Cryptology ePrint Archive: Report 1997/004

A note on negligible functions

Mihir Bellare

Abstract: In theoretical cryptography, one formalizes the notion of an adversary's success probability being ``too small to matter'' by asking that it be a negligible function of the security parameter. We argue that the issue that really arises is what it might mean for a collection of functions to be ``negligible.'' We consider (and define) two such notions, and prove them equivalent. Roughly, this enables us to say that any cryptographic primitive has a specific associated ``security level.'' In particular we say this for any one-way function. We also reconcile different definitions of negligible error arguments and computational proofs of knowledge that have appeared in the literature. Although the motivation is cryptographic, the main result is purely about negligible functions.

Category / Keywords: theory, one-way functions, computationally sound proofs, proofs of knowledge

Publication Info: Appears in Journal of Cryptology, Vol. 15, 2002, pp. 271-284. Earlier version was Technical Report CS97-529, Department of Computer Science and Engineering, UCSD, March 1997.

Date: Received 12 Mar 1997, last revised 7 Oct 2002

Contact author: mihir at cs ucsd edu

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