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 Unification modulo a partial theory of exponentiation


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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.



Author: Deepak Kapur; Andrew Marshall; Paliath Narendran

Source: https://archive.org/



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