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 ...

• Type: Conference
• Year: 2010
• Where: COCO
• Authors: Iftach Haitner, Mohammad Mahmoody, David Xiao
• Keywords: Algorithms, COCO 2010, Collisionresistant Hash Functions, Constant-round Public-coin Protocol, Oracle