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In this paper we model a class of stream and block ciphers as systems of(ordinary) explicit difference equations over a finite field. We call thisclass "difference ciphers" and we show that ciphers of application interest, asfor example systems of LFSRs with a combiner, Trivium and Keeloq, belong to theclass. By using Difference Algebra, that is, the formal theory of differenceequations, we can properly define and study important properties of theseciphers, such as their invertibility and periodicity. We describe then generalcryptanalytic methods for difference ciphers that follow from these propertiesand are useful to assess the security. We illustrate such algebraic attacks inpractice by means of the ciphers Bivium and Keeloq.

Stream/block ciphers, difference equations and algebraic attacks