Unification modulo a partial theory of exponentiation

Deepak Kapur
(University of New Mexico)
Andrew Marshall
(University at Albany-SUNY)
Paliath Narendran
(University at Albany-SUNY)

Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work, we gave many decidability as well as undecidability results for multiple equational theories, involving various properties of modular exponentiation. Here, we consider a partial subtheory focussing only on exponentiation and multiplication operators. Two main results are proved. The first result is positive, namely, that the unification problem for the above theory (in which no additional property is assumed of the multiplication operators) is decidable. The second result is negative: if we assume that the two multiplication operators belong to two different abelian groups, then the unification problem becomes undecidable.

In Maribel Fernandez: Proceedings 24th International Workshop on Unification (UNIF 2010), Edinburgh, United Kingdom, 14th July 2010, Electronic Proceedings in Theoretical Computer Science 42, pp. 12–23.
Published: 21st December 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.42.2 bibtex PDF

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