Paper 2008/033
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.
Metadata
- Available format(s)
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- signature schemesrandom oraclesymmetric primitives
- Contact author(s)
- mohammad @ cs princeton edu
- History
- 2019-03-31: revised
- 2008-01-28: received
- See all versions
- Short URL
- https://ia.cr/2008/033
- License
-
CC BY