Rafail Ostrovsky - Publications

Efficiency Preserving Transformations for Concurrent Non-Malleable Zero Knowledge

Rafail Ostrovsky, Omkant Pandey, Ivan Visconti

Abstract:

Ever since the invention of Zero-Knowledge by Goldwasser, Micali, and Rackoff[1], Zero-Knowledge has become a central building block in cryptography - with numerous applications, ranging from electronic cash to digital signatures. The properties of Zero-Knowledge range from the most simple (and not particularly useful in practice) requirements, such as honest-verifier zero-knowledge to the most demanding (and most useful in applications) such as non-malleable and concurrent zero-knowledge. In this paper, we study the complexity of efficient zero-knowledge reductions, from the first type to the second type. More precisely, under a standard complexity assumption (DDH), on input a public-coin honest-verifier statistical zero knowledge argument of knowledge Π for a language L we show a compiler that produces an argument system Π for L that is concurrent non-malleable zero-knowledge (under non-adaptive inputs -- which is the best one can hope to achieve [2,3]. If k is the security parameter, the overhead of our compiler is as follows:

• The round complexity of Π is r+\tilde{O}(\log k) rounds, where $r$ is the round complexity of Π'.
• The new prover P (resp., the new verifier V) incurs an additional overhead of (at most) r+k \tilde(O)(\log^2 k) modular exponentiations. If tags of length \tilde{O}(\log k) are provided, the overhead is only r+\tilde(O)\log ^2 k) modular exponentiations.

comment: Preliminary version in TCC 2010.

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