Cryptology ePrint Archive: Report 2018/327

A Note On Groth-Ostrovsky-Sahai Non-Interactive Zero-Knowledge Proof System

Zhengjun Cao and Lihua Liu

Abstract: In 2006, Groth, Ostrovsky and Sahai designed one non-interactive zero-knowledge (NIZK) proof system [new version, J. ACM, 59(3), 1-35, 2012] for plaintext being zero or one using bilinear groups with composite order. Based on the system, they presented the first perfect NIZK argument system for any NP language and the first universal composability secure NIZK argument for any NP language in the presence of a dynamic/adaptive adversary. This resolves a central open problem concerning NIZK protocols. In this note, we remark that in their proof system the prover has not to invoke the trapdoor key to generate witnesses. The mechanism was dramatically different from the previous works, such as Blum-Feldman-Micali proof system and Blum-Santis-Micali-Persiano proof system. We would like to stress that the prover can cheat the verifier to accept a false claim if the trapdoor key is available to him.

Category / Keywords: cryptographic protocols / Non-interactive zero-knowledge proof; bilinear groups with composite order; subgroup decision problem

Date: received 8 Apr 2018

Contact author: liulh at shmtu edu cn

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Version: 20180409:121722 (All versions of this report)

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