One-Way Functions in Worst-Case Cryptography: Algebraic and Security Properties

A. Beygelzimer; L. A. Hemaspaandra; C. M. Homan; J. Rothe

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One-Way Functions in Worst-Case Cryptography: Algebraic and Security Properties

A. Beygelzimer·L. A. Hemaspaandra·C. M. Homan·J. Rothe

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Abstract

We survey recent developments in the study of (worst-case) one-way functions having strong algebraic and security properties. According to [RS93], this line of research was initiated in 1984 by Rivest and Sherman who designed two-party secret-key agreement protocols that use strongly noninvertible, total, associative one-way functions as their key building blocks. If commutativity is added as an ingredient, these protocols can be used by more than two parties, as noted by Rabi and Sherman [RS93] who also developed digital signature protocols that are based on such enhanced one-way functions. Until recently, it was an open question whether one-way functions having the algebraic and security properties that these protocols require could be created from any given one-way function. Recently, Hemaspaandra and Rothe [HR99] resolved this open issue in the affirmative, by showing that one-way functions exist if and only if strong, total, commutative, associative one-way functions exist. We discuss this result, and the work of Rabi, Rivest, and Sherman, and recent work of Homan [Hom99] that makes progress on related issues.

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A. Beygelzimer, L. A. Hemaspaandra, C. M. Homan, J. Rothe. 1999-11-15. One-Way Functions in Worst-Case Cryptography: Algebraic and Security Properties. https://arxiv.org/abs/cs/9911007

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