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Construction and Analysis of Cryptographic Functions [electronic resource] / by Lilya Budaghyan.

By: Budaghyan, Lilya [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Cham : Springer International Publishing : Imprint: Springer, 2014Description: VIII, 168 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319129914.Subject(s): Computer science | Data encryption (Computer science) | Coding theory | Difference equations | Functional equations | Combinatorics | Computer Science | Coding and Information Theory | Data Encryption | Difference and Functional Equations | CombinatoricsAdditional physical formats: Printed edition:: No titleDDC classification: 003.54 Online resources: Click here to access online
Contents:
Introduction -- Generalities -- Equivalence relations of functions -- Bent functions -- New classes of APN and AB polynomials -- Construction of planar functions.
In: Springer eBooksSummary: This book covers novel research on construction and analysis of optimal cryptographic functions such as almost perfect nonlinear (APN), almost bent (AB), planar and bent functions. These functions have optimal resistance to linear and/or differential attacks, which are the two most powerful attacks on symmetric cryptosystems. Besides cryptographic applications, these functions are significant in many branches of mathematics and information theory including coding theory, combinatorics, commutative algebra, finite geometry, sequence design and quantum information theory. The author analyzes equivalence relations for these functions and develops several new methods for construction of their infinite families. In addition, the book offers solutions to two longstanding open problems, including the problem on characterization of APN and AB functions via Boolean, and the problem on the relation between two classes of bent functions.
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Introduction -- Generalities -- Equivalence relations of functions -- Bent functions -- New classes of APN and AB polynomials -- Construction of planar functions.

This book covers novel research on construction and analysis of optimal cryptographic functions such as almost perfect nonlinear (APN), almost bent (AB), planar and bent functions. These functions have optimal resistance to linear and/or differential attacks, which are the two most powerful attacks on symmetric cryptosystems. Besides cryptographic applications, these functions are significant in many branches of mathematics and information theory including coding theory, combinatorics, commutative algebra, finite geometry, sequence design and quantum information theory. The author analyzes equivalence relations for these functions and develops several new methods for construction of their infinite families. In addition, the book offers solutions to two longstanding open problems, including the problem on characterization of APN and AB functions via Boolean, and the problem on the relation between two classes of bent functions.

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