One-Way Permutations, Interactive Hashing and Statistically Hiding Commitments

We present a lower bound on the round complexity of a natural class of black-box constructions of statistically hiding commitments from one-way permutations. This implies a Ω( n log n ) lower bound on the round complexity of a computational form of interactive hashing, which has been used to construct statistically hiding commitments (and related primitives) from various classes of one-way functions, starting with the work of Naor, Ostrovsky, Venkatesan and Yung (J. Cryptology, 1998). Our lower bound matches the round complexity of the protocol studied by Naor et al. Keywords. Interactive hashing, statistically hiding commitments, black-box lower bounds

• Type: Conference
• Year: 2007
• Where: TCC
• Authors: Hoeteck Wee
• Keywords: Black-box Constructions, Cryptography, Interactive Hashing, Lower Bounds, TCC 2007