Year: 2012
Type: preprint
Abstract: We extend symbolic protocol analysis to apply to protocols using Diffie-Hellman operations. Diffie-Hellman operations act on a cyclic group of prime order, together with an exponentiation operator. The exponents form a finite field. This rich algebraic structure has resisted previous symbolic approaches. We work in an algebra defined by the normal forms of a rewriting theory (modulo associativity and commutativity). These normal forms allow us to define our crucial notion of indicator, a vector of integers that summarizes how many times each secret exponent appears in a message. We prove that the adversary can never construct a message with a new indicator in our adversary model. Using this invariant, we prove the main security goals achieved by several different protocols that use Diffie-Hellman operators in subtle ways. We also give a model-theoretic justification of our rewriting theory: the theory proves all equations that are uniformly true as the order of the cyclic group varies.
Source: arXiv (Cornell University)
Authors: Dougherty, Daniel J., Guttman, Joshua D.
Institution: Worcester Polytechnic Institute
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2150438708