Constant-Round Leakage-Resilient Zero-Knowledge Argument for NP from the Knowledge-of-Exponent Assumption

In this paper, we study the design of constant-round or even 3-round zero-knowledge protocols for all NP languages resistant against side channel attack. Garg, Jain, and Sahai firstly formalize a meaningful definition of \((1+\epsilon )\)-leakage-resilient zero-knowledge(LRZK), and give a construction of \((1+\epsilon )\)-LRZK, for every constant \(\epsilon >0\). Then, with Barak’s non-black-box (NBB) simulation technique, Pandey presents the first construction of constant-round LRZK satisfying the ideal requirement \(\epsilon =0\). In this paper, we focus on the construction of constant-round (especially 3-round) LRZK protocols for all NP languages satisfying the ideal requirement \(\epsilon =0\), by means of other techniques. Specially, based on extended Knowledge-of-Exponent Assumption over bilinear groups, we obtain a constant-round LRZK argument for Hamiltonian Cycle (HC) problem, and a 3-round LRZK arguments for circuit satisfiability, which is the first 3-round LRZK protocol for NP.