By Lilya Budaghyan

ISBN-10: 3319129902

ISBN-13: 9783319129907

ISBN-10: 3319129910

ISBN-13: 9783319129914

This booklet covers novel study on development and research of optimum cryptographic features similar to virtually ideal nonlinear (APN), nearly bent (AB), planar and bent features. those capabilities have optimum resistance to linear and/or differential assaults, that are the 2 strongest assaults on symmetric cryptosystems. along with cryptographic purposes, those capabilities are major in lots of branches of arithmetic and data thought together with coding conception, combinatorics, commutative algebra, finite geometry, series layout and quantum details idea. the writer analyzes equivalence relatives for those services and develops numerous new tools for building in their endless households. furthermore, the publication deals options to 2 longstanding open difficulties, together with the matter on characterization of APN and AB services through Boolean, and the matter at the relation among periods of bent functions.

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**Extra info for Construction and Analysis of Cryptographic Functions**

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Advances in Math. 217, pp. 282–304, 2008. 45. R. S. Coulter and R. W. Matthews. Planar functions and planes of Lenz-Barlotti class II. , Codes, Cryptogr. 10, pp. 167–184, 1997. 46. R. S. Coulter, M. Henderson, P. Kosick. Planar polynomials for commutative semifields with specified nuclei. Des. Codes Cryptogr. 44, pp. 275–286, 2007. 47. T. Cusick and H. Dobbertin. Some new 3-valued crosscorrelation functions of binary msequences. IEEE Trans. Inform. 1238–1240, 1996. 48. J. Daemen and V. Rijmen. AES proposal: Rijndael.

Cryptography and Communications: Discrete Structures, Boolean Functions and Sequences, v. 3(1), pp. 1–16, 2011. 24. L. Budaghyan, C. Carlet, A. Pott. New Classes of Almost Bent and Almost Perfect Nonlinear Functions. IEEE Trans. Inform. Theory, vol. 52, no. 3, pp. 1141–1152, March 2006. 25. L. Budaghyan, C. Carlet, G. Leander. Two classes of quadratic APN binomials inequivalent to power functions. IEEE Trans. Inform. Theory, 54(9), pp. 4218–4229, 2008. 26. L. Budaghyan, C. Carlet, G. Leander. On inequivalence between known power APN functions.

Then we get f (x) = l(F1−1 (x)) + f (F1−1 (x)) = l(x + af (x)) + f (x + af (x)). If f (x) = 0 then f (x) = l(x). If f (x) = 1 then f (x + a) = 1 (see the proof of Lemma 1), and, therefore f (x) = l(x) + l(a) + 1. Thus, f (x) = l(x) + (1 + l(a))f (x) for every x. Note that l(a) = 0. 2 CCZ-Equivalence of (n, m)-Functions 43 has two solutions (0, 0) and (a, 1) which contradicts L being a permutation. Hence, f (x) = l(x) + f (x) and f is EA-equivalent to f , a contradiction. Let now L be 2-to-1. 6) takes place.

### Construction and Analysis of Cryptographic Functions by Lilya Budaghyan

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