Geodesic
On local exponents of the mixing graphs for the functions realized by A5/1 type algorithms
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 11-13.

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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 $\nu,\mu,\pi$ are primitive. The following lower and upper bounds for the mixing graph exponent and local exponent depending on these parameters take place: $1+\max\{\lceil n/\nu\rceil,\lceil m/\mu\rceil,\lceil p/\pi\rceil\}\le\exp\Gamma\le\max\{n,m,p\}$. It is obtained that, for A5/1 algorithm, exponent $\exp\Gamma$ and local exponent $*J$-exp $\Gamma$, $J=\{1,20,42\}$, are equal to 21. This matches the idle running length of A5/1 generator.
Keywords: A5/1 generator, primitive graph, exponent, local exponent. 
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     author = {S. N. Kyazhin and V. M. Fomichev},
     title = {On local exponents of the mixing graphs for the functions realized by {A5/1} type algorithms},
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S. N. Kyazhin; V. M. Fomichev. On local exponents of the mixing graphs for the functions realized by A5/1 type algorithms. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 11-13. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a2/

[1] Fomichev V. M., Metody diskretnoi matematiki v kriptologii, Dialog-MIFI, M., 2010

[2] Kyazhin S. N., Fomichev V. M., “Lokalnaya primitivnost grafov i neotritsatelnykh matrits”, Prikladnaya diskretnaya matematika, 2014, no. 3(25), 68–80

[3] Fomichev V. M., “Svoistva putei v grafakh i multigrafakh”, Prikladnaya diskretnaya matematika, 2010, no. 1(7), 118–124