Constructive method for the synthesis of nonlinear S-boxes satisfying the strict avalanche criterion
DOI:
https://doi.org/10.3103/S0735272713080049Keywords:
S-box, strict avalanche criterion, high nonlinearity criterion, bent function, cryptographic transformationAbstract
A constructive method is proposed for the synthesis of cryptographic substitution boxes (S-boxes) satisfying both the strict avalanche criterion and the high nonlinearity criterion, where smaller length S-boxes and highly nonlinear bent functions are used as a source material. In addition, effective algorithms for the reproduction of the above S-boxes have been developed.
References
MAIER, W. AND STAFFELBACH, O. Nonlinearity criteria for cryptographic functions. Advances in Cryptology, EUROCRYPT’89, Lecture Notes in Computer Science. Springer-Verlag, 1990, v.434, p.549-562.
WEBSTER, A.F. AND TAVARES, S.E. On the design of S-boxes. Proc. of CRYPTO’85. Springer-Verlag, 1985.
NYBERG, K. Differentially uniform mappings for cryptography. Advances in Cryptology, Proceedings of EUROCRYPT’93, Lecture Notes in Computer Science. Berlin–Heidelberg–New York: Springer-Verlag, 1994, v.765, p.55-65.
MAZURKOV, M.I. AND SOKOLOV, A.V. Cryptographic properties of the nonlinear conversion of Rijndael cipher on the basis of complete classes of irreducible polynomials. Trudy OPU, n.2(39), p.183-189, 2012.
GORBENKO, I.D.; POTII, O.V.; IZBENKO, YU.A. Analytical and statistical investigations of properties of Boolean functions of the RIJNDAL crypto-algorithm (FIPS 197). Radiotekhnika (Kharkiv), v.126, p.132-138, 2004.
GAO, S.; MA, W.; SHEN, D. Design of bijective S-boxes satisfying the strict avalanche criterion. J. Computational Inf. Syst., v.7, n.6, p.1967-1973, 2011, http://www.jofcis.com/publishedpapers/2011_7_6_1967_1973.pdf"> http://www.jofcis.com/publishedpapers/2011_7_6_1967_1973.pdf.
KIM, K.; MATSUMOTO, T.; IMAI, H. A recursive construction method of S-boxes satisfying the strict avalanche criterion. Proc. of CRYPTO’90. Springer-Verlag, 1990, p.565-574.
ROTHAUS, O. On Bent Functions. Alexandria–Virginia: IDA CRD W.P., 1966, n.169.
MCFARLAND, R.L. A family of difference sets in non-cyclic groups. J. Combin. Theory. Ser. A, v.15, n.1, p.1-10, 1973. doi: http://dx.doi.org/10.1016/0097-3165(73)90031-9">10.1016/0097-3165(73)90031-9.
MAZURKOV, M.I.; CHECHEL’NITSKII, V.YA.; MEL’NIK, M.A.; SOKOLOV, A.V. A synthesis algorithm for optimal cryptographic S-boxes based on regular operators of decimation, permutation and m-shift. Trudy OPU, n.1(38), p.179-187, 2012.