Lower Bounds on Signatures From Symmetric Primitives

We show that every construction of one-time signature schemes from a random oracle achieves black-box security at most 2(1+o(1))q , where q is the total number of oracle queries asked by the key generation, signing, and verification algorithms. That is, any such scheme can be broken with probability close to 1 by a (computationally unbounded) adversary making 2(1+o(1))q queries to the oracle. This is tight up to a constant factor in the number of queries, since a simple modification of Lamport’s one-time signatures (Lamport ’79) achieves 2(0.812−o(1))q black-box security using q queries to the oracle. Our result extends (with a loss of a constant factor in the number of queries) also to the random permutation and ideal-cipher oracles. Since the symmetric primitives (e.g. block ciphers, hash functions, and message authentication codes) can be constructed by a constant number of queries to the mentioned oracles, as corollary we get lower bounds on the efficiency of signature sch...

• Type: Conference
• Year: 2007
• Where: FOCS
• Authors: Boaz Barak, Mohammad Mahmoody-Ghidary
• Keywords: Black-box Security, FOCS 2007, One-time Signatures, Signature Schemes, Theoretical Computer Science