Abstract : We analyse the asymptotic behaviour in the mean of a non-commutative rational series, which originates from differential cryptanalysis, using tools from probability theory, and from analytic number theory. We derive a Fourier representation of a first-order summation function obtained by interpreting this rational series as a non-classical rational sequence via the octal numeration system. The method is applicable to a wide class of sequences rational with respect to a numeration system essentially under the condition that they admit a linear representation with nonnegative coefficients.
https://hal.inria.fr/hal-00966501
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Philippe Dumas, Helger Lipmaa, Johan Wallén. Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representation. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2007, 9 (1), pp.247--272. ⟨hal-00966501⟩
