We study the round complexity of various cryptographic protocols. Our main result is a tight lower
bound on the round complexity of any fully-black-box construction of a statistically-hiding
commitment scheme from one-way permutations, and even from trapdoor permutations. This lower bound matches the round complexity of the statistically-hiding commitment scheme due to Naor, Ostrovsky, Venkatesan and Yung (CRYPTO '92). As a corollary, we derive similar tight lower bounds for several other cryptographic protocols, such as single-server private information retrieval, interactive hashing, and oblivious transfer that guarantees statistical security for one of the parties.
Our techniques extend the collision-finding oracle due to Simon (EUROCRYPT '98) to the setting of
interactive protocols (our extension also implies an alternative proof for the main property of the
original oracle). In addition, we substantially extend the reconstruction paradigm of Gennaro and
Trevisan (FOCS `00). In both cases, our extensions are quite delicate and may be found useful in
proving additional black-box separation results.
Joint work with Iftach Haitner, Omer Reingold and Gil Segev.