bulletproofs

Documentation

Index

• Variables
• func HashBP(A, S *p256.P256) (*big.Int, *big.Int, error)
• func IsPowerOfTwo(x int64) bool
• func ScalarProduct(a, b []*big.Int) (*big.Int, error)
• func SetupGeneric(a, b int64) (*bprp, error)
• func VectorAdd(a, b []*big.Int) ([]*big.Int, error)
• func VectorConvertToBig(a []int64, n int64) ([]*big.Int, error)
• func VectorCopy(a *big.Int, n int64) ([]*big.Int, error)
• func VectorECAdd(a, b []*p256.P256) ([]*p256.P256, error)
• func VectorExp(a []*p256.P256, b []*big.Int) (*p256.P256, error)
• func VectorMul(a, b []*big.Int) ([]*big.Int, error)
• func VectorScalarMul(a []*big.Int, b *big.Int) ([]*big.Int, error)
• func VectorSub(a, b []*big.Int) ([]*big.Int, error)
• type BulletProof
  • func Prove(secret *big.Int, params BulletProofSetupParams) (BulletProof, error)
  • func (proof *BulletProof) Verify() (bool, error)
• type BulletProofSetupParams
  • func Setup(b int64) (BulletProofSetupParams, error)
• type InnerProductParams
• type InnerProductProof
  • func (proof InnerProductProof) Verify() (bool, error)
• type ProofBPRP
  • func ProveGeneric(secret *big.Int, params *bprp) (ProofBPRP, error)
  • func (proof ProofBPRP) Verify() (bool, error)

Variables

var MAX_RANGE_END int64 = 4294967296 // 2**32

var MAX_RANGE_END_EXPONENT = 32 // 2**32

var ORDER = p256.CURVE.N

var SEEDH = "BulletproofsDoesNotNeedTrustedSetupH"

var SEEDU = "BulletproofsDoesNotNeedTrustedSetupU"

Functions

func HashBP

func HashBP(A, S *p256.P256) (*big.Int, *big.Int, error)

Hash is responsible for the computing a Zp element given elements from GT and G1.

func IsPowerOfTwo

func IsPowerOfTwo(x int64) bool

IsPowerOfTwo returns true for arguments that are a power of 2, false otherwise. https://stackoverflow.com/a/600306/844313

func ScalarProduct

func ScalarProduct(a, b []*big.Int) (*big.Int, error)

ScalarProduct return the inner product between a and b.

func SetupGeneric

func SetupGeneric(a, b int64) (*bprp, error)

SetupGeneric is responsible for calling the Setup algorithm for each BulletProof.

func VectorAdd

func VectorAdd(a, b []*big.Int) ([]*big.Int, error)

VectorAdd computes vector addition componentwisely.

func VectorConvertToBig

func VectorConvertToBig(a []int64, n int64) ([]*big.Int, error)

VectorConvertToBig converts an array of int64 to an array of big.Int.

func VectorCopy

func VectorCopy(a *big.Int, n int64) ([]*big.Int, error)

VectorCopy returns a vector composed by copies of a.

func VectorECAdd

func VectorECAdd(a, b []*p256.P256) ([]*p256.P256, error)

VectorECMul computes vector EC addition componentwisely.

func VectorExp

func VectorExp(a []*p256.P256, b []*big.Int) (*p256.P256, error)

VectorExp computes Prod_i^n{a[i]^b[i]}.

func VectorMul

func VectorMul(a, b []*big.Int) ([]*big.Int, error)

VectorMul computes vector multiplication componentwisely.

func VectorScalarMul

func VectorScalarMul(a []*big.Int, b *big.Int) ([]*big.Int, error)

VectorScalarMul computes vector scalar multiplication componentwisely.

func VectorSub

func VectorSub(a, b []*big.Int) ([]*big.Int, error)

VectorSub computes vector addition componentwisely.

Types

type BulletProof

type BulletProof struct {
	V                 *p256.P256
	A                 *p256.P256
	S                 *p256.P256
	T1                *p256.P256
	T2                *p256.P256
	Taux              *big.Int
	Mu                *big.Int
	Tprime            *big.Int
	InnerProductProof InnerProductProof
	Commit            *p256.P256
	Params            BulletProofSetupParams
}

BulletProofs structure contains the elements that are necessary for the verification of the Zero Knowledge Proof.

func Prove

func Prove(secret *big.Int, params BulletProofSetupParams) (BulletProof, error)

Prove computes the ZK rangeproof. The documentation and comments are based on eprint version of Bulletproofs papers: https://eprint.iacr.org/2017/1066.pdf

func (*BulletProof) Verify

func (proof *BulletProof) Verify() (bool, error)

Verify returns true if and only if the proof is valid.

type BulletProofSetupParams

type BulletProofSetupParams struct {
	// N is the bit-length of the range.
	N int64
	// G is the Elliptic Curve generator.
	G *p256.P256
	// H is a new generator, computed using MapToGroup function,
	// such that there is no discrete logarithm relation with G.
	H *p256.P256
	// Gg and Hh are sets of new generators obtained using MapToGroup.
	// They are used to compute Pedersen Vector Commitments.
	Gg []*p256.P256
	Hh []*p256.P256
	// InnerProductParams is the setup parameters for the inner product proof.
	InnerProductParams InnerProductParams
}

BulletProofSetupParams is the structure that stores the parameters for the Zero Knowledge Proof system.

func Setup

func Setup(b int64) (BulletProofSetupParams, error)

SetupInnerProduct is responsible for computing the common parameters. Only works for ranges to 0 to 2^n, where n is a power of 2 and n <= 32 TODO: allow n > 32 (need uint64 for that).

type InnerProductParams

type InnerProductParams struct {
	N  int64
	Cc *big.Int
	Uu *p256.P256
	H  *p256.P256
	Gg []*p256.P256
	Hh []*p256.P256
	P  *p256.P256
}

InnerProductParams contains elliptic curve generators used to compute Pedersen commitments.

type InnerProductProof

type InnerProductProof struct {
	N      int64
	Ls     []*p256.P256
	Rs     []*p256.P256
	U      *p256.P256
	P      *p256.P256
	Gg     *p256.P256
	Hh     *p256.P256
	A      *big.Int
	B      *big.Int
	Params InnerProductParams
}

InnerProductProof contains the elements used to verify the Inner Product Proof.

func (InnerProductProof) Verify

func (proof InnerProductProof) Verify() (bool, error)

Verify is responsible for the verification of the Inner Product Proof.

type ProofBPRP

type ProofBPRP struct {
	P1 BulletProof
	P2 BulletProof
}

ProofBPRP stores the generic ZKRP.

func ProveGeneric

func ProveGeneric(secret *big.Int, params *bprp) (ProofBPRP, error)

BulletProof only works for interval in the format [0, 2^N). In order to allow generic intervals in the format [A, B) it is necessary to use 2 BulletProofs, as explained in Section 4.3 from the following paper: https://infoscience.epfl.ch/record/128718/files/CCS08.pdf

func (ProofBPRP) Verify

func (proof ProofBPRP) Verify() (bool, error)

Verify call the Verification algorithm for each BulletProof argument.