Some Low Round Zero Knowledge Protocols

In this paper, we focus on zero-knowledge protocols for NP with low round complexity under the augmented black-box simulation technique, in which the simulator has access to the verifier\u27s secret information, and obtain positive results on 3-round zero-knowledge proofs and 2-round zero-knowledge arguments for NP and 2-round zero-knowledge proofs for QNR. More precisely, our contributions are five-fold: (i) we propose the notion of generalized claw-free function and the notion of trapdoor generalized claw-free function, and then we show a construction of trapdoor generalized claw-free function under the discrete logarithm assumption and the knowledge of exponent assumption, (ii) we propose the notion of completely extractable bit-commitment and give a construction of it from trapdoor generalized claw-free functions, (iii) we present a 3-round zero-knowledge proof for NP based on the completely extractable bit-commitment schemes and Yao\u27s garbling circuit technique, (iv) we show a 2-round zero-knowledge argument for NP based on indistinguishable obfuscator, (v) we transform the basic 2-round honest verifier zero-knowledge proof protocol for quadratic non-residue into a 2-round zero-knowledge proof protocol

From Point Obfuscation To 3-round Zero-Knowledge

We construct 3-round proofs and arguments with negligible soundness error satisfying two relaxed notions of {\em zero-knowledge}: {\em Weak ZK} and {\em witness hiding} (WH). At the heart of our constructions lie new techniques based on {\em point obfuscation with auxiliary input} (AIPO). It is known that such protocols cannot be proven secure using black-box reductions (or simulation). Our constructions circumvent these lower bounds, utilizing AIPO (and extensions) as the ``non-black-box component in the security reduction. We also investigate the relation between AIPO and the assumptions previously used to achieve 3-round ZK