mta

Documentation

Index

• Constants
• func AliceEnd(Session []byte, ec elliptic.Curve, pkA *paillier.PublicKey, pf *ProofBob, ...) (*big.Int, error)
• func AliceEndWC(Session []byte, ec elliptic.Curve, pkA *paillier.PublicKey, pf *ProofBobWC, ...) (*big.Int, error)
• type ProofBob
  • func BobMid(Session []byte, ec elliptic.Curve, pkA *paillier.PublicKey, ...) (beta, cB, betaPrm *big.Int, piB *ProofBob, err error)
  • func ProofBobFromBytes(bzs [][]byte) (*ProofBob, error)
  • func ProveBob(Session []byte, ec elliptic.Curve, pk *paillier.PublicKey, ...) (*ProofBob, error)
  • func (pf *ProofBob) Bytes() [ProofBobBytesParts][]byte
  • func (pf *ProofBob) ValidateBasic() bool
  • func (pf *ProofBob) Verify(Session []byte, ec elliptic.Curve, pk *paillier.PublicKey, ...) bool
• type ProofBobWC
  • func BobMidWC(Session []byte, ec elliptic.Curve, pkA *paillier.PublicKey, ...) (beta, cB, betaPrm *big.Int, piB *ProofBobWC, err error)
  • func ProofBobWCFromBytes(ec elliptic.Curve, bzs [][]byte) (*ProofBobWC, error)
  • func ProveBobWC(Session []byte, ec elliptic.Curve, pk *paillier.PublicKey, ...) (*ProofBobWC, error)
  • func (pf *ProofBobWC) Bytes() [ProofBobWCBytesParts][]byte
  • func (pf *ProofBobWC) ValidateBasic() bool
  • func (pf *ProofBobWC) Verify(Session []byte, ec elliptic.Curve, pk *paillier.PublicKey, ...) bool
• type RangeProofAlice
  • func AliceInit(ec elliptic.Curve, pkA *paillier.PublicKey, a, NTildeB, h1B, h2B *big.Int, ...) (cA *big.Int, pf *RangeProofAlice, err error)
  • func ProveRangeAlice(ec elliptic.Curve, pk *paillier.PublicKey, c, NTilde, h1, h2, m, r *big.Int, ...) (*RangeProofAlice, error)
  • func RangeProofAliceFromBytes(bzs [][]byte) (*RangeProofAlice, error)
  • func (pf *RangeProofAlice) Bytes() [RangeProofAliceBytesParts][]byte
  • func (pf *RangeProofAlice) ValidateBasic() bool
  • func (pf *RangeProofAlice) Verify(ec elliptic.Curve, pk *paillier.PublicKey, NTilde, h1, h2, c *big.Int) bool

Constants

const (
	// ProofBobBytesParts is the number of byte parts in a serialized ProofBob.
	ProofBobBytesParts = 10
	// ProofBobWCBytesParts is the number of byte parts in a serialized ProofBobWC.
	ProofBobWCBytesParts = 12
)

const (
	// RangeProofAliceBytesParts is the number of byte parts in a serialized RangeProofAlice.
	RangeProofAliceBytesParts = 6
)

Functions

func AliceEnd

func AliceEnd(
	Session []byte,
	ec elliptic.Curve,
	pkA *paillier.PublicKey,
	pf *ProofBob,
	h1A, h2A, cA, cB, NTildeA *big.Int,
	sk *paillier.PrivateKey,
) (*big.Int, error)

AliceEnd completes the MtA protocol for Alice by verifying Bob's proof and decrypting the result.

func AliceEndWC

func AliceEndWC(
	Session []byte,
	ec elliptic.Curve,
	pkA *paillier.PublicKey,
	pf *ProofBobWC,
	B *crypto.ECPoint,
	cA, cB, NTildeA, h1A, h2A *big.Int,
	sk *paillier.PrivateKey,
) (*big.Int, error)

AliceEndWC completes the MtA protocol for Alice with the consistency check by verifying Bob's proof and decrypting the result.

Types

type ProofBob

type ProofBob struct {
	Z, ZPrm, T, V, W, S, S1, S2, T1, T2 *big.Int
}

ProofBob is Bob's zero-knowledge proof used in the MtA protocol without the consistency check.

func BobMid

func BobMid(
	Session []byte,
	ec elliptic.Curve,
	pkA *paillier.PublicKey,
	pf *RangeProofAlice,
	b, cA, NTildeA, h1A, h2A, NTildeB, h1B, h2B *big.Int,
	rand io.Reader,
) (beta, cB, betaPrm *big.Int, piB *ProofBob, err error)

BobMid performs Bob's middle step in the MtA protocol without the consistency check.

func ProofBobFromBytes

func ProofBobFromBytes(bzs [][]byte) (*ProofBob, error)

ProofBobFromBytes reconstructs a ProofBob from a slice of byte slices.

func ProveBob

func ProveBob(Session []byte, ec elliptic.Curve, pk *paillier.PublicKey, NTilde, h1, h2, c1, c2, x, y, r *big.Int, rand io.Reader) (*ProofBob, error)

ProveBob implements Bob's proof "ProveMta_Bob" used in the MtA protocol from GG18Spec (9) Fig. 11.

func (*ProofBob) Bytes

func (pf *ProofBob) Bytes() [ProofBobBytesParts][]byte

Bytes serializes the ProofBob into a fixed-size array of byte slices.

func (*ProofBob) ValidateBasic

func (pf *ProofBob) ValidateBasic() bool

ValidateBasic checks that all fields of the ProofBob are non-nil.

func (*ProofBob) Verify

func (pf *ProofBob) Verify(Session []byte, ec elliptic.Curve, pk *paillier.PublicKey, NTilde, h1, h2, c1, c2 *big.Int) bool

ProveBob.Verify implements verification of Bob's proof without check "VerifyMta_Bob" used in the MtA protocol from GG18Spec (9) Fig. 11.

type ProofBobWC

type ProofBobWC struct {
	*ProofBob
	U *crypto.ECPoint
}

ProofBobWC is Bob's zero-knowledge proof used in the MtA protocol with the consistency check (X = g^x).

func BobMidWC

func BobMidWC(
	Session []byte,
	ec elliptic.Curve,
	pkA *paillier.PublicKey,
	pf *RangeProofAlice,
	b, cA, NTildeA, h1A, h2A, NTildeB, h1B, h2B *big.Int,
	B *crypto.ECPoint,
	rand io.Reader,
) (beta, cB, betaPrm *big.Int, piB *ProofBobWC, err error)

BobMidWC performs Bob's middle step in the MtA protocol with the consistency check (B = g^b).

func ProofBobWCFromBytes

func ProofBobWCFromBytes(ec elliptic.Curve, bzs [][]byte) (*ProofBobWC, error)

ProofBobWCFromBytes reconstructs a ProofBobWC from a slice of byte slices and the elliptic curve.

func ProveBobWC

func ProveBobWC(Session []byte, ec elliptic.Curve, pk *paillier.PublicKey, NTilde, h1, h2, c1, c2, x, y, r *big.Int, X *crypto.ECPoint, rand io.Reader) (*ProofBobWC, error)

ProveBobWC implements Bob's proof both with or without check "ProveMtawc_Bob" and "ProveMta_Bob" used in the MtA protocol from GG18Spec (9) Figs. 10 & 11. an absent `X` generates the proof without the X consistency check X = g^x

func (*ProofBobWC) Bytes

func (pf *ProofBobWC) Bytes() [ProofBobWCBytesParts][]byte

Bytes serializes the ProofBobWC into a fixed-size array of byte slices including the ECPoint U.

func (*ProofBobWC) ValidateBasic

func (pf *ProofBobWC) ValidateBasic() bool

ValidateBasic checks that all fields of the ProofBobWC are non-nil, including the embedded ProofBob.

func (*ProofBobWC) Verify

func (pf *ProofBobWC) Verify(Session []byte, ec elliptic.Curve, pk *paillier.PublicKey, NTilde, h1, h2, c1, c2 *big.Int, X *crypto.ECPoint) bool

ProveBobWC.Verify implements verification of Bob's proof with check "VerifyMtawc_Bob" used in the MtA protocol from GG18Spec (9) Fig. 10. an absent `X` verifies a proof generated without the X consistency check X = g^x

type RangeProofAlice

type RangeProofAlice struct {
	Z, U, W, S, S1, S2 *big.Int
}

RangeProofAlice is Alice's range proof used in the MtA protocol to prove her secret is within a valid range.

func AliceInit

func AliceInit(
	ec elliptic.Curve,
	pkA *paillier.PublicKey,
	a, NTildeB, h1B, h2B *big.Int,
	rand io.Reader,
) (cA *big.Int, pf *RangeProofAlice, err error)

AliceInit encrypts Alice's secret and produces a range proof for the MtA protocol.

func ProveRangeAlice

func ProveRangeAlice(ec elliptic.Curve, pk *paillier.PublicKey, c, NTilde, h1, h2, m, r *big.Int, rand io.Reader) (*RangeProofAlice, error)

ProveRangeAlice implements Alice's range proof used in the MtA and MtAwc protocols from GG18Spec (9) Fig. 9.

func RangeProofAliceFromBytes

func RangeProofAliceFromBytes(bzs [][]byte) (*RangeProofAlice, error)

RangeProofAliceFromBytes reconstructs a RangeProofAlice from a slice of byte slices.

func (*RangeProofAlice) Bytes

func (pf *RangeProofAlice) Bytes() [RangeProofAliceBytesParts][]byte

Bytes serializes the RangeProofAlice into a fixed-size array of byte slices.

func (*RangeProofAlice) ValidateBasic

func (pf *RangeProofAlice) ValidateBasic() bool

ValidateBasic checks that all fields of the RangeProofAlice are non-nil.

func (*RangeProofAlice) Verify

func (pf *RangeProofAlice) Verify(ec elliptic.Curve, pk *paillier.PublicKey, NTilde, h1, h2, c *big.Int) bool

Verify checks whether Alice's range proof is valid for the given public parameters and ciphertext.