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.

Source : oai:HAL:hal-00966501v1

Volume: Vol. 9 no. 1

Section: Analysis of Algorithms

Published on: January 1, 2007

Submitted on: March 26, 2015

Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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