ENRU
English version: Journal of Applied and Industrial Mathematics, 2017, 11:2, 215226 

Volume 24, No 2, 2017, P. 3252 UDC 519.17
Keywords: additive generator, modified additive generator, mixing di?graph, primitive digraph, shift register, exponent of digraph. DOI: 10.17377/daio.2017.24.528 Alisa M. Koreneva ^{1} Received 19 February 2016 References[1] A. M. Dorokhova and V. M. Fomichev, Revised values of exponents for mixing graphs of bijective shift registers over a set of binary vectors, Prikl. Diskretn. Mat., No. 1, 77–83, 2014 [Russian].[2] K. G. Kogos and V. M. Fomichev, Positive properties of nonnegative matrices, Prikl. Diskretn. Mat., No. 4, 5–13, 2012 [Russian]. [3] A. M. Koreneva and V. M. Fomichev, On a Feistel block cipher generalization, Prikl. Diskretn. Mat., No. 3, 34–40, 2012 [Russian]. [4] S. N. Kyazhin and V. M. Fomichev, Local primitiveness of graphs and nonnegative matrices, Prikl. Diskretn. Mat., No. 3, 68–80, 2014 [Russian]. [5] V. N. Sachkov and V. E. Tarakanov, Kombinatorika neotritsatel’nykh matrits, TVP, Moscow, 2000 [Russian]. Translated under the title Combinatorics of nonnegative matrices, AMS, Providence, 2002 (Transl. Math. Monogr., Vol. 213). [6] V. M. Fomichev, Metody diskretnoi matematiki v kriptologii (Methods of Discrete Mathematics in Cryptology), DialogMIFI, Moscow, 2010 [Russian]. [7] V. M. Fomichev, Properties of paths in graphs and multigraphs, Prikl. Diskretn. Mat., No. 1, 118–124, 2010 [Russian]. [8] V. M. Fomichev, The estimates for exponents of primitive graphs, Prikl. Diskretn. Mat., No. 2, 101–112, 2011 [Russian]. [9] V. M. Fomichev, Estimates for exponent of some graphs by means of Frobenius’s numbers of three arguments, Prikladn. Diskretn. Matem., 24, No. 2, 88–96, 2014 [Russian]. [10] B. Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C, Wiley, New York, 1996. Translated under the title Prikladnaya kriptografiya: Protokoly, algoritmy, iskhodnye teksty na yazyke Si, Triumf, Moscow, 2002 [Russian]. [11] B. M. Kim, B. C. Song, and W. Hwang, Nonnegative primitive matrices with exponent 2, Linear Algebra Appl., 407, 162–168, 2005. [12] B. L. Shader and S. Suwilo, Exponents of nonnegative matrix pairs, Linear Algebra Appl., 363, 275–293, 2003. [13] H. Wielandt, Unzerlegbare, nicht negative Matrizen, Math. Z., 52, 642–648, 1950 [German]. 

© Sobolev Institute of Mathematics, 2015  