient-wise with a
// constant-time Montgomery modular reduction and adds the result on p3.
// Result is within [0, 2q-1]
func (r *Ring) MulCoeffsMontgomeryLazyThenAddLazy(p1, p2, p3 Poly) {
if r.RingQ != nil {
r.RingQ.MulCoeffsMontgomeryLazyThenAddLazy(p1.Q, p2.Q, p3.Q)
}
if r.RingP != nil {
r.RingP.MulCoeffsMontgomeryLazyThenAddLazy(p1.P, p2.P, p3.P)
}
}
// MulCoeffsMontgomeryThenSub multiplies p1 by p2 coefficient-wise with
// a Montgomery modular reduction and subtracts the result from p3.
func (r *Ring) MulCoeffsMontgomeryThenSub(p1, p2, p3 Poly) {
if r.RingQ != nil {
r.RingQ.MulCoeffsMontgomeryThenSub(p1.Q, p2.Q, p3.Q)
}
if r.RingP != nil {
r.RingP.MulCoeffsMontgomeryThenSub(p1.P, p2.P, p3.P)
}
}
// MulCoeffsMontgomeryLazyThenSubLazy multiplies p1 by p2 coefficient-wise with
// a Montgomery modular reduction and subtracts the result from p3.
func (r *Ring) MulCoeffsMontgomeryLazyThenSubLazy(p1, p2, p3 Poly) {
if r.RingQ != nil {
r.RingQ.MulCoeffsMontgomeryLazyThenSubLazy(p1.Q, p2.Q, p3.Q)
}
if r.RingP != nil {
r.RingP.MulCoeffsMontgomeryLazyThenSubLazy(p1.P, p2.P, p3.P)
}
}
// MulCoeffsMontgomeryThenAdd multiplies p1 by p2 coefficient-wise with a
// Montgomery modular reduction and adds the result to p3.
func (r *Ring) MulCoeffsMontgomeryThenAdd(p1, p2, p3 Poly) {
if r.RingQ != nil {
r.RingQ.MulCoeffsMontgomeryThenAdd(p1.Q, p2.Q, p3.Q)
}
if r.RingP != nil {
r.RingP.MulCoeffsMontgomeryThenAdd(p1.P, p2.P, p3.P)
}
}
// MulRNSScalarMontgomery multiplies p with a scalar value expressed in the CRT decomposition.
// It assumes the scalar decomposition to be in Montgomery form.
func (r *Ring) MulRNSScalarMontgomery(p Poly, scalar []uint64, pOut Poly) {
scalarQ, scalarP := scalar[:r.RingQ.ModuliChainLength()], scalar[r.RingQ.ModuliChainLength():]
if r.RingQ != nil {
r.RingQ.MulRNSScalarMontgomery(p.Q, scalarQ, pOut.Q)
}
if r.RingP != nil {
r.RingP.MulRNSScalarMontgomery(p.P, scalarP, pOut.P)
}
}
// Inverse computes the modular inverse of a scalar a expressed in a CRT decomposition.
// The inversion is done in-place and assumes that a is in Montgomery form.
func (r *Ring) Inverse(scalar ring.RNSScalar) {
scalarQ, scalarP := scalar[:r.RingQ.ModuliChainLength()], scalar[r.RingQ.ModuliChainLength():]
if r.RingQ != nil {
r.RingQ.Inverse(scalarQ)
}
if r.RingP != nil {
r.RingP.Inverse(scalarP)
}
}
// Reduce applies the modular reduction on the coefficients of p1 and returns the result on p2.
func (r *Ring) Reduce(p1, p2 Poly) {
if r.RingQ != nil {
r.RingQ.Reduce(p1.Q, p2.Q)
}
if r.RingP != nil {
r.RingP.Reduce(p1.P, p2.P)
}
}
// PermuteNTTWithIndex applies the automorphism X^{5^j} on p1 and writes the result on p2.
// Index of automorphism must be provided.
// Method is not in place.
func (r *Ring) PermuteNTTWithIndex(p1 Poly, index []uint64, p2 Poly) {
if r.RingQ != nil {
r.RingQ.PermuteNTTWithIndex(p1.Q, index, p2.Q)
}
if r.RingP != nil {
r.RingP.PermuteNTTWithIndex(p1.P, index, p2.P)
}
}
// PermuteNTTWithIndexThenAddLazy applies the automorphism X^{5^j} on p1 and adds the result on p2.
// Index of automorphism must be provided.
// Method is not in place.
func (r *Ring) PermuteNTTWithIndexThenAddLazy(p1 Poly, index []uint64, p2 Poly) {
if r.RingQ != nil {
r.RingQ.PermuteNTTWithIndexThenAddLazy(p1.Q, index, p2.Q)
}
if r.RingP != nil {
r.RingP.PermuteNTTWithIndexThenAddLazy(p1.P, index, p2.P)
}
}
// ExtendBasisSmallNormAndCenter extends a small-norm polynomial polQ in R_Q to a polynomial
// polQP in R_QP.
func (r *Ring) ExtendBasisSmallNormAndCenter(polyInQ *ring.Poly, levelP int, polyOutQ, polyOutP *ring.Poly) {
var coeff, Q, QHalf, sign uint64
Q = r.RingQ.SubRings[0].Modulus
QHalf = Q >> 1
if polyInQ != polyOutQ && polyOutQ != nil {
polyOutQ.Copy(polyInQ)
}
P := r.RingP.ModuliChain()
N := r.RingQ.N()
for j := 0; j < N; j++ {
coeff = polyInQ.Coeffs[0][j]
sign = 1
if coeff > QHalf {
coeff = Q - coeff
sign = 0
}
for i, pi := range P[:levelP+1] {
polyOutP.Coeffs[i][j] = (coeff * sign) | (pi-coeff)*(sign^1)
}
}
}
// MarshalBinarySize64 returns the length in byte of the target Poly.
// Assumes that each coefficient uses 8 bytes.
func (p *Poly) MarshalBinarySize64() (dataLen int) {
dataLen = 2
if p.Q != nil {
dataLen += p.Q.MarshalBinarySize64()
}
if p.P != nil {
dataLen += p.P.MarshalBinarySize64()
}
return
}
// Encode64 writes a Poly on the input data.
// Encodes each coefficient on 8 bytes.
func (p *Poly) Encode64(data []byte) (pt int, err error) {
var inc int
if p.Q != nil {
data[0] = 1
}
if p.P != nil {
data[1] = 1
}
pt = 2
if data[0] == 1 {
if inc, err = p.Q.Encode64(data[pt:]); err != nil {
return
}
pt += inc
}
if data[1] == 1 {
if inc, err = p.P.Encode64(data[pt:]); err != nil {
return
}
pt += inc
}
return
}
// Decode64 decodes the input bytes on the target Poly.
// Writes on pre-allocated coefficients.
// Assumes that each coefficient is encoded on 8 bytes.
func (p *Poly) Decode64(data []byte) (pt int, err error) {
var inc int
pt = 2
if data[0] == 1 {
if p.Q == nil {
p.Q = new(ring.Poly)
}
if inc, err = p.Q.Decode64(data[pt:]); err != nil {
return
}
pt += inc
}
if data[1] == 1 {
if p.P == nil {
p.P = new(ring.Poly)
}
if inc, err = p.P.Decode64(data[pt:]); err != nil {
return
}
pt += inc
}
return
}
func (p *Poly) MarshalBinary() ([]byte, error) {
b := make([]byte, p.MarshalBinarySize64())
_, err := p.Encode64(b)
return b, err
}
func (p *Poly) UnmarshalBinary(b []byte) error {
_, err := p.Decode64(b)
return err
}
// UniformSampler is a type for sampling polynomials in Ring.
type UniformSampler struct {
samplerQ, samplerP *ring.UniformSampler
}
// NewUniformSampler instantiates a new UniformSampler from a given PRNG.
func NewUniformSampler(prng utils.PRNG, r Ring) (s UniformSampler) {
if r.RingQ != nil {
s.samplerQ = ring.NewUniformSampler(prng, r.RingQ)
}
if r.RingP != nil {
s.samplerP = ring.NewUniformSampler(prng, r.RingP)
}
return s
}
// AtLevel returns a shallow copy of the target sampler that operates at the specified levels.
func (s UniformSampler) AtLevel(levelQ, levelP int) UniformSampler {
var samplerQ, samplerP *ring.UniformSampler
if levelQ > -1 {
samplerQ = s.samplerQ.AtLevel(levelQ)
}
if levelP > -1 {
samplerP = s.samplerP.AtLevel(levelP)
}
return UniformSampler{
samplerQ: samplerQ,
samplerP: samplerP,
}
}
// Read samples a new polynomial in Ring and stores it into p.
func (s UniformSampler) Read(p Poly) {
if p.Q != nil && s.samplerQ != nil {
s.samplerQ.Read(p.Q)
}
if p.P != nil && s.samplerP != nil {
s.samplerP.Read(p.P)
}
}
func (s UniformSampler) WithPRNG(prng utils.PRNG) UniformSampler {
sp := UniformSampler{samplerQ: s.samplerQ.WithPRNG(prng)}
if s.samplerP != nil {
sp.samplerP = s.samplerP.WithPRNG(prng)
}
return sp
}