By Lilya Budaghyan
This booklet covers novel study on building and research of optimum cryptographic capabilities resembling virtually ideal nonlinear (APN), virtually bent (AB), planar and bent services. 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 features are major in lots of branches of arithmetic and data idea together with coding conception, combinatorics, commutative algebra, finite geometry, series layout and quantum details concept. the writer analyzes equivalence relatives for those features and develops a number of new tools for development in their endless households. moreover, the publication deals recommendations 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 services.
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