Spectral-linear and spectral-differential methods for generating S-boxes having almost optimal cryptographic parameters
Matematičeskie voprosy kriptografii, Tome 8 (2017) no. 2, pp. 97-116 Cet article a éte moissonné depuis la source Math-Net.Ru

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S-boxes are important parts of modern ciphers. To construct S-boxes having cryptographic parameters close to optimal is an unsolved problem at present time. In this paper some new methods for generating such S-boxes are introduced.
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A. V. Menyachikhin. Spectral-linear and spectral-differential methods for generating S-boxes having almost optimal cryptographic parameters. Matematičeskie voprosy kriptografii, Tome 8 (2017) no. 2, pp. 97-116. http://geodesic.mathdoc.fr/item/MVK_2017_8_2_a8/

[1] Agievich S. V., Afonenko A. A., “On the properties of exponential substitutions”, Vesti NAN Belarusi, 1 (2005), 106–112 (in Russian) | MR

[2] Agievich S. V., Galinsky B. A., Mikulich N. D., Kharin U. S., Algorithm of block encryption BelT, (in Russian) http://apmi.bsu.by/assets/files/agievich/BelT.pdf

[3] Alekseychuk A., Kovalchuk L., Pal'chenko S., “Cryptographic parameters of s-boxes that characterize the security of GOST-like block ciphers against linear and differential cryptanalysis”, Zakhist Inform., 2 (2007), 12–23 (in Ukrainian)

[4] Alekseychuk A., Kovalchuk L., “Upper bounds of maximum values of average differential and linear characteristic probabilities of Feistel cipher with adder modulo $2^m$”, Theory of Stochastic Processes, 12(28):1–2 (2006), 20–32 | MR | Zbl

[5] Barreto P., Rijmen V., The ANUBIS block cipher, NESSIE submission, 2000

[6] Barreto P., Rijmen V., The KHAZAD block cipher, NESSIE submission, 2000

[7] Biham E., Biryukov A., Shamir A., “Cryptanalysis of Skipjack reduced to 31 rounds using impossible differentials”, EUROCRYPT'99, Lect. Notes Comput. Sci., 1592, 1999, 12–23 | DOI | Zbl

[8] Bugrov A. D., “Piecewise affine substitution of finite fields”, Prikl. Diskr. Matem., 2015, no. 4(30), 5–23 (in Russian)

[9] Blondeau C., Gerard B., “Links between theoretical and effective differential probabilities: experiments on PRESENT”, ECRYPT II Workshop on Tools for Cryptanalysis (2010) https://eprint.iacr.org/2010/261.pdf

[10] Bogdanov A., Knudsen L. R., Leander G., Paar C., Poschmann A., Robshaw M. J. B., Seurin Y., Vikkelsoe C., “PRESENT: An ultra-lightweight block cipher”, CHES 2007, Lect. Notes Comput. Sci., 4727, 2007, 450–466 | DOI | Zbl

[11] Carlet C., Ding C., “Nonlinearities of S-boxes”, Finite Fields Appl., 13 (2007), 121–135 | DOI | MR | Zbl

[12] Chabaud F., Vaudenay S., “Links between differential and linear cryptanalysis”, EUROCRYPT, Lect. Notes Comput. Sci., 950, 1994, 356–365 | DOI | MR

[13] Daemen J., Rijmen V., “Probability distributions of correlations and differentials in block ciphers”, J. Math. Crypt., 1 (2007), 221–242 | MR | Zbl

[14] Daemen J., Rijmen V., The Design of Rinjdael. AES — The Advanced Encryption Standard, Springer, Heidelberg etc., 2002 | MR

[15] Dygin D. M., Lavrikov I. V., Marshalko G. B., Rudsky V. I., Trifonov D. I., Shishkin V. A., “On a new Russian Encryption Standard”, Mathematical Aspects of Cryptography, 6:2 (2015), 29–34 | MR

[16] Evans A., Orthomorphism Graphs of Groups, Lect. Notes Math., 1535, Springer-Verlag, Heidelberg etc., 1992, 116 pp. | DOI | MR | Zbl

[17] Gluhov M. M., “On the matrices of transitions of differences when using some modular groups”, Mathematical Aspects of Cryptography, 4:4 (2013), 27–47 (in Russian)

[18] Gluhov M. M., “On a method of construction of orthogonal quasigroups systems by means of groups”, Mathematical Aspects of Cryptography, 2:4 (2011), 5–24 (in Russian)

[19] Goldberg D., Genetic Algorithms in Search, Optimization and Machine Learning, Addsion-Wesley, Readings, MA, 1985, 432 pp.

[20] Information technology. Cryptographic protection of information. Block ciphers, GOST R 34.12-2015, Standartinform, M., 2015 (in Russian)

[21] Information technology. Cryptographic protection of information. Hash function, GOST R 34.11-2012, Standartinform, M., 2012 (in Russian)

[22] Izbenko Y., Kovtun V., Kuznetsov A., “The design of Boolean functions by modified hill climbing method”, Sixth International Conference on Information Technology: New Generations, IEEE Computer Soc., 2009, 356–361 | DOI

[23] Jacobson Jr. M., Huber K., The MAGENTA Block Cipher Algorithm, , NIST AES Proposal, 1998 http://edipermadi.files.wordpress.com/2008/09/magenta-spec.pdf

[24] Kazymyrov O. V., Kazymyrova V. N., Oliynykov R. V., “A method for generation of highnonlinear S-boxes based on gradient descent”, Mathematical Aspects of Cryptography, 5:2 (2014), 71–78

[25] Knuth D., Art of Computer Programming, v. 2, Seminumerical Algorithms, 3rd ed., Addison-Wesley Professional, 1997 | MR

[26] Leander G., Poschmann A., “On the classification of 4-bit s-boxes”, Lect. Notes Comput. Sci., 4547, 2007, 159–176 | DOI | MR | Zbl

[27] Malyshev F. M., “Doubly transitive XSL-families of permutations”, Mathematical aspects of cryptography, 1:2 (2010), 93–103 (in Russian)

[28] Malyshev F. M., “The duality of difference and linear methods in cryptography”, Mathematical aspects of cryptography, 5:3 (2014), 35–47 (in Russian)

[29] Matsumoto M., Nishimura T., “Mersenne Twister: a 623-dimensionally equidistributed uniform pseudo-random generator”, ACM Trans. Modeling and Computer Simul. (TOMACS), 8:1 (1998), 3–30 | DOI | Zbl

[30] Millan W., Clark A., Dawson E., “Smart hill climbing finds better Boolean functions”, Lect. Notes Comput. Sci., 1334, 1997, 149–158 | DOI | Zbl

[31] Millan W., “How to improve the nonlinearity of bijective S-boxes”, Lect. Notes Comput. Sci., 1438, 1998, 181–192 | DOI | MR | Zbl

[32] Nyberg K., “On the construction of highly nonlinear permutations”, EUROCRYPT'92, Lect. Notes Comput. Sci., 1992, 92–98 | MR

[33] Nyberg K., “Perfect nonlinear S-boxes”, EUROCRYPT'91, Lect. Notes Comput. Sci., 547, 1991, 378–386 | DOI | MR | Zbl

[34] Nyberg K., Knudsen L., “Provable security against differential cryptanalysis”, J. Cryptology, 8:1 (1992), 27–37 | MR

[35] Pichkur A. B., “Description of the set of permutations represented as a product of two permutations with fixed number of mobile points”, Mathematical Aspects of Cryptography, 3:2 (2012), 79–95 (in Russian)

[36] Pichkur A. B., “Description of the set of permutations represented as a product of two permutations with fixed number of mobile points. II”, Mathematical Aspects of Cryptography, 4:1 (2013), 87–109 (in Russian)

[37] Pieprzyk J., “Non-linearity of exponent permutations”, EUROCRYPT'89, Lect. Notes Comput. Sci., 434, 1990, 81–92 | MR

[38] Pogorelov B. A., “Substitution groups. Part 1 (the review over 1981–95)”, Trudy po Diskretnoi Matematike, 2 (1998), 237–281 (in Russian) | Zbl

[39] Pogorelov B. A., Pudovkina M. A., “On the distance from permutations to the union of all imprimitive groups with identical parameters of imprimitivity systems”, Discrete Math. Appl., 24:3 (2014), 163–173 | DOI | MR | Zbl

[40] Sachkov V. N., “Combinatorial properties of differentially 2-uniform substitutions”, Mathematical Aspects of Cryptography, 6:1 (2015), 159–179 (in Russian) | MR

[41] Sachkov V. N., “Random mapping with fixed elements”, Mathematical Aspects of Cryptography, 2:2 (2011), 95–118 (in Russian)

[42] Shemyakina O. V., “On the estimation of the characteristics of partitions of various algebraic structures”, Inf. security of Russian regions, ISRR-2011, SPOISU, St-Pb., 2011, 137 (in Russian)

[43] Skipjack and KEA Algorithm Specifications, Version 2.0, , 1998 http://csrc.nist.gov/encryption/skipjack-kea/htm

[44] Information technologies. Information security. Cryptographic algorithms of enciphering and continuity test, STB 34.101.31-2011, Gosstandart, Minsk, 2011 (in Russian)

[45] Tokareva N. N., “Quadratic approximations of the special type for the 4-bit permutations in S-boxes”, Prikl. Diskr. Matem., 1 (2008), 50–54 (in Russian)

[46] Tokareva N. N., “On quadratic approximations in block ciphers”, Probl. Inf. Transmiss., 44:3 (2008), 266–286 | DOI | MR | Zbl

[47] Trishin A. E., “The nonlinearity index for a piecewise-linear substitution of the additive group of the field”, Prikl. Diskr. Matem., 4(30) (2015), 32–42 (in Russian)

[48] Trishin A. E., “The method of constructing orthogonal Latin squares on the basis of substitution binomials of finite fields”, Obozr. prikl. i prom. matem., 15:4 (2008), 764–765 (in Russian)