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sharing/v1/feldman.go

@@ -0,0 +1,107 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"crypto/elliptic"
+	"encoding/binary"
+	"fmt"
+
+	"github.com/sonr-io/sonr/crypto/core/curves"
+)
+
+// Feldman Verifiable Secret Sharing Scheme
+type Feldman struct {
+	threshold, limit uint32
+	curve            elliptic.Curve
+}
+
+// FeldmanResult contains all the data from calling Split
+type FeldmanResult struct {
+	SecretShares []*ShamirShare
+	Verifiers    []*ShareVerifier
+}
+
+func NewFeldman(threshold, limit uint32, curve elliptic.Curve) (*Feldman, error) {
+	if limit < threshold {
+		return nil, fmt.Errorf("limit cannot be less than threshold")
+	}
+	if threshold < 2 {
+		return nil, fmt.Errorf("threshold must be at least 2")
+	}
+	return &Feldman{
+		threshold, limit, curve,
+	}, nil
+}
+
+func (f Feldman) Split(secret []byte) ([]*ShareVerifier, []*ShamirShare, error) {
+	field := curves.NewField(f.curve.Params().N)
+	shamir := Shamir{f.threshold, f.limit, field}
+	shares, poly, err := shamir.GetSharesAndPolynomial(secret)
+	if err != nil {
+		return nil, nil, err
+	}
+	// Generate the verifiable commitments to the polynomial for the shares
+	verifiers := make([]*ShareVerifier, len(poly.Coefficients))
+	for i, c := range poly.Coefficients {
+		v, err := curves.NewScalarBaseMult(f.curve, c.Value)
+		if err != nil {
+			return nil, nil, err
+		}
+		verifiers[i] = v
+	}
+	return verifiers, shares, nil
+}
+
+func (f Feldman) Combine(shares ...*ShamirShare) ([]byte, error) {
+	field := curves.NewField(f.curve.Params().N)
+	shamir := Shamir{f.threshold, f.limit, field}
+	return shamir.Combine(shares...)
+}
+
+// Verify checks a share for validity
+func (f Feldman) Verify(share *ShamirShare, verifiers []*ShareVerifier) (bool, error) {
+	if len(verifiers) < int(f.threshold) {
+		return false, fmt.Errorf("not enough verifiers to check")
+	}
+	field := curves.NewField(f.curve.Params().N)
+
+	xBytes := make([]byte, 4)
+	binary.BigEndian.PutUint32(xBytes, share.Identifier)
+	x := field.ElementFromBytes(xBytes)
+
+	i := share.Value.Modulus.One()
+
+	// c_0
+	rhs := verifiers[0]
+
+	// Compute the sum of products
+	// c_0 * c_1^i * c_2^{i^2} * c_3^{i^3} ... c_t^{i_t}
+	for j := 1; j < len(verifiers); j++ {
+		// i *= x
+		i = i.Mul(x)
+
+		c, err := verifiers[j].ScalarMult(i.Value)
+		if err != nil {
+			return false, err
+		}
+
+		// ... * c_j^{i^j}
+		rhs, err = rhs.Add(c)
+		if err != nil {
+			return false, err
+		}
+	}
+
+	lhs, err := curves.NewScalarBaseMult(f.curve, share.Value.Value)
+	if err != nil {
+		return false, err
+	}
+
+	// Check if lhs == rhs
+	return lhs.Equals(rhs), nil
+}