E. V. Minaeva: Using Numerical Methods for Non-Linear Approximations of Symmetric Block Ciphers CSIT 2000 : 69-74
There is a single way to provide confidence of the data transfer systems reliability consisted in applying of modern methods of cryptanalysis. Symmetric block ciphers play a very important role in cryptographic support today because of their using in bulk encryption. Linear cryptanalysis of symmetric block ciphers is a known-plaintext attack which uses a linear approximation to describe the behavior of the block cipher. Kaliski and Robshaw  showed that a linear cryptanalytic attack using multiple approximations might allow for a reduction in the amount of data required for a successful attack. The same results may be obtained applying a variant of a linear cryptanalytic attack using non-linear approximations . There are several ways to build a non-linear approximation for some cryptographic function. Interpolation is one of the most popular ones. Real ciphers are generally pseudorandom mappings. That is why it is desirable to apply "smooth" approximation by polynoms or rational fractions, which minimize either weigh mean-square error of approximation, or maximum of the absolute error on the whole interval of interpolation. Proposed decision is a method of polynomial sequences reduction. If calculation of the coefficients for linear-independent functions is more difficult, than calculation pieces of polynomial sequences for interpolated function f(x), then we can reduce degree of this (with slight lost of precision) by expressing higher degrees of x in terms of lower degrees and Tchebyshev polynoms.
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Heinz Schweppe and Yuri S. Kabalnov (Eds.): CSIT'2000, Proceedings of 2nd International Workshop on Computer Science and Information Technologies, September 18-23, 2000, Ufa, Russia. USATU Publishers & JurInfoR-MSU Publishing 2000, ISBN 5-86911-312-1
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