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Title:
Lower Bounds on Signatures From Symmetric Primitives
Authors: Boaz Barak, Mohammad Mahmoody
Abstract: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 schemes from symmetric primitives when the construction is black-box. This can be taken as evidence of an inherent efficiency gap between signature schemes and symmetric primitives.
ePrint: https://eprint.iacr.org/2008/033
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