## Cryptology ePrint Archive: Report 2005/365

Derandomization in Cryptography

Boaz Barak and Shien Jin Ong and Salil Vadhan

Abstract: We give two applications of Nisan--Wigderson-type ("non-cryptographic") pseudorandom generators in cryptography. Specifically, assuming the existence of an appropriate NW-type generator, we construct:

A one-message witness-indistinguishable proof system for every language in NP, based on any trapdoor permutation. This proof system does not assume a shared random string or any setup assumption, so it is actually an "NP proof system."

A noninteractive bit commitment scheme based on any one-way function.

The specific NW-type generator we need is a hitting set generator fooling nondeterministic circuits. It is known how to construct such a generator if ETIME = DTIME(2^O(n)) has a function of nondeterministic circuit complexity 2^\Omega(n) (Miltersen and Vinodchandran, FOCS 99).

Our witness-indistinguishable proofs are obtained by using the NW-type generator to derandomize the ZAPs of Dwork and Naor (FOCS 00). To our knowledge, this is the first construction of an NP proof system achieving a secrecy property.

Our commitment scheme is obtained by derandomizing the interactive commitment scheme of Naor (J. Cryptology, 1991). Previous constructions of noninteractive commitment schemes were only known under incomparable assumptions.

Category / Keywords: foundations /

Publication Info: An extended abstract of this paper appeared in CRYPTO 2003.

Date: received 9 Oct 2005

Contact author: shienjin at eecs harvard edu

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Short URL: ia.cr/2005/365

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