Paper 2018/327

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

Zhengjun Cao and Lihua Liu


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.

Available format(s)
Cryptographic protocols
Publication info
Preprint. MINOR revision.
Non-interactive zero-knowledge proofbilinear groups with composite ordersubgroup decision problem
Contact author(s)
liulh @ shmtu edu cn
2018-04-09: received
Short URL
Creative Commons Attribution


      author = {Zhengjun Cao and Lihua Liu},
      title = {A Note On Groth-Ostrovsky-Sahai Non-Interactive  Zero-Knowledge Proof System},
      howpublished = {Cryptology ePrint Archive, Paper 2018/327},
      year = {2018},
      note = {\url{}},
      url = {}
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