This paper presents a 4-move perfect ZKIP of knowledge with no cryptographic assumption for the random self reducible problems [TW87] whose domain is NP∩BPP. The certified discrete log problem is such an example. (Finding a witness is more difficult than the language membership problem.) A largely simplified 4-move ZKIP for the Hamilton Circuit problem is also shown. In our ZKIP, a trapdoor coin flipping protocol is introduced to generate a challenge bit. P and V cooperatively generate a random bit in a coin flipping protocol. In a trapdoor coin flipping protocol, V who knows the trapdoor can create the view which he can later reveal in two possible ways: both as head and as tail.
CITATION STYLE
Saito, T., Kurosawa, K., & Sakurai, K. (1993). 4 move perfect ZKIP of knowledge with no assumption. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 739 LNCS, pp. 321–330). Springer Verlag. https://doi.org/10.1007/3-540-57332-1_27
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