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2010
Springer

A New Sampling Protocol and Applications to Basing Cryptographic Primitives on the Hardness of NP

9 years 2 months ago
A New Sampling Protocol and Applications to Basing Cryptographic Primitives on the Hardness of NP
We investigate the question of what languages can be decided efficiently with the help of a recursive collisionfinding oracle. Such an oracle can be used to break collisionresistant hash functions or, more generally, statistically hiding commitments. The oracle we consider, Samd where d is the recursion depth, is based on the identically-named oracle defined in the work of Haitner et al. (FOCS '07). Our main result is a constant-round public-coin protocol "AM-Sam" that allows an efficient verifier to emulate a Samd oracle for any constant depth d = O(1) with the help of a BPPNP prover. AM-Sam allows us to conclude that if L is decidable by a k-adaptive randomized oracle algorithm with access to a SamO(1) oracle, then L AM[k] coAM[k]. The above yields the following corollary: assume there exists an O(1)-adaptive reduction that bases constant-round statistically hiding commitment on NP-hardness, then NP coAM and the polynomial hierarchy collapses. The same result holds ...
Iftach Haitner, Mohammad Mahmoody, David Xiao
Added 08 Nov 2010
Updated 08 Nov 2010
Type Conference
Year 2010
Where COCO
Authors Iftach Haitner, Mohammad Mahmoody, David Xiao
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