Groth-Sahai Proofs Revisited Again
نویسنده
چکیده
The Groth-Sahai proof system (EUROCRYPT 2008, SIAM Journal of Computing 41(5) [GS12]) provides e cient non-interactive witness-indistinguishable (NIWI) and zero-knowledge (NIZK) proof systems for languages over bilinear groups and is a widely-used versatile tool to design e cient cryptographic schemes and protocols. We revisit randomization of the prover in the GS proof system. We nd an unnoticed bug in the “optimized” randomization in the symmetric bilinear setting with several assumptions, say, the DLIN assumption or the matrix-DH assumption. This bug leads to security issues of the GS NIWI proof system with “optimized” randomization for multi-scalar multiplication equations and the GS NIZK proof system with “optimized” randomization for certain cases of pairing product equations and multi-scalar multiplication equations.
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