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Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representation
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.
Cited literature [18 references]
https://hal.inria.fr/hal-00966501
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Submitted on : Wednesday, March 26, 2014 - 4:59:16 PM
Last modification on : Tuesday, June 30, 2020 - 12:20:03 PM
Long-term archiving on: : Thursday, June 26, 2014 - 11:55:53 AM
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Submitted on : Wednesday, March 26, 2014 - 4:59:16 PM
Last modification on : Tuesday, June 30, 2020 - 12:20:03 PM
Long-term archiving on: : Thursday, June 26, 2014 - 11:55:53 AM
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