forked from tuneinsight/lattigo
-
Notifications
You must be signed in to change notification settings - Fork 0
/
modular_reduction.go
187 lines (140 loc) · 3.66 KB
/
modular_reduction.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
package ring
import (
"math/big"
"math/bits"
)
// MForm switches a to the Montgomery domain by computing
// a*2^64 mod q.
func MForm(a, q uint64, u []uint64) (r uint64) {
mhi, _ := bits.Mul64(a, u[1])
r = -(a*u[0] + mhi) * q
if r >= q {
r -= q
}
return
}
// MFormConstant switches a to the Montgomery domain by computing
// a*2^64 mod q in constant time.
// The result is between 0 and 2*q-1.
func MFormConstant(a, q uint64, u []uint64) (r uint64) {
mhi, _ := bits.Mul64(a, u[1])
r = -(a*u[0] + mhi) * q
return
}
// InvMForm switches a from the Montgomery domain back to the
// standard domain by computing a*(1/2^64) mod q.
func InvMForm(a, q, qInv uint64) (r uint64) {
r, _ = bits.Mul64(a*qInv, q)
r = q - r
if r >= q {
r -= q
}
return
}
// InvMFormConstant switches a from the Montgomery domain back to the
// standard domain by computing a*(1/2^64) mod q in constant time.
// The result is between 0 and 2*q-1.
func InvMFormConstant(a, q, qInv uint64) (r uint64) {
r, _ = bits.Mul64(a*qInv, q)
r = q - r
return
}
// MRedParams computes the parameter qInv = (q^-1) mod 2^64,
// required for MRed.
func MRedParams(q uint64) (qInv uint64) {
qInv = 1
for i := 0; i < 63; i++ {
qInv *= q
q *= q
}
return
}
// MRed computes x * y * (1/2^64) mod q.
func MRed(x, y, q, qInv uint64) (r uint64) {
mhi, mlo := bits.Mul64(x, y)
hhi, _ := bits.Mul64(mlo*qInv, q)
r = mhi - hhi + q
if r >= q {
r -= q
}
return
}
// MRedConstant computes x * y * (1/2^64) mod q in constant time.
// The result is between 0 and 2*q-1.
func MRedConstant(x, y, q, qInv uint64) (r uint64) {
ahi, alo := bits.Mul64(x, y)
H, _ := bits.Mul64(alo*qInv, q)
r = ahi - H + q
return
}
// BRedParams computes the parameters for the BRed algorithm.
// Returns ((2^128)/q)/(2^64) and (2^128)/q mod 2^64.
func BRedParams(q uint64) (params []uint64) {
bigR := new(big.Int).Lsh(NewUint(1), 128)
bigR.Quo(bigR, NewUint(q))
mhi := new(big.Int).Rsh(bigR, 64).Uint64()
mlo := bigR.Uint64()
return []uint64{mhi, mlo}
}
// BRedAdd computes a mod q.
func BRedAdd(a, q uint64, u []uint64) (r uint64) {
mhi, _ := bits.Mul64(a, u[0])
r = a - mhi*q
if r >= q {
r -= q
}
return
}
// BRedAddConstant computes a mod q in constant time.
// The result is between 0 and 2*q-1.
func BRedAddConstant(x, q uint64, u []uint64) uint64 {
s0, _ := bits.Mul64(x, u[0])
return x - s0*q
}
// BRed computes x*y mod q.
func BRed(x, y, q uint64, u []uint64) (r uint64) {
var mhi, mlo, lhi, hhi, hlo, s0, carry uint64
mhi, mlo = bits.Mul64(x, y)
// computes r = mhi * uhi + (mlo * uhi + mhi * ulo)<<64 + (mlo * ulo)) >> 128
r = mhi * u[0] // r = mhi * uhi
hhi, hlo = bits.Mul64(mlo, u[0]) // mlo * uhi
r += hhi
lhi, _ = bits.Mul64(mlo, u[1]) // mlo * ulo
s0, carry = bits.Add64(hlo, lhi, 0)
r += carry
hhi, hlo = bits.Mul64(mhi, u[1]) // mhi * ulo
r += hhi
_, carry = bits.Add64(hlo, s0, 0)
r += carry
r = mlo - r*q
if r >= q {
r -= q
}
return
}
// BRedConstant computes x*y mod q in constant time.
// The result is between 0 and 2*q-1.
func BRedConstant(x, y, q uint64, u []uint64) (r uint64) {
var mhi, mlo, lhi, hhi, hlo, s0, carry uint64
mhi, mlo = bits.Mul64(x, y)
// computes r = mhi * uhi + (mlo * uhi + mhi * ulo)<<64 + (mlo * ulo)) >> 128
r = mhi * u[0] // r = mhi * uhi
hhi, hlo = bits.Mul64(mlo, u[0]) // mlo * uhi
r += hhi
lhi, _ = bits.Mul64(mlo, u[1]) // mlo * ulo
s0, carry = bits.Add64(hlo, lhi, 0)
r += carry
hhi, hlo = bits.Mul64(mhi, u[1]) // mhi * ulo
r += hhi
_, carry = bits.Add64(hlo, s0, 0)
r += carry
r = mlo - r*q
return
}
// CRed reduce returns a mod q where a is between 0 and 2*q-1.
func CRed(a, q uint64) uint64 {
if a >= q {
return a - q
}
return a
}