On local exponents of the mixing graphs for the functions realized by A5/1 type algorithms

It is shown that the mixing graphs for the functions realized by A5/1 type algorithms based on linear feedback shift registers of lengths n, m, p with characteristic polynomials of weights v, n are primitive. The following lower and upper bounds for the mixing graph exponent and local exponent depending on these parameters take place: 1 + max{\n/v], \m/^\, \p/n]} ^ exp Г ^ max{n, m,p}. It is obtained that, for A5/1 algorithm, exponent exp Г and local exponent *J-expT, J = {1, 20, 42}, are equal to 21. This matches the idle running length of A5/1 generator.

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