# Download Bent functions : results and applications to cryptography by Natalia Tokareva PDF

By Natalia Tokareva

Bent capabilities: effects and functions to Cryptography offers a different survey of the items of discrete arithmetic often called Boolean bent features. As those maximal, nonlinear Boolean services and their generalizations have many theoretical and functional functions in combinatorics, coding conception, and cryptography, the textual content presents a close survey in their major effects, providing a scientific assessment in their generalizations and purposes, and contemplating open difficulties in class and systematization of bent features.

The textual content is acceptable for newbies and complex researchers, discussing proofs of a number of effects, together with the automorphism staff of bent features, the reduce certain for the variety of bent features, and more.

• Provides a close survey of bent services and their major effects, featuring a scientific review in their generalizations and applications
• Presents a scientific and specific survey of thousands of ends up in the world of hugely nonlinear Boolean capabilities in cryptography
• Appropriate assurance for college students from complicated experts in cryptography, arithmetic, and creators of ciphers

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Extra resources for Bent functions : results and applications to cryptography

Example text

Unfortunately these results remain unpublished. At the crossroads CHAPTER 4 Applications of Bent Functions INTRODUCTION Distinct applications of bent functions are discussed. First, we consider the use of bent functions in cryptography for constructing the ciphers CAST, Grain, and hash function HAVAL. Further we review connections between bent functions and distinct objects of discrete mathematics and coding theory (Hadamard matrices, strongly regular graphs, and Reed-Muller and Kerdock codes).

There are N parallel data flows. We can represent the transmitted information as a binary vector c of length N (one bit from each flow). The signal in multicode CDMA is modeled as N−1 Sc (t) = (−1)cj ajt , j=0 where t = 0, 1, . . , N − 1 is a discrete time parameter—that is, the jth row of the matrix A is multiplied by (−1)cj , and the transmitted signal Sc is the sum of these new rows. At every moment of time, one bit of the sequence Sc is transmitted. An important parameter is the peak to average power ratio of the signal, which is defined as PAPR(c) = 1 max |Sc (t)|2 .

00004-2 Copyright © 2015 Elsevier Inc. All rights reserved. 31 32 Bent Functions K is found. For this method to work reliably, N should be proportional to |ε|−2 . There are many papers devoted to various generalizations and applications of the linear cryptanalysis method. We describe some of them. A detailed analysis of the linear cryptanalysis method (in particular, for DES) is given by K. Nyberg; see also papers of other authors [29, 98, 151, 258]. To improve the efficiency of the linear cryptanalysis method, Kaliski and Robshaw [191] proposed considering several linear approximations for one combination of key bits; this subject was further developed by Biryukov et al.