-
Notifications
You must be signed in to change notification settings - Fork 136
/
ss.go
145 lines (126 loc) · 4.44 KB
/
ss.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
// Package secretsharing provides methods to split secrets into shares.
//
// Let n be the number of parties, and t the number of corrupted parties such
// that 0 <= t < n. A (t,n) secret sharing allows to split a secret into n
// shares, such that the secret can be recovered from any subset of at least t+1
// different shares.
//
// A Shamir secret sharing [1] relies on Lagrange polynomial interpolation.
// A Feldman secret sharing [2] extends Shamir's by committing the secret,
// which allows to verify that a share is part of the committed secret.
//
// New returns a SecretSharing compatible with Shamir secret sharing.
// The SecretSharing can be verifiable (compatible with Feldman secret sharing)
// using the CommitSecret and Verify functions.
//
// In this implementation, secret sharing is defined over the scalar field of
// a prime order group.
//
// References
//
// [1] Shamir, How to share a secret. https://dl.acm.org/doi/10.1145/359168.359176/
// [2] Feldman, A practical scheme for non-interactive verifiable secret sharing. https://ieeexplore.ieee.org/document/4568297/
package secretsharing
import (
"fmt"
"io"
"github.com/cloudflare/circl/group"
"github.com/cloudflare/circl/math/polynomial"
)
// Share represents a share of a secret.
type Share struct {
// ID uniquely identifies a share in a secret sharing instance. ID is never zero.
ID group.Scalar
// Value stores the share generated by a secret sharing instance.
Value group.Scalar
}
// SecretCommitment is the set of commitments generated by splitting a secret.
type SecretCommitment = []group.Element
// SecretSharing provides a (t,n) Shamir's secret sharing. It allows splitting
// a secret into n shares, such that the secret can be only recovered from
// any subset of t+1 shares.
type SecretSharing struct {
g group.Group
t uint
poly polynomial.Polynomial
}
// New returns a SecretSharing providing a (t,n) Shamir's secret sharing.
// It allows splitting a secret into n shares, such that the secret is
// only recovered from any subset of at least t+1 shares.
func New(rnd io.Reader, t uint, secret group.Scalar) SecretSharing {
c := make([]group.Scalar, t+1)
c[0] = secret.Copy()
g := secret.Group()
for i := 1; i < len(c); i++ {
c[i] = g.RandomScalar(rnd)
}
return SecretSharing{g: g, t: t, poly: polynomial.New(c)}
}
// Share creates n shares with an ID monotonically increasing from 1 to n.
func (ss SecretSharing) Share(n uint) []Share {
shares := make([]Share, n)
id := ss.g.NewScalar()
for i := range shares {
shares[i] = ss.ShareWithID(id.SetUint64(uint64(i + 1)))
}
return shares
}
// ShareWithID creates one share of the secret using the ID as identifier.
// Notice that shares with the same ID are considered equal.
// Panics, if the ID is zero.
func (ss SecretSharing) ShareWithID(id group.Scalar) Share {
if id.IsZero() {
panic("secretsharing: id cannot be zero")
}
return Share{
ID: id.Copy(),
Value: ss.poly.Evaluate(id),
}
}
// CommitSecret creates a commitment to the secret for further verifying shares.
func (ss SecretSharing) CommitSecret() SecretCommitment {
c := make(SecretCommitment, ss.poly.Degree()+1)
for i := range c {
c[i] = ss.g.NewElement().MulGen(ss.poly.Coefficient(uint(i)))
}
return c
}
// Verify returns true if the share s was produced by sharing a secret with
// threshold t and commitment of the secret c.
func Verify(t uint, s Share, c SecretCommitment) bool {
if len(c) != int(t+1) {
return false
}
if s.ID.IsZero() {
return false
}
g := s.ID.Group()
lc := len(c) - 1
sum := g.NewElement().Set(c[lc])
for i := lc - 1; i >= 0; i-- {
sum.Mul(sum, s.ID)
sum.Add(sum, c[i])
}
polI := g.NewElement().MulGen(s.Value)
return polI.IsEqual(sum)
}
// Recover returns a secret provided more than t different shares are given.
// Returns an error if the number of shares is not above the threshold t.
// Panics if some shares are duplicated, i.e., shares must have different IDs.
func Recover(t uint, shares []Share) (secret group.Scalar, err error) {
if l := len(shares); l <= int(t) {
return nil, errThreshold(t, uint(l))
}
x := make([]group.Scalar, t+1)
px := make([]group.Scalar, t+1)
for i := range shares[:t+1] {
x[i] = shares[i].ID
px[i] = shares[i].Value
}
l := polynomial.NewLagrangePolynomial(x, px)
zero := shares[0].ID.Group().NewScalar()
return l.Evaluate(zero), nil
}
func errThreshold(t, n uint) error {
return fmt.Errorf("secretsharing: number of shares (n=%v) must be above the threshold (t=%v)", n, t)
}