Construction and Analysis of Cryptographic Functions by Lilya Budaghyan

By Lilya Budaghyan

This booklet covers novel learn on building and research of optimum cryptographic features resembling virtually excellent 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. in addition to cryptographic functions, those services are major in lots of branches of arithmetic and knowledge idea together with coding concept, combinatorics, commutative algebra, finite geometry, series layout and quantum info concept. the writer analyzes equivalence family members for those capabilities and develops a number of new tools for development in their countless households. moreover, the booklet deals suggestions to 2 longstanding open difficulties, together with the matter on characterization of APN and AB capabilities through Boolean, and the matter at the relation among periods of bent functions.

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L. Budaghyan, C. Carlet, G. Leander. On inequivalence between known power APN functions. Proceedings of the International Workshop on Boolean Functions: Cryptography and Applications, BFCA 2008, Copenhagen, Denmark, May 2008. 27. L. Budaghyan, C. Carlet, G. Leander. On a construction of quadratic APN functions. Proceedings of IEEE Information Theory Workshop, ITW’09, pp. 374–378, Taormina, Sicily, Oct. 2009. 28. L. Budaghyan, C. Carlet, G. Leander. Constructing new APN functions from known ones.

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