**Lower Bounds on Signatures From Symmetric Primitives**

*Boaz Barak, Mohammad Mahmoody-Ghidardy*

**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.

**Category / Keywords: **signature schemes, random oracle, symmetric primitives

**Date: **received 23 Jan 2008, last revised 27 Jan 2008

**Contact author: **mohammad at cs princeton edu

**Available format(s): **PDF | BibTeX Citation

**Version: **20080128:152433 (All versions of this report)

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