backend_bn256

Documentation

Index

• Constants
• func FFT(a []fr.Element, w fr.Element)
• type Domain
  • func NewDomain(rootOfUnity fr.Element, maxOrderRoot uint, m int) *Domain
• type LinearExpression
  • func (l LinearExpression) String() string
• type R1C
  • func (r R1C) String() string
• type R1CS
  • func Cast(r1cs *frontend.R1CS) R1CS
  • func New(cs *frontend.CS) R1CS
  • func (r1cs *R1CS) Inspect(solution backend.Assignments, showsInputs bool) (map[string]fr.Element, error)
  • func (r1cs *R1CS) Solve(assignment backend.Assignments, a, b, c, wireValues []fr.Element) error
  • func (r1cs *R1CS) Write(path string) error
• type Term
  • func (t Term) String() string

Constants

const (
	SingleOutput solvingMethod = iota
	BinaryDec
)

const MaxOrder = 28

const RootOfUnityStr = "19103219067921713944291392827692070036145651957329286315305642004821462161904"

Functions

func FFT

func FFT(a []fr.Element, w fr.Element)

FFT computes the discrete Fourier transform of a and stores the result in a. The result is in bit-reversed order. len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. The algorithm is recursive, decimation-in-frequency. [cite]

Types

type Domain

type Domain struct {
	Generator        fr.Element
	GeneratorInv     fr.Element
	GeneratorSqRt    fr.Element // generator of 2 adic subgroup of order 2*nb_constraints
	GeneratorSqRtInv fr.Element
	Cardinality      int
	CardinalityInv   fr.Element
}

domain with a power of 2 cardinality compute a field element of order 2x and store it in GeneratorSqRt all other values can be derived from x, GeneratorSqrt

func NewDomain

func NewDomain(rootOfUnity fr.Element, maxOrderRoot uint, m int) *Domain

newDomain returns a subgroup with a power of 2 cardinality cardinality >= m compute a field element of order 2x and store it in GeneratorSqRt all other values can be derived from x, GeneratorSqrt

type LinearExpression

type LinearExpression []Term

LinearExpression lightweight version of linear expression

func (LinearExpression) String

func (l LinearExpression) String() string

String helper for LinearExpression

type R1C

type R1C struct {
	L      LinearExpression
	R      LinearExpression
	O      LinearExpression
	Solver frontend.SolvingMethod
}

R1C used to compute the wires (wo pointers)

func (R1C) String

func (r R1C) String() string

String helper for a Rank1 Constraint

type R1CS

type R1CS struct {
	// Wires
	NbWires        int
	NbPublicWires  int // includes ONE wire
	NbPrivateWires int
	PrivateWires   []string         // private wire names, correctly ordered (the i-th entry is the name of the (offset+)i-th wire)
	PublicWires    []string         // public wire names, correctly ordered (the i-th entry is the name of the (offset+)i-th wire)
	WireTags       map[int][]string // optional tags -- debug info

	// Constraints
	NbConstraints   int // total number of constraints
	NbCOConstraints int // number of constraints that need to be solved, the first of the Constraints slice
	Constraints     []R1C
}

R1CS decsribes a set of R1CS constraint

func Cast

func Cast(r1cs *frontend.R1CS) R1CS

Cast casts a frontend.R1CS (whose coefficients are big.Int) into a specialized R1CS whose coefficients are fr elements

func New

func New(cs *frontend.CS) R1CS

New return a typed R1CS with the curve from frontend.R1CS

func (*R1CS) Inspect

func (r1cs *R1CS) Inspect(solution backend.Assignments, showsInputs bool) (map[string]fr.Element, error)

Inspect returns the tagged variables with their corresponding value If showsInput is set, it also puts in the resulting map the inputs (public and private).

func (*R1CS) Solve

func (r1cs *R1CS) Solve(assignment backend.Assignments, a, b, c, wireValues []fr.Element) error

Solve sets all the wires and returns the a, b, c vectors. the r1cs system should have been compiled before. The entries in a, b, c are in Montgomery form. assignment: map[string]value: contains the input variables a, b, c vectors: ab-c = hz wireValues = [intermediateVariables | privateInputs | publicInputs]

func (*R1CS) Write

func (r1cs *R1CS) Write(path string) error

type Term

type Term struct {
	ID    int64      // index of the constraint used to compute this wire
	Coeff fr.Element // coefficient by which the wire is multiplied
}

Term lightweight version of a term, no pointers

func (Term) String

func (t Term) String() string

String helper for Term