/
ring_sampler_gaussian.go
292 lines (245 loc) · 11.3 KB
/
ring_sampler_gaussian.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
package ring
import (
"encoding/binary"
"math"
"github.com/ldsec/lattigo/v2/utils"
)
// GaussianSampler keeps the state of a truncated Gaussian polynomial sampler.
type GaussianSampler struct {
baseSampler
sigma float64
bound int
randomBufferN []byte
ptr uint64
}
// NewGaussianSampler creates a new instance of GaussianSampler from a PRNG, a ring definition and the truncated
// Gaussian distribution parameters. Sigma is the desired standard deviation and bound is the maximum coefficient norm in absolute
// value.
func NewGaussianSampler(prng utils.PRNG, baseRing *Ring, sigma float64, bound int) *GaussianSampler {
gaussianSampler := new(GaussianSampler)
gaussianSampler.prng = prng
gaussianSampler.randomBufferN = make([]byte, 1024)
gaussianSampler.ptr = 0
gaussianSampler.baseRing = baseRing
gaussianSampler.sigma = sigma
gaussianSampler.bound = bound
return gaussianSampler
}
// Read samples a truncated Gaussian polynomial on "pol" at the maximum level in the default ring, standard deviation and bound.
func (gaussianSampler *GaussianSampler) Read(pol *Poly) {
gaussianSampler.ReadLvl(len(gaussianSampler.baseRing.Modulus)-1, pol)
}
// ReadLvl samples a truncated Gaussian polynomial at the provided level, in the default ring, standard deviation and bound.
func (gaussianSampler *GaussianSampler) ReadLvl(level int, pol *Poly) {
gaussianSampler.readLvl(level, pol, gaussianSampler.baseRing, gaussianSampler.sigma, gaussianSampler.bound)
}
// ReadNew samples a new truncated Gaussian polynomial at the maximum level in the default ring, standard deviation and bound.
func (gaussianSampler *GaussianSampler) ReadNew() (pol *Poly) {
pol = gaussianSampler.baseRing.NewPoly()
gaussianSampler.Read(pol)
return pol
}
// ReadLvlNew samples a new truncated Gaussian polynomial at the provided level, in the default ring, standard deviation and bound.
func (gaussianSampler *GaussianSampler) ReadLvlNew(level int) (pol *Poly) {
pol = gaussianSampler.baseRing.NewPolyLvl(level)
gaussianSampler.ReadLvl(level, pol)
return pol
}
// ReadFromDistLvl samples a truncated Gaussian polynomial at the given level in the provided ring, standard deviation and bound.
func (gaussianSampler *GaussianSampler) ReadFromDistLvl(level int, pol *Poly, ring *Ring, sigma float64, bound int) {
gaussianSampler.readLvl(level, pol, ring, sigma, bound)
}
// ReadAndAddLvl samples a truncated Gaussian polynomial at the given level for the receiver's default standard deviation and bound and adds it on "pol".
func (gaussianSampler *GaussianSampler) ReadAndAddLvl(level int, pol *Poly) {
gaussianSampler.ReadAndAddFromDistLvl(level, pol, gaussianSampler.baseRing, gaussianSampler.sigma, gaussianSampler.bound)
}
// ReadAndAddFromDistLvl samples a truncated Gaussian polynomial at the given level in the provided ring, standard deviation and bound and adds it on "pol".
func (gaussianSampler *GaussianSampler) ReadAndAddFromDistLvl(level int, pol *Poly, ring *Ring, sigma float64, bound int) {
var coeffFlo float64
var coeffInt, sign uint64
gaussianSampler.prng.Clock(gaussianSampler.randomBufferN)
modulus := ring.Modulus[:level+1]
for i := 0; i < ring.N; i++ {
for {
coeffFlo, sign = gaussianSampler.normFloat64()
if coeffInt = uint64(coeffFlo*sigma + 0.5); coeffInt <= uint64(bound) {
break
}
}
for j, qi := range modulus {
pol.Coeffs[j][i] = CRed(pol.Coeffs[j][i]+((coeffInt*sign)|(qi-coeffInt)*(sign^1)), qi)
}
}
}
func (gaussianSampler *GaussianSampler) readLvl(level int, pol *Poly, ring *Ring, sigma float64, bound int) {
var coeffFlo float64
var coeffInt uint64
var sign uint64
gaussianSampler.prng.Clock(gaussianSampler.randomBufferN)
modulus := ring.Modulus[:level+1]
for i := 0; i < ring.N; i++ {
for {
coeffFlo, sign = gaussianSampler.normFloat64()
if coeffInt = uint64(coeffFlo*sigma + 0.5); coeffInt <= uint64(bound) {
break
}
}
for j, qi := range modulus {
pol.Coeffs[j][i] = (coeffInt * sign) | (qi-coeffInt)*(sign^1)
}
}
}
// randFloat64 returns a uniform float64 value between 0 and 1.
func randFloat64(randomBytes []byte) float64 {
return float64(binary.BigEndian.Uint64(randomBytes)&0x1fffffffffffff) / float64(0x1fffffffffffff)
}
// NormFloat64 returns a normally distributed float64 in
// the range [-math.MaxFloat64, +math.MaxFloat64], bounds included,
// with standard normal distribution (mean = 0, stddev = 1).
// To produce a different normal distribution, callers can
// adjust the output using:
//
// sample = NormFloat64() * desiredStdDev + desiredMean
// Algorithm adapted from https://golang.org/src/math/rand/normal.go
// to use a secure PRNG instead of math/rand.
func (gaussianSampler *GaussianSampler) normFloat64() (float64, uint64) {
for {
if gaussianSampler.ptr == uint64(len(gaussianSampler.randomBufferN)) {
gaussianSampler.prng.Clock(gaussianSampler.randomBufferN)
gaussianSampler.ptr = 0
}
juint32 := binary.BigEndian.Uint32(gaussianSampler.randomBufferN[gaussianSampler.ptr : gaussianSampler.ptr+4])
gaussianSampler.ptr += 8
j := int32(juint32 & 0x7fffffff)
sign := uint64(juint32 >> 31)
i := j & 0x7F
x := float64(j) * float64(wn[i])
// 1
if uint32(j) < kn[i] {
// This case should be hit more than 99% of the time.
return x, sign
}
// 2
if i == 0 {
// This extra work is only required for the base strip.
for {
if gaussianSampler.ptr == uint64(len(gaussianSampler.randomBufferN)) {
gaussianSampler.prng.Clock(gaussianSampler.randomBufferN)
gaussianSampler.ptr = 0
}
x = -math.Log(randFloat64(gaussianSampler.randomBufferN[gaussianSampler.ptr:gaussianSampler.ptr+8])) * (1.0 / 3.442619855899)
gaussianSampler.ptr += 8
if gaussianSampler.ptr == uint64(len(gaussianSampler.randomBufferN)) {
gaussianSampler.prng.Clock(gaussianSampler.randomBufferN)
gaussianSampler.ptr = 0
}
y := -math.Log(randFloat64(gaussianSampler.randomBufferN[gaussianSampler.ptr : gaussianSampler.ptr+8]))
gaussianSampler.ptr += 8
if y+y >= x*x {
break
}
}
return x + 3.442619855899, sign
}
if gaussianSampler.ptr == uint64(len(gaussianSampler.randomBufferN)) {
gaussianSampler.prng.Clock(gaussianSampler.randomBufferN)
gaussianSampler.ptr = 0
}
// 3
if fn[i]+float32(randFloat64(gaussianSampler.randomBufferN[gaussianSampler.ptr:gaussianSampler.ptr+8]))*(fn[i-1]-fn[i]) < float32(math.Exp(-0.5*x*x)) {
gaussianSampler.ptr += 8
return x, sign
}
gaussianSampler.ptr += 8
}
}
var kn = [128]uint32{
0x76ad2212, 0x0, 0x600f1b53, 0x6ce447a6, 0x725b46a2,
0x7560051d, 0x774921eb, 0x789a25bd, 0x799045c3, 0x7a4bce5d,
0x7adf629f, 0x7b5682a6, 0x7bb8a8c6, 0x7c0ae722, 0x7c50cce7,
0x7c8cec5b, 0x7cc12cd6, 0x7ceefed2, 0x7d177e0b, 0x7d3b8883,
0x7d5bce6c, 0x7d78dd64, 0x7d932886, 0x7dab0e57, 0x7dc0dd30,
0x7dd4d688, 0x7de73185, 0x7df81cea, 0x7e07c0a3, 0x7e163efa,
0x7e23b587, 0x7e303dfd, 0x7e3beec2, 0x7e46db77, 0x7e51155d,
0x7e5aabb3, 0x7e63abf7, 0x7e6c222c, 0x7e741906, 0x7e7b9a18,
0x7e82adfa, 0x7e895c63, 0x7e8fac4b, 0x7e95a3fb, 0x7e9b4924,
0x7ea0a0ef, 0x7ea5b00d, 0x7eaa7ac3, 0x7eaf04f3, 0x7eb3522a,
0x7eb765a5, 0x7ebb4259, 0x7ebeeafd, 0x7ec2620a, 0x7ec5a9c4,
0x7ec8c441, 0x7ecbb365, 0x7ece78ed, 0x7ed11671, 0x7ed38d62,
0x7ed5df12, 0x7ed80cb4, 0x7eda175c, 0x7edc0005, 0x7eddc78e,
0x7edf6ebf, 0x7ee0f647, 0x7ee25ebe, 0x7ee3a8a9, 0x7ee4d473,
0x7ee5e276, 0x7ee6d2f5, 0x7ee7a620, 0x7ee85c10, 0x7ee8f4cd,
0x7ee97047, 0x7ee9ce59, 0x7eea0eca, 0x7eea3147, 0x7eea3568,
0x7eea1aab, 0x7ee9e071, 0x7ee98602, 0x7ee90a88, 0x7ee86d08,
0x7ee7ac6a, 0x7ee6c769, 0x7ee5bc9c, 0x7ee48a67, 0x7ee32efc,
0x7ee1a857, 0x7edff42f, 0x7ede0ffa, 0x7edbf8d9, 0x7ed9ab94,
0x7ed7248d, 0x7ed45fae, 0x7ed1585c, 0x7ece095f, 0x7eca6ccb,
0x7ec67be2, 0x7ec22eee, 0x7ebd7d1a, 0x7eb85c35, 0x7eb2c075,
0x7eac9c20, 0x7ea5df27, 0x7e9e769f, 0x7e964c16, 0x7e8d44ba,
0x7e834033, 0x7e781728, 0x7e6b9933, 0x7e5d8a1a, 0x7e4d9ded,
0x7e3b737a, 0x7e268c2f, 0x7e0e3ff5, 0x7df1aa5d, 0x7dcf8c72,
0x7da61a1e, 0x7d72a0fb, 0x7d30e097, 0x7cd9b4ab, 0x7c600f1a,
0x7ba90bdc, 0x7a722176, 0x77d664e5,
}
var wn = [128]float32{
1.7290405e-09, 1.2680929e-10, 1.6897518e-10, 1.9862688e-10,
2.2232431e-10, 2.4244937e-10, 2.601613e-10, 2.7611988e-10,
2.9073963e-10, 3.042997e-10, 3.1699796e-10, 3.289802e-10,
3.4035738e-10, 3.5121603e-10, 3.616251e-10, 3.7164058e-10,
3.8130857e-10, 3.9066758e-10, 3.9975012e-10, 4.08584e-10,
4.1719309e-10, 4.2559822e-10, 4.338176e-10, 4.418672e-10,
4.497613e-10, 4.5751258e-10, 4.651324e-10, 4.7263105e-10,
4.8001775e-10, 4.87301e-10, 4.944885e-10, 5.015873e-10,
5.0860405e-10, 5.155446e-10, 5.2241467e-10, 5.2921934e-10,
5.359635e-10, 5.426517e-10, 5.4928817e-10, 5.5587696e-10,
5.624219e-10, 5.6892646e-10, 5.753941e-10, 5.818282e-10,
5.882317e-10, 5.946077e-10, 6.00959e-10, 6.072884e-10,
6.135985e-10, 6.19892e-10, 6.2617134e-10, 6.3243905e-10,
6.386974e-10, 6.449488e-10, 6.511956e-10, 6.5744005e-10,
6.6368433e-10, 6.699307e-10, 6.7618144e-10, 6.824387e-10,
6.8870465e-10, 6.949815e-10, 7.012715e-10, 7.075768e-10,
7.1389966e-10, 7.202424e-10, 7.266073e-10, 7.329966e-10,
7.394128e-10, 7.4585826e-10, 7.5233547e-10, 7.58847e-10,
7.653954e-10, 7.719835e-10, 7.7861395e-10, 7.852897e-10,
7.920138e-10, 7.987892e-10, 8.0561924e-10, 8.125073e-10,
8.194569e-10, 8.2647167e-10, 8.3355556e-10, 8.407127e-10,
8.479473e-10, 8.55264e-10, 8.6266755e-10, 8.7016316e-10,
8.777562e-10, 8.8545243e-10, 8.932582e-10, 9.0117996e-10,
9.09225e-10, 9.174008e-10, 9.2571584e-10, 9.341788e-10,
9.427997e-10, 9.515889e-10, 9.605579e-10, 9.697193e-10,
9.790869e-10, 9.88676e-10, 9.985036e-10, 1.0085882e-09,
1.0189509e-09, 1.0296151e-09, 1.0406069e-09, 1.0519566e-09,
1.063698e-09, 1.0758702e-09, 1.0885183e-09, 1.1016947e-09,
1.1154611e-09, 1.1298902e-09, 1.1450696e-09, 1.1611052e-09,
1.1781276e-09, 1.1962995e-09, 1.2158287e-09, 1.2369856e-09,
1.2601323e-09, 1.2857697e-09, 1.3146202e-09, 1.347784e-09,
1.3870636e-09, 1.4357403e-09, 1.5008659e-09, 1.6030948e-09,
}
var fn = [128]float32{
1, 0.9635997, 0.9362827, 0.9130436, 0.89228165, 0.87324303,
0.8555006, 0.8387836, 0.8229072, 0.8077383, 0.793177,
0.7791461, 0.7655842, 0.7524416, 0.73967725, 0.7272569,
0.7151515, 0.7033361, 0.69178915, 0.68049186, 0.6694277,
0.658582, 0.6479418, 0.63749546, 0.6272325, 0.6171434,
0.6072195, 0.5974532, 0.58783704, 0.5783647, 0.56903,
0.5598274, 0.5507518, 0.54179835, 0.5329627, 0.52424055,
0.5156282, 0.50712204, 0.49871865, 0.49041483, 0.48220766,
0.4740943, 0.46607214, 0.4581387, 0.45029163, 0.44252872,
0.43484783, 0.427247, 0.41972435, 0.41227803, 0.40490642,
0.39760786, 0.3903808, 0.3832238, 0.37613547, 0.36911446,
0.3621595, 0.35526937, 0.34844297, 0.34167916, 0.33497685,
0.3283351, 0.3217529, 0.3152294, 0.30876362, 0.30235484,
0.29600215, 0.28970486, 0.2834622, 0.2772735, 0.27113807,
0.2650553, 0.25902456, 0.2530453, 0.24711695, 0.241239,
0.23541094, 0.22963232, 0.2239027, 0.21822165, 0.21258877,
0.20700371, 0.20146611, 0.19597565, 0.19053204, 0.18513499,
0.17978427, 0.17447963, 0.1692209, 0.16400786, 0.15884037,
0.15371831, 0.14864157, 0.14361008, 0.13862377, 0.13368265,
0.12878671, 0.12393598, 0.119130544, 0.11437051, 0.10965602,
0.104987256, 0.10036444, 0.095787846, 0.0912578, 0.08677467,
0.0823389, 0.077950984, 0.073611505, 0.06932112, 0.06508058,
0.06089077, 0.056752663, 0.0526674, 0.048636295, 0.044660863,
0.040742867, 0.03688439, 0.033087887, 0.029356318,
0.025693292, 0.022103304, 0.018592102, 0.015167298,
0.011839478, 0.008624485, 0.005548995, 0.0026696292,
}