Introduction

This resource implements an improved SigmaProtocol——UGZK protocol():let $n$ be a positive integer and let $i \in [1,n]$. For a given vector ${Z_i}{i \in [1,n]}$, the protocol is a proof of knowledge of a vector ${[x_i]}{i \in[1,n]}$ such that $Z_i = [x_i]$ , where $[x_i] = OneWayHomomorphismFun(x)$

The resource implements the struct of Non-interactive Sigma Protocol in SigmaProtocol.h, which includes five main part:

• SigmaProtocolCommonInput: consists of public parameters used in the protocol

• SigmaProtocolResponseMsgShort & SigmaProtocolResponseMsgBatch: the two correspond to two different implementation ways of sigma protocol

• SigmaProtocolProver: SigmaProtocolProverShort & SigmaProtocolProverBatch

• SigmaProtocolVerifier: SigmaProtocolVerifierShort & SigmaProtocolVerifierBatch

• function SigmaProtocolGetchallenge: used to compute the challenge message in SigmaProtocol

The resource implements four sigma protocols:

• Schnorr protocol: proving knowledge of the discrete logarithm $w$ of a point $Y$ in base $G$
• DlogEquality protocol: proving equality of the known discrete logarithm $w$ of $Y_1$ in base $G$ and $Y_2$
• PedersenCommitmentOpen: proving knowledge of a valid opening of a Pedersen commitment
• Diffie-Hellman triple Protocol: proving knowledge of the exponents of a valid Diffie-Hellman triple