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
|
package nizk
import (
"log"
"math/rand"
"slices"
"strings"
"sync"
"testing"
. "kesim.org/seal/common"
)
func runVickrey(n int, bitlength int, tb testing.TB) {
var vals = make([]int, n)
var ids = make([]Bytes, n)
for i := range n {
vals[i] = rand.Intn(1<<(bitlength-1) - 1)
ids[i] = Curve.RandomScalar()
}
max := slices.Max(vals)
max_idx := slices.Index(vals, max)
if max_idx < len(vals)-1 && max == slices.Max(vals[max_idx+1:]) {
max_idx = -1
}
var bits = make([][]*Bit, n)
for i, b := range vals {
bits[i] = Int2Bits(ids[i], b, bitlength)
}
var c = make([]*StageCommitment, n)
var Xs = make([]*Point, n)
var r = make([]*StageReveal, n)
var p1 = make([]*Stage1Proof, n)
var Zs = make([]*Point, n)
var bj = make([]*Bit, n)
var p2 = make([]*Stage2Proof, n)
var lost = make([]bool, n)
instage1 := true
junction := -1
winner := -1
result := 0
isWinner := func(Z *Point, i int, idx int) bool {
Z2 := Z.Div(Zs[i])
xu := Curve.Identity()
xl := Curve.Identity()
for k := range n {
if k < i {
xu = xu.Mul(Xs[k])
} else if k > i {
xl = xl.Div(Xs[k])
}
}
xu = xu.Exp(bits[i][idx].Stage.x)
xl = xl.Exp(bits[i][idx].Stage.x)
X2 := xu.Mul(xl)
if X2.Equal(Z2) {
tb.Logf("equal by value")
winner = i
}
if winner < 0 {
// BUG! TODO!
s1 := X2.String()
s2 := Z2.String()
if strings.HasPrefix(s1, s2[:len(s2)-2]) {
log.Printf("BUG! TODO! equal only by string")
winner = i
}
}
tb.Logf("testing max_idx %d, i %d, bit %d:\n%v vs %v", max_idx, i, idx, X2, Z2)
return winner >= 0
}
for idx := range bitlength {
for i := range n {
c[i] = bits[i][idx].StageCommit()
Xs[i] = c[i].X
}
if instage1 {
var wg sync.WaitGroup
wg.Add(n)
for i := range n {
go func() {
r[i], p1[i] = bits[i][idx].RevealStage1(Xs...)
if !bits[i][idx].Commitment.VerifyStage1(c[i], r[i], p1[i]) {
tb.Fatalf("bits[%d][%d] commitment failed to verify in stage1", i, idx)
}
Zs[i] = r[i].Z
wg.Done()
}()
}
wg.Wait()
Z := Curve.Product(Zs...)
if !Id.Equal(Z) {
junction = idx
instage1 = false
for i := range bits {
if !lost[i] && !bits[i][idx].IsSet() {
lost[i] = true
}
// Winner test
if !lost[i] {
isWinner(Z, i, idx)
}
}
result |= 1 << (bitlength - 1 - idx)
}
continue
}
// Stage 2
for i := range bits {
bj[i] = bits[i][junction]
}
var wg sync.WaitGroup
wg.Add(n)
for i := range n {
go func() {
r[i], p2[i] = bits[i][idx].RevealStage2(lost[i], bj[i], Xs...)
if !bits[i][idx].Commitment.VerifyStage2(bj[i].StageCommitment, c[i], bj[i].StageReveal, r[i], p2[i]) {
tb.Fatalf("bits[%d][%d] commitment failed to verify in stage2, result so far: %05b", i, idx, result)
}
Zs[i] = r[i].Z
wg.Done()
}()
}
wg.Wait()
Z := Curve.Product(Zs...)
if !Id.Equal(Z) {
junction = idx
for i := range n {
if !lost[i] && !bits[i][idx].IsSet() {
lost[i] = true
}
// Winner test
if !lost[i] && winner < 0 {
isWinner(Z, i, idx)
}
}
result |= 1 << (bitlength - 1 - idx)
}
}
if result != max {
tb.Fatalf("wrong result: %0[1]*[2]b, expected: %0[1]*[3]b", bitlength, result, max)
}
if max_idx != winner {
tb.Fatalf("wrong winner, max_idx: %d vs winner: %d val %08b\nvals=%08b", max_idx, winner, max, vals)
}
}
func TestVickrey100on24bit(t *testing.T) { runVickrey(100, 32, t) }
|
