sw_bls24315

package
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 Go to latest Published: Apr 22, 2024 License: Apache-2.0 Imports: 16 Imported by: 12

Documentation

Overview

Package sw_bls24315 implements the arithmetics of G1, G2 and the pairing computation on BLS24-315 as a SNARK circuit over BW6-633. These two curves form a 2-chain so the operations use native field arithmetic.

References: BLS24-315/BW6-633: https://eprint.iacr.org/2021/1359 Pairings in R1CS: https://eprint.iacr.org/2022/1162

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func GetHints added in v0.10.0 

func GetHints() []solver.Hint

func PairingCheck added in v0.10.0 

func PairingCheck(api frontend.API, P []G1Affine, Q []G2Affine) error

PairingCheck calculates the reduced pairing for a set of points and asserts if the result is One ∏ᵢ e(Pᵢ, Qᵢ) =? 1

This function doesn't check that the inputs are in the correct subgroups. See AssertIsOnG1 and AssertIsOnG2.

Types

type Curve added in v0.9.1 

type Curve struct {
	// contains filtered or unexported fields
}

Curve allows G1 operations in BLS24-315.

func NewCurve added in v0.9.1 

func NewCurve(api frontend.API) (*Curve, error)

NewCurve initializes a new Curve instance.

func (*Curve) Add added in v0.9.1 

func (c *Curve) Add(P, Q *G1Affine) *G1Affine

Add points P and Q and return the result. Does not modify the inputs.

func (*Curve) AddUnified added in v0.10.0 

func (c *Curve) AddUnified(P, Q *G1Affine) *G1Affine

AddUnified adds any two points and returns the sum. It does not modify the input points.

func (*Curve) AssertIsEqual added in v0.9.1 

func (c *Curve) AssertIsEqual(P, Q *G1Affine)

AssertIsEqual asserts the equality of P and Q.

func (*Curve) Lookup2 added in v0.10.0 

func (c *Curve) Lookup2(b1, b2 frontend.Variable, p1, p2, p3, p4 *G1Affine) *G1Affine

Lookup2 performs a 2-bit lookup between p1, p2, p3, p4 based on bits b0 and b1. Returns:

  • p1 if b0=0 and b1=0,
  • p2 if b0=1 and b1=0,
  • p3 if b0=0 and b1=1,
  • p4 if b0=1 and b1=1.

func (*Curve) MarshalG1 added in v0.10.0 

func (c *Curve) MarshalG1(P G1Affine) []frontend.Variable

MarshalG1 returns [P.X || P.Y] in binary. Both P.X and P.Y are in little endian.

func (*Curve) MarshalScalar added in v0.10.0 

func (c *Curve) MarshalScalar(s Scalar) []frontend.Variable

MarshalScalar returns

func (*Curve) MultiScalarMul added in v0.9.1 

func (c *Curve) MultiScalarMul(P []*G1Affine, scalars []*Scalar, opts ...algopts.AlgebraOption) (*G1Affine, error)

MultiScalarMul computes ∑scalars_i * P_i and returns it. It doesn't modify the inputs. It returns an error if there is a mismatch in the lengths of the inputs.

func (*Curve) Mux added in v0.10.0 

func (c *Curve) Mux(sel frontend.Variable, inputs ...*G1Affine) *G1Affine

Mux performs a lookup from the inputs and returns inputs[sel]. It is most efficient for power of two lengths of the inputs, but works for any number of inputs.

func (*Curve) Neg added in v0.9.1 

func (c *Curve) Neg(P *G1Affine) *G1Affine

Neg negates P and returns the result. Does not modify P.

func (*Curve) ScalarMul added in v0.9.1 

func (c *Curve) ScalarMul(P *G1Affine, s *Scalar, opts ...algopts.AlgebraOption) *G1Affine

ScalarMul computes scalar*P and returns the result. It doesn't modify the inputs.

func (*Curve) ScalarMulBase added in v0.9.1 

func (c *Curve) ScalarMulBase(s *Scalar, opts ...algopts.AlgebraOption) *G1Affine

ScalarMulBase computes scalar*G where G is the standard base point of the curve. It doesn't modify the scalar.

func (*Curve) Select added in v0.10.0 

func (c *Curve) Select(b frontend.Variable, p1, p2 *G1Affine) *G1Affine

Select sets p1 if b=1, p2 if b=0, and returns it. b must be boolean constrained

type G1Affine 

type G1Affine struct {
	X, Y frontend.Variable
}

G1Affine point in affine coords

func NewG1Affine added in v0.9.1 

func NewG1Affine(v bls24315.G1Affine) G1Affine

NewG1Affine allocates a witness from the native G1 element and returns it.

func (*G1Affine) AddAssign 

func (p *G1Affine) AddAssign(api frontend.API, p1 G1Affine) *G1Affine

AddAssign adds p1 to p using the affine formulas with division, and return p

func (*G1Affine) AddUnified added in v0.10.0 

func (p *G1Affine) AddUnified(api frontend.API, q G1Affine) *G1Affine

func (*G1Affine) AssertIsEqual 

func (p *G1Affine) AssertIsEqual(api frontend.API, other G1Affine)

AssertIsEqual constraint self to be equal to other into the given constraint system

func (*G1Affine) Assign 

func (p *G1Affine) Assign(p1 *bls24315.G1Affine)

Assign a value to self (witness assignment)

func (*G1Affine) Double 

func (p *G1Affine) Double(api frontend.API, p1 G1Affine) *G1Affine

Double double a point in affine coords

func (*G1Affine) DoubleAndAdd 

func (p *G1Affine) DoubleAndAdd(api frontend.API, p1, p2 *G1Affine) *G1Affine

DoubleAndAdd computes 2*p1+p in affine coords

func (*G1Affine) Lookup2 added in v0.10.0 

func (p *G1Affine) Lookup2(api frontend.API, b1, b2 frontend.Variable, p1, p2, p3, p4 G1Affine) *G1Affine

Lookup2 performs a 2-bit lookup between p1, p2, p3, p4 based on bits b0 and b1. Returns:

  • p1 if b0=0 and b1=0,
  • p2 if b0=1 and b1=0,
  • p3 if b0=0 and b1=1,
  • p4 if b0=1 and b1=1.

func (*G1Affine) Neg 

func (p *G1Affine) Neg(api frontend.API, p1 G1Affine) *G1Affine

Neg outputs -p

func (*G1Affine) ScalarMul 

func (P *G1Affine) ScalarMul(api frontend.API, Q G1Affine, s interface{}, opts ...algopts.AlgebraOption) *G1Affine

ScalarMul sets P = [s] Q and returns P.

The method chooses an implementation based on scalar s. If it is constant, then the compiled circuit depends on s. If it is variable type, then the circuit is independent of the inputs.

func (*G1Affine) ScalarMulBase 

func (P *G1Affine) ScalarMulBase(api frontend.API, s frontend.Variable, opts ...algopts.AlgebraOption) *G1Affine

ScalarMulBase computes s * g1 and returns it, where g1 is the fixed generator. It doesn't modify s.

func (*G1Affine) Select 

func (p *G1Affine) Select(api frontend.API, b frontend.Variable, p1, p2 G1Affine) *G1Affine

Select sets p1 if b=1, p2 if b=0, and returns it. b must be boolean constrained

type G2Affine 

type G2Affine struct {
	P     g2AffP
	Lines *lineEvaluations
}

G2Affine point in affine coords

func NewG2Affine added in v0.9.1 

func NewG2Affine(v bls24315.G2Affine) G2Affine

func NewG2AffineFixed added in v0.10.0 

func NewG2AffineFixed(v bls24315.G2Affine) G2Affine

NewG2AffineFixed returns witness of v with precomputations for efficient pairing computation.

func NewG2AffineFixedPlaceholder added in v0.10.0 

func NewG2AffineFixedPlaceholder() G2Affine

NewG2AffineFixedPlaceholder returns a placeholder for the circuit compilation when witness will be given with line precomputations using NewG2AffineFixed.

type GT 

type GT = fields_bls24315.E24

GT target group of the pairing

func FinalExponentiation 

func FinalExponentiation(api frontend.API, e1 GT) GT

FinalExponentiation computes the exponentiation e1ᵈ where d = (p²⁴-1)/r = (p²⁴-1)/Φ₂₄(p) ⋅ Φ₂₄(p)/r = (p¹²-1)(p⁴+1)(p⁸ - p⁴ +1)/r we use instead d=s ⋅ (p¹²-1)(p⁴+1)(p⁸ - p⁴ +1)/r where s is the cofactor 3 (Hayashida et al.)

func MillerLoop 

func MillerLoop(api frontend.API, P []G1Affine, Q []G2Affine) (GT, error)

MillerLoop computes the product of n miller loops (n can be 1) ∏ᵢ { fᵢ_{x₀,Q}(P) }

func NewGTEl added in v0.9.1 

func NewGTEl(v bls24315.GT) GT

NewGTEl allocates a witness from the native target group element and returns it.

func Pair 

func Pair(api frontend.API, P []G1Affine, Q []G2Affine) (GT, error)

PairingCheck calculates the reduced pairing for a set of points and returns True if the result is One ∏ᵢ e(Pᵢ, Qᵢ) =? 1

This function doesn't check that the inputs are in the correct subgroup. See IsInSubGroup.

type Pairing added in v0.9.1 

type Pairing struct {
	// contains filtered or unexported fields
}

Pairing allows computing pairing-related operations in BLS24-315.

func NewPairing added in v0.9.1 

func NewPairing(api frontend.API) *Pairing

NewPairing initializes a Pairing instance.

func (*Pairing) AssertIsEqual added in v0.9.1 

func (p *Pairing) AssertIsEqual(e1, e2 *GT)

AssertIsEqual asserts the equality of the target group elements.

func (*Pairing) AssertIsOnG1 added in v0.10.0 

func (p *Pairing) AssertIsOnG1(P *G1Affine)

func (*Pairing) AssertIsOnG2 added in v0.10.0 

func (p *Pairing) AssertIsOnG2(P *G2Affine)

func (*Pairing) FinalExponentiation added in v0.9.1 

func (p *Pairing) FinalExponentiation(e *GT) *GT

FinalExponentiation performs the final exponentiation on the target group element. It doesn't modify the input.

func (*Pairing) MillerLoop added in v0.9.1 

func (p *Pairing) MillerLoop(P []*G1Affine, Q []*G2Affine) (*GT, error)

MillerLoop computes the Miller loop between the pairs of inputs. It doesn't modify the inputs. It returns an error if there is a mismatch betwen the lengths of the inputs.

func (*Pairing) Pair added in v0.9.1 

func (p *Pairing) Pair(P []*G1Affine, Q []*G2Affine) (*GT, error)

Pair computes a full multi-pairing on the input pairs.

func (*Pairing) PairingCheck added in v0.9.1 

func (p *Pairing) PairingCheck(P []*G1Affine, Q []*G2Affine) error

PairingCheck computes the multi-pairing of the input pairs and asserts that the result is an identity element in the target group. It returns an error if there is a mismatch between the lengths of the inputs.

type Scalar added in v0.9.1 

type Scalar = emulated.Element[ScalarField]

Scalar is a scalar in the groups. As the implementation is defined on a 2-chain, then this type is an alias to frontend.Variable.

func NewScalar added in v0.10.0 

func NewScalar(v fr_bls24315.Element) Scalar

NewScalar allocates a witness from the native scalar and returns it.

type ScalarField added in v0.10.0 

type ScalarField = emparams.BLS24315Fr

ScalarField defines the emulated.FieldParams implementation on a one limb of the scalar field.

Source Files

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