vrf

Documentation

Overview

Numbers are deterministically generated from seeds and a secret key, and are statistically indistinguishable from uniform sampling from {0,...,2**256-1}, to computationally-bounded observers who know the seeds, don't know the key, and only see the generated numbers. But each number also comes with a proof that it was generated according to the procedure mandated by a public key associated with that secret key.

See VRF.sol for design notes.

Usage -----

You should probably not be using this directly. chainlink/store/core/models/vrfkey.PrivateKey provides a simple, more misuse-resistant interface to the same functionality, via the CreateKey and MarshaledProof methods.

Nonetheless, a secret key sk should be securely sampled uniformly from {0,...,Order-1}. Its public key can be calculated from it by

secp256k1.Secp256k1{}.Point().Mul(secretKey, Generator)

To generate random output from a big.Int seed, pass sk and the seed to GenerateProof, and use the Output field of the returned Proof object.

To verify a Proof object p, run p.Verify(); or to verify it on-chain pass p.MarshalForSolidityVerifier() to randomValueFromVRFProof on the VRF solidity contract.

Index

• Constants
• Variables
• func FieldHash(msg []byte) *big.Int
• func HashToCurve(p kyber.Point, input *big.Int, ordinates func(x *big.Int)) (kyber.Point, error)
• func HashUint256s(xs ...*big.Int) (*big.Int, error)
• func IsCurveXOrdinate(x *big.Int) bool
• func IsSquare(x *big.Int) bool
• func ProjectiveECAdd(p, q kyber.Point) (x, y, z fieldElt)
• func ScalarFromCurvePoints(hash, pk, gamma kyber.Point, uWitness [20]byte, v kyber.Point) *big.Int
• func SquareRoot(x *big.Int) *big.Int
• func YSquared(x *big.Int) *big.Int
• type MarshaledProof
  • func (m MarshaledProof) String() string
• type Proof
  • func GenerateProof(secretKey, seed common.Hash) (*Proof, error)
  • func UnmarshalSolidityProof(proof []byte) (rv Proof, err error)
  • func (p *Proof) MarshalForSolidityVerifier() (MarshaledProof, error)
  • func (p *Proof) SolidityPrecalculations() (*SolidityProof, error)
  • func (p *Proof) String() string
  • func (p *Proof) VerifyVRFProof() (bool, error)
  • func (p *Proof) WellFormed() bool
• type SolidityProof
  • func (p *SolidityProof) MarshalForSolidityVerifier() (proof MarshaledProof)
  • func (p *SolidityProof) String() string

Constants

const ProofLength = 64 +
	64 +
	32 +
	32 +
	32 +
	32 +
	64 +
	64 +

	32 // zInv  (Leave Output out, because that can be efficiently calculated)

Length of marshaled proof, in bytes

Variables

var ErrCGammaEqualsSHash = fmt.Errorf(
	"pick a different nonce; c*gamma = s*hash, with this one")

var FieldSize = bigFromHex(
	"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F")

FieldSize is number of elements in secp256k1's base field, i.e. GF(FieldSize)

var Generator = secp256k1Curve.Point().Base()

Generator is the generator point of secp256k1

Functions

func FieldHash

func FieldHash(msg []byte) *big.Int

FieldHash hashes xs uniformly into {0, ..., fieldSize-1}. msg is assumed to already be a 256-bit hash

func HashToCurve

func HashToCurve(p kyber.Point, input *big.Int, ordinates func(x *big.Int),
) (kyber.Point, error)

HashToCurve is a cryptographic hash function which outputs a secp256k1 point, or an error. It passes each candidate x ordinate to ordinates function.

func HashUint256s

func HashUint256s(xs ...*big.Int) (*big.Int, error)

HashUint256s returns a uint256 representing the hash of the concatenated byte representations of the inputs

func IsCurveXOrdinate

func IsCurveXOrdinate(x *big.Int) bool

IsCurveXOrdinate returns true iff there is y s.t. y^2=x^3+7

func IsSquare

func IsSquare(x *big.Int) bool

IsSquare returns true iff x = y^2 for some y in GF(p)

func ProjectiveECAdd

func ProjectiveECAdd(p, q kyber.Point) (x, y, z fieldElt)

ProjectiveECAdd(px, py, qx, qy) duplicates the calculation in projective coordinates of VRF.sol#projectiveECAdd, so we can reliably get the denominator (i.e, z)

func ScalarFromCurvePoints

func ScalarFromCurvePoints(
	hash, pk, gamma kyber.Point, uWitness [20]byte, v kyber.Point) *big.Int

ScalarFromCurve returns a hash for the curve points. Corresponds to the hash computed in VRF.sol#ScalarFromCurvePoints

func SquareRoot

func SquareRoot(x *big.Int) *big.Int

SquareRoot returns a s.t. a^2=x, as long as x is a square

func YSquared

func YSquared(x *big.Int) *big.Int

YSquared returns x^3+7 mod fieldSize, the right-hand side of the secp256k1 curve equation.

Types

type MarshaledProof

type MarshaledProof [ProofLength]byte

MarshaledProof contains a VRF proof for randomValueFromVRFProof.

NB: when passing one of these to randomValueFromVRFProof via the geth blockchain simulator, it must be passed as a slice ("proof[:]"). Passing it as-is sends hundreds of single bytes, each padded to their own 32-byte word.

func (MarshaledProof) String

func (m MarshaledProof) String() string

String returns m as 0x-hex bytes

type Proof

type Proof struct {
	PublicKey kyber.Point // secp256k1 public key of private key used in proof
	Gamma     kyber.Point
	C         *big.Int
	S         *big.Int
	Seed      *big.Int // Seed input to verifiable random function
	Output    *big.Int // verifiable random function output;, uniform uint256 sample
}

Proof represents a proof that Gamma was constructed from the Seed according to the process mandated by the PublicKey.

N.B.: The kyber.Point fields must contain secp256k1.secp256k1Point values, C, S and Seed must be secp256k1Point, and Output must be at most 256 bits. See Proof.WellFormed.

func GenerateProof

func GenerateProof(secretKey, seed common.Hash) (*Proof, error)

GenerateProof returns gamma, plus proof that gamma was constructed from seed as mandated from the given secretKey, with public key secretKey*Generator

secretKey and seed must be less than secp256k1 group order. (Without this constraint on the seed, the samples and the possible public keys would deviate very slightly from uniform distribution.)

func UnmarshalSolidityProof

func UnmarshalSolidityProof(proof []byte) (rv Proof, err error)

func (*Proof) MarshalForSolidityVerifier

func (p *Proof) MarshalForSolidityVerifier() (MarshaledProof, error)

MarshalForSolidityVerifier renders p as required by randomValueFromVRFProof

func (*Proof) SolidityPrecalculations

func (p *Proof) SolidityPrecalculations() (*SolidityProof, error)

SolidityPrecalculations returns the precomputed values needed by the solidity verifier, or an error on failure.

func (*Proof) String

func (p *Proof) String() string

func (*Proof) VerifyVRFProof

func (p *Proof) VerifyVRFProof() (bool, error)

VerifyProof is true iff gamma was generated in the mandated way from the given publicKey and seed, and no error was encountered

func (*Proof) WellFormed

func (p *Proof) WellFormed() bool

WellFormed is true iff p's attributes satisfy basic domain checks

type SolidityProof

type SolidityProof struct {
	P                           *Proof         // The core proof
	UWitness                    common.Address // Address of P.C*P.PK+P.S*G
	CGammaWitness, SHashWitness kyber.Point    // P.C*P.Gamma, P.S*HashToCurve(P.Seed)
	ZInv                        *big.Int       // Inverse of Z coord from ProjectiveECAdd(CGammaWitness, SHashWitness)
}

SolidityProof contains precalculations which VRF.sol needs to verifiy proofs

func (*SolidityProof) MarshalForSolidityVerifier

func (p *SolidityProof) MarshalForSolidityVerifier() (proof MarshaledProof)

MarshalForSolidityVerifier renders p as required by randomValueFromVRFProof

func (*SolidityProof) String

func (p *SolidityProof) String() string

String returns the values in p, in hexadecimal format