Abstract
This paper shows that the protocol presented by Goyal et al. can be further simplified for a one-way function, with the simplified protocol being more practical for the decisional Diffie-Hellman assumption. Goyal et al. provided a general transformation from any honest verifier statistical zero-knowledge argument to a concurrent statistical zero-knowledge argument. Their transformation relies only on the existence of one-way functions. For the simplified transformation, the witness indistinguishable proof of knowledge protocols in “parallel” not only plays the role of preamble but also removes some computational zero-knowledge proofs, which Goyal et al. used to prove the existence of the valid openings to the commitments. Therefore, although some computational zero-knowledge proofs are replaced with a weaker notion, the witness indistinguishable protocol, the proof of soundness can still go through.
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