An Algebraic Characterization of Security of Cryptographic Protocols

TL;DR

This paper explores the algebraic structures underlying cryptographic protocols, providing a formal framework to analyze their security, extending existing models to private-key protocols, and proposing concrete realizations using pseudo-free groups.

Contribution

It introduces an algebraic characterization of cryptographic protocol security, extending the Dolev-Yao model to private-key protocols and proposing pseudo-free groups for concrete realization.

Findings

Algebraic structures can model security properties of protocols

Extension of formal models to private-key protocols

Proposed use of pseudo-free groups for realization

Abstract

Several of the basic cryptographic constructs have associated algebraic structures. Formal models proposed by Dolev and Yao to study the (unconditional) security of public key protocols form a group. The security of some types of protocols can be neatly formulated in this algebraic setting. We investigate classes of two-party protocols. We then consider extension of the formal algebraic framework to private-key protocols. We also discuss concrete realization of the formal models. In this case, we propose a definition in terms of pseudo-free groups.