%0 Journal Article
%T Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representation
%A Philippe Dumas
%A Helger Lipmaa
%A Johan Wall¨Śn
%J Discrete Mathematics & Theoretical Computer Science
%D 2007
%I Discrete Mathematics & Theoretical Computer Science
%X 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.
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/478