ceremonyclient/nekryptology/pkg/bulletproof/helpers.go

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2023-07-05 05:32:28 +00:00
//
// Copyright Coinbase, Inc. All Rights Reserved.
//
// SPDX-License-Identifier: Apache-2.0
//
package bulletproof
import (
"github.com/pkg/errors"
"source.quilibrium.com/quilibrium/monorepo/nekryptology/pkg/core/curves"
)
// innerProduct takes two lists of scalars (a, b) and performs the dot product returning a single scalar.
func innerProduct(a, b []curves.Scalar) (curves.Scalar, error) {
if len(a) != len(b) {
return nil, errors.New("length of scalar vectors must be the same")
}
if len(a) < 1 {
return nil, errors.New("length of vectors must be at least one")
}
// Get a new scalar of value zero of the same curve as input arguments
innerProduct := a[0].Zero()
for i, aElem := range a {
bElem := b[i]
// innerProduct = aElem*bElem + innerProduct
innerProduct = aElem.MulAdd(bElem, innerProduct)
}
return innerProduct, nil
}
// splitPointVector takes a vector of points, splits it in half returning each half.
func splitPointVector(points []curves.Point) ([]curves.Point, []curves.Point, error) {
if len(points) < 1 {
return nil, nil, errors.New("length of points must be at least one")
}
if len(points)&0x01 != 0 {
return nil, nil, errors.New("length of points must be even")
}
nPrime := len(points) >> 1
firstHalf := points[:nPrime]
secondHalf := points[nPrime:]
return firstHalf, secondHalf, nil
}
// splitScalarVector takes a vector of scalars, splits it in half returning each half.
func splitScalarVector(scalars []curves.Scalar) ([]curves.Scalar, []curves.Scalar, error) {
if len(scalars) < 1 {
return nil, nil, errors.New("length of scalars must be at least one")
}
if len(scalars)&0x01 != 0 {
return nil, nil, errors.New("length of scalars must be even")
}
nPrime := len(scalars) >> 1
firstHalf := scalars[:nPrime]
secondHalf := scalars[nPrime:]
return firstHalf, secondHalf, nil
}
// multiplyScalarToPointVector takes a single scalar and a list of points, multiplies each point by scalar.
func multiplyScalarToPointVector(x curves.Scalar, g []curves.Point) []curves.Point {
products := make([]curves.Point, len(g))
for i, gElem := range g {
product := gElem.Mul(x)
products[i] = product
}
return products
}
// multiplyScalarToScalarVector takes a single scalar (x) and a list of scalars (a), multiplies each scalar in the vector by the scalar.
func multiplyScalarToScalarVector(x curves.Scalar, a []curves.Scalar) []curves.Scalar {
products := make([]curves.Scalar, len(a))
for i, aElem := range a {
product := aElem.Mul(x)
products[i] = product
}
return products
}
// multiplyPairwisePointVectors takes two lists of points (g, h) and performs a pairwise multiplication returning a list of points.
func multiplyPairwisePointVectors(g, h []curves.Point) ([]curves.Point, error) {
if len(g) != len(h) {
return nil, errors.New("length of point vectors must be the same")
}
product := make([]curves.Point, len(g))
for i, gElem := range g {
product[i] = gElem.Add(h[i])
}
return product, nil
}
// multiplyPairwiseScalarVectors takes two lists of points (a, b) and performs a pairwise multiplication returning a list of scalars.
func multiplyPairwiseScalarVectors(a, b []curves.Scalar) ([]curves.Scalar, error) {
if len(a) != len(b) {
return nil, errors.New("length of point vectors must be the same")
}
product := make([]curves.Scalar, len(a))
for i, aElem := range a {
product[i] = aElem.Mul(b[i])
}
return product, nil
}
// addPairwiseScalarVectors takes two lists of scalars (a, b) and performs a pairwise addition returning a list of scalars.
func addPairwiseScalarVectors(a, b []curves.Scalar) ([]curves.Scalar, error) {
if len(a) != len(b) {
return nil, errors.New("length of scalar vectors must be the same")
}
sum := make([]curves.Scalar, len(a))
for i, aElem := range a {
sum[i] = aElem.Add(b[i])
}
return sum, nil
}
// subtractPairwiseScalarVectors takes two lists of scalars (a, b) and performs a pairwise subtraction returning a list of scalars.
func subtractPairwiseScalarVectors(a, b []curves.Scalar) ([]curves.Scalar, error) {
if len(a) != len(b) {
return nil, errors.New("length of scalar vectors must be the same")
}
diff := make([]curves.Scalar, len(a))
for i, aElem := range a {
diff[i] = aElem.Sub(b[i])
}
return diff, nil
}
// invertScalars takes a list of scalars then returns a list with each element inverted.
func invertScalars(xs []curves.Scalar) ([]curves.Scalar, error) {
xinvs := make([]curves.Scalar, len(xs))
for i, x := range xs {
xinv, err := x.Invert()
if err != nil {
return nil, errors.Wrap(err, "bulletproof helpers invertx")
}
xinvs[i] = xinv
}
return xinvs, nil
}
// isPowerOfTwo returns whether a number i is a power of two or not.
func isPowerOfTwo(i int) bool {
return i&(i-1) == 0
}
// get2nVector returns a scalar vector 2^n such that [1, 2, 4, ... 2^(n-1)]
// See k^n and 2^n definitions on pg 12 of https://eprint.iacr.org/2017/1066.pdf
func get2nVector(length int, curve curves.Curve) []curves.Scalar {
vector2n := make([]curves.Scalar, length)
vector2n[0] = curve.Scalar.One()
for i := 1; i < length; i++ {
vector2n[i] = vector2n[i-1].Double()
}
return vector2n
}
func get1nVector(length int, curve curves.Curve) []curves.Scalar {
vector1n := make([]curves.Scalar, length)
for i := 0; i < length; i++ {
vector1n[i] = curve.Scalar.One()
}
return vector1n
}
func getknVector(k curves.Scalar, length int, curve curves.Curve) []curves.Scalar {
vectorkn := make([]curves.Scalar, length)
vectorkn[0] = curve.Scalar.One()
vectorkn[1] = k
for i := 2; i < length; i++ {
vectorkn[i] = vectorkn[i-1].Mul(k)
}
return vectorkn
}