Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representationReport as inadecuate




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1 ALGORITHMS - Algorithms Inria Paris-Rocquencourt 2 University of Tartu 3 TCS - Laboratory for Theoretical Computer Science Espoo

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.





Author: Philippe Dumas - Helger Lipmaa - Johan Wallén -

Source: https://hal.archives-ouvertes.fr/



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