International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Lower Bounds on Signatures From Symmetric Primitives

Boaz Barak
Mohammad Mahmoody-Ghidardy
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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.
  title={Lower Bounds on Signatures From Symmetric Primitives},
  booktitle={IACR Eprint archive},
  keywords={signature schemes, random oracle, symmetric primitives},
  note={ 13905 received 23 Jan 2008, last revised 27 Jan 2008},
  author={Boaz Barak and Mohammad Mahmoody-Ghidardy},