An Approach to the Construction of a Recursive Argument of Polynomial Evaluation in the Discrete Log Setting

【Author】 Kim, Sungwook

【Source】ELECTRONICS

【影响因子】2.690

【Abstract】Succinct Non-interactive Arguments of Knowledge (SNARks) are receiving a lot of attention as a core privacy-enhancing technology for blockchain applications. Polynomial commitment schemes are important building blocks for the construction of SNARks. Polynomial commitment schemes enable the prover to commit to a secret polynomial of the prover and convince the verifier that the evaluation of the committed polynomial is correct at a public point later. Bunz et al. recently presented a novel polynomial commitment scheme with no trusted setup in Eurocrypt'20. To provide a transparent setup, their scheme is built over an ideal class group of imaginary quadratic fields (or briefly, class group). However, cryptographic assumptions on a class group are relatively new and have, thus far, not been well-analyzed. In this paper, we study an approach to transpose Bunz et al.'s techniques in the discrete log setting because the discrete log setting brings a significant improvement in efficiency and security compared to class groups. We show that the transposition to the discrete log setting can be obtained by employing a proof system for the equality of discrete logarithms over multiple bases. Theoretical analysis shows that the transposition preserves security requirements for a polynomial commitment scheme.

【Keywords】blockchain privacy; zero-knowledge proof; proof of knowledge; polynomial commitment; recursive argument; discrete log

【发表时间】2022 JAN

【收录时间】2022-01-19

【文献类型】期刊

【主题类别】

区块链技术--