A Note on One Popular Non-Interactive Zero-Knowledge Proof System

Zhengjun Cao ； Xiqi Wang ； Lihua Liu

《International Journal of Network Security》 22卷4期 (2020/07) Pp. 681-685

https://doi.org/10.6633/IJNS.202007_22(4).17

摘要

At Eurocrypt'06, Groth et al. have proposed one non-interactive zero-knowledge (NIZK) proof system for plaintext being 0 or 1 [its revision published by J. ACM, 59(3), 1-35, 2012]. Based on the system, they presented the first perfect NIZK argument system for any NP language and the first secure NIZK argument with universal composability for any NP language in the presence of a dynamic/adaptive adversary. In this note, we remark that in the scheme the prover is not compelled to invoke any trapdoor key to generate witnesses. The mechanism is dramatically different from the previous works, such as Blum-Feldman-Micali proof system and Blum-Santis-Micali-Persiano proof system. We find if the trapdoor key is available to the prover then he can cheat the verifier to accept a false claim. The characteristic is essentially incompatible with the general primitive of zero-knowledge proof, which does not require any extra trust.

關鍵字

Bilinear Groups with Composite Order ； Extended Euclid Algorithm ； Non-interactive Zero-knowledge Proof ； Subgroup Decision Problem