Download Bent Functions: Fundamentals and Results by Sihem Mesnager PDF

By Sihem Mesnager

This e-book offers a close survey of the most effects on bent capabilities over finite fields, offers a scientific assessment in their generalizations, diversifications and purposes, considers open difficulties in type and systematization of bent capabilities, and discusses proofs of a number of effects. This ebook uniquely presents an important accomplished assurance of bent functions.It serves as an invaluable reference for researchers in discrete arithmetic, coding and cryptography. scholars and professors in arithmetic and laptop technology also will locate the content material helpful, specially these drawn to mathematical foundations of cryptography. it may be used as a supplementary textual content for collage classes on discrete arithmetic, Boolean capabilities, or cryptography, and is acceptable for either uncomplicated sessions for under-graduate scholars and complicated classes for experts in cryptography and mathematics.

Show description

Read or Download Bent Functions: Fundamentals and Results PDF

Similar information theory books

Quantum communications and cryptography

All present equipment of safe communique reminiscent of public-key cryptography can ultimately be damaged by way of quicker computing. on the interface of physics and laptop technological know-how lies a strong resolution for safe communications: quantum cryptography. simply because eavesdropping adjustments the actual nature of the data, clients in a quantum trade can simply observe eavesdroppers.

Philosophy of Physics,

The instruction manual of Philosophy of Physics is a part of the multi-volume sequence instruction manual of Philosophy of technology less than the overall editorship of Dov Gabbay, Paul Thagard, and John Woods. As mirrored within the titles of volumes within the sequence, the philosophy of technology has turn into more and more really expert right into a variety of sub-fields (philosophy of biology, philosophy of psychology and the cognitive sciences, philosophy of economics, and so forth.

Komplexitätstheorie. Grenzen der Effizienz von Algorithmen

Die Komplexitätstheorie ist inzwischen eine ausgefeilte Theorie. Viele wichtige und nützliche Ergebnisse sind schwer vermittelbar, da der Weg zu Ergebnissen für konkrete Probleme lang und beschwerlich ist. Während die NP-Vollständigkeitstheorie die gesamte Informatik beeinflußt hat, werden die neueren Ergebnisse in der Ausbildung an den Rand gedrängt.

Extra info for Bent Functions: Fundamentals and Results

Sample text

3 Involutions In many situations, both the permutation polynomial and its compositional inverse are required. For instance, in block ciphers, a permutation is used as an S-box to build the confusion layer during the encryption process. While decrypting the cipher, the compositional inverse of the S-box comes into the picture. Therefore, if both the permutation and its compositional inverse are efficient in terms of implementation, it is advantageous to the designer. This motivates the use of an involution.

2m and generator of the cyclic group U. Let i 2 f0; 1g. a; a//=3: u2U where 0 D 2 and 1 D 1. Proof. a j v//: v2V Now, recall that m being odd, one can decompose U as follows UDV[ V[ 2 V where V D fu3 j u 2 Ug. Thus, every element u 2 U can be uniquely decomposed as u D j v with j 2 f0; 1; 2g and v 2 V. mod 6/, integers 3 and 2 3C1 are co-prime. The mapping v 7! i; j/ 2 f0; 1; 2g2, we have (in the second equality, we use the fact that the mapping v 7! 4 (which contains two elements of absolute trace 1 on F4 and one element of absolute trace 0 on F4 ).

A j v//: v2V Now, recall that m being odd, one can decompose U as follows UDV[ V[ 2 V where V D fu3 j u 2 Ug. Thus, every element u 2 U can be uniquely decomposed as u D j v with j 2 f0; 1; 2g and v 2 V. mod 6/, integers 3 and 2 3C1 are co-prime. The mapping v 7! i; j/ 2 f0; 1; 2g2, we have (in the second equality, we use the fact that the mapping v 7! 4 (which contains two elements of absolute trace 1 on F4 and one element of absolute trace 0 on F4 ). a//=2: t u In Chap. 17, we will need to exhibit necessary and sufficient conditions so that the sum involved in the previous proposition takes the value 1.

Download PDF sample

Rated 4.49 of 5 – based on 19 votes