Abstract
Some results are obtained concerning the influence of bitwise (modular) addition on the structure of the quotient group of a particular subgroup under the operation of modular (bitwise) addition on the set of binary vectors depending on the type of the chosen subgroup.
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O. V. Shemyakina, “Mixing properties of operations in a finite field,” in: Proc. 8th All-Russian Sci. Conf. “Mathematics and Security of Information Technologies,” (MaBIT-09), October 30–November 2, 2009, Vol. 2, MTsNMO, Moscow (2010), pp. 87–90.
Yu. N. Gorchinskii, “Homomorphisms of multibase universal algebras in the context of cryptographic applications,” in: Trans. Discrete Mathematics, Vol. 1, TNP, Moscow (1997), pp. 67–84.
Yu. N. Gorchinskii, “Stochastic algebras,” in: Trans. Discrete Mathematics, Vol. 2, TNP, Moscow (1997), pp. 55–87.
GOST 2814789, Information Processing Systems. Cryptographic Protection. Cryptographic Transformation Algorithm [in Russian], Gosstandart SSSR, Moscow (1989).
I. D. Gorbenko, O. S. Totskii, and S. V. Kazmina, “A promising block cipher Kalina: General provisions and specification,” Prikladnaya Radioelektronika, 6, No. 2, 195–208 (2007).
X. Lai, J. L. Massey, and S. Murphy, “Markov ciphers and differential cryptanalysis,” in: Proc. EUROCRYPT’91, Adv. in Cryptology, Springer-Verlag, Berlin (1991), pp. 17–38.
E. Biham and A. Shamir, “Differential cryptanalysis of DES-like cryptosystems,” J. Cryptology, 4, No. 1, 3–72 (1991).
T. A. Berson, “Differential cryptanalysis mod 232 with applications to MD5,” in: Proc. CRYPTO’98 (LNCS 372), Adv. in Cryptology, Springer-Verlag, New York (1999), pp. 95–103.
L. V. Kovalchuk, “Upper-bound estimation of the average probabilities of integer-valued differentials in the composition of key adder, substitution block, and shift operator,” Cybern. Syst. Analysis, 46, No. 6, 936–944 (2010).
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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 83–97, September–October 2011.
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Kovalchuk, L.V., Sirenko, O.A. Analysis of mixing properties of the operations of modular addition and bitwise addition defined on one carrier. Cybern Syst Anal 47, 741–753 (2011). https://doi.org/10.1007/s10559-011-9353-z
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DOI: https://doi.org/10.1007/s10559-011-9353-z