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circuit CalculateWitness, added - & / in GenerateR1CS(), added doc

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arnaucube
2018-12-28 00:46:42 +01:00
parent 0806af6b80
commit aefb298bb0
10 changed files with 216 additions and 100 deletions
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16
r1csqap/r1csqap.go
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@@ -6,6 +6,7 @@ import (
"github.com/arnaucube/go-snark/fields"
)
// Transpose transposes the *big.Int matrix
func Transpose(matrix [][]*big.Int) [][]*big.Int {
var r [][]*big.Int
for i := 0; i < len(matrix[0]); i++ {
@@ -18,6 +19,7 @@ func Transpose(matrix [][]*big.Int) [][]*big.Int {
return r
}
// ArrayOfBigZeros creates a *big.Int array with n elements to zero
func ArrayOfBigZeros(num int) []*big.Int {
bigZero := big.NewInt(int64(0))
var r []*big.Int
@@ -27,15 +29,19 @@ func ArrayOfBigZeros(num int) []*big.Int {
return r
}
// PolynomialField is the Polynomial over a Finite Field where the polynomial operations are performed
type PolynomialField struct {
F fields.Fq
}
// NewPolynomialField creates a new PolynomialField with the given FiniteField
func NewPolynomialField(f fields.Fq) PolynomialField {
return PolynomialField{
f,
}
}
// Mul multiplies two polinomials over the Finite Field
func (pf PolynomialField) Mul(a, b []*big.Int) []*big.Int {
r := ArrayOfBigZeros(len(a) + len(b) - 1)
for i := 0; i < len(a); i++ {
@@ -47,6 +53,8 @@ func (pf PolynomialField) Mul(a, b []*big.Int) []*big.Int {
}
return r
}
// Div divides two polinomials over the Finite Field, returning the result and the remainder
func (pf PolynomialField) Div(a, b []*big.Int) ([]*big.Int, []*big.Int) {
// https://en.wikipedia.org/wiki/Division_algorithm
r := ArrayOfBigZeros(len(a) - len(b) + 1)
@@ -70,6 +78,7 @@ func max(a, b int) int {
return b
}
// Add adds two polinomials over the Finite Field
func (pf PolynomialField) Add(a, b []*big.Int) []*big.Int {
r := ArrayOfBigZeros(max(len(a), len(b)))
for i := 0; i < len(a); i++ {
@@ -81,6 +90,7 @@ func (pf PolynomialField) Add(a, b []*big.Int) []*big.Int {
return r
}
// Sub substracts two polinomials over the Finite Field
func (pf PolynomialField) Sub(a, b []*big.Int) []*big.Int {
r := ArrayOfBigZeros(max(len(a), len(b)))
for i := 0; i < len(a); i++ {
@@ -92,6 +102,7 @@ func (pf PolynomialField) Sub(a, b []*big.Int) []*big.Int {
return r
}
// Eval evaluates the polinomial over the Finite Field at the given value x
func (pf PolynomialField) Eval(v []*big.Int, x *big.Int) *big.Int {
r := big.NewInt(int64(0))
for i := 0; i < len(v); i++ {
@@ -102,6 +113,7 @@ func (pf PolynomialField) Eval(v []*big.Int, x *big.Int) *big.Int {
return r
}
// NewPolZeroAt generates a new polynomial that has value zero at the given value
func (pf PolynomialField) NewPolZeroAt(pointPos, totalPoints int, height *big.Int) []*big.Int {
fac := 1
for i := 1; i < totalPoints+1; i++ {
@@ -122,6 +134,7 @@ func (pf PolynomialField) NewPolZeroAt(pointPos, totalPoints int, height *big.In
return r
}
// LagrangeInterpolation performs the Lagrange Interpolation / Lagrange Polynomials operation
func (pf PolynomialField) LagrangeInterpolation(v []*big.Int) []*big.Int {
// https://en.wikipedia.org/wiki/Lagrange_polynomial
var r []*big.Int
@@ -132,6 +145,7 @@ func (pf PolynomialField) LagrangeInterpolation(v []*big.Int) []*big.Int {
return r
}
// R1CSToQAP converts the R1CS values to the QAP values
func (pf PolynomialField) R1CSToQAP(a, b, c [][]*big.Int) ([][]*big.Int, [][]*big.Int, [][]*big.Int, []*big.Int) {
aT := Transpose(a)
bT := Transpose(b)
@@ -157,6 +171,7 @@ func (pf PolynomialField) R1CSToQAP(a, b, c [][]*big.Int) ([][]*big.Int, [][]*bi
return alphas, betas, gammas, z
}
// CombinePolynomials combine the given polynomials arrays into one, also returns the P(x)
func (pf PolynomialField) CombinePolynomials(r []*big.Int, ap, bp, cp [][]*big.Int) ([]*big.Int, []*big.Int, []*big.Int, []*big.Int) {
var alpha []*big.Int
for i := 0; i < len(r); i++ {
@@ -178,6 +193,7 @@ func (pf PolynomialField) CombinePolynomials(r []*big.Int, ap, bp, cp [][]*big.I
return alpha, beta, gamma, px
}
// DivisorPolynomial returns the divisor polynomial given two polynomials
func (pf PolynomialField) DivisorPolinomial(px, z []*big.Int) []*big.Int {
quo, _ := pf.Div(px, z)
return quo