Four decades of research on bent functions

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August undefined, 2024

WebJul 1, 2016 · Bent functions are maximally nonlinear Boolean functions. They are important functions introduced by Rothaus and studied firstly by Dillon and next by many researchers for four decades. Since the complete classification of bent functions seems elusive, many researchers turn to design constructions of bent functions. WebJan 10, 2009 · The nature of the Fourier coefficients of a bent function is examined and a proof for the non-existence of bent functions over Jqm, m odd, is given for many values …

Further Results on Bent–Negabent Boolean Functions

WebNov 27, 2024 · Bent functions are maximally nonlinear Boolean functions. Introduced by Rothaus and first examined by Dillon, these important functions have subsequently been studied by many researchers over the last four decades. Since a complete classification of bent functions appears elusive, many researchers concentrate on methods for … WebFinding bent functions in univariate trace form is in general difficult and of theoretical interest, since it gives more insight on bent functions. Moreover, the output to such functions is often faster to compute thanks to their particular form. gingerbread story book

Four decades of research on bent functions - Springer

WebDec 26, 2015 · Four decades of research on bent functions Carlet, Claude; Mesnager, Sihem Designs, Codes and Cryptography , Volume 78 (1) – Dec 26, 2015 Read Article Download PDF Share Full Text for Free 46 pages Article Details Recommended References Bookmark Add to Folder Cite Social Times Cited: Web of Science Journals / Designs, … WebJan 24, 2024 · Bent functions have been intensively studied over the last decades due to applications in cryptography and coding theory, and due to interesting connections to … Web1. Fujian Provincial Key Laboratory of Network Security and Cryptology, Fujian Normal University, Fuzhou 350117, China; 2. College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117, China; 3. Fujian Provincial Key Laboratory of Applied Mathematics, Putian University, Putian 351100, China Funds: gingerbread starbucks coffee

Further Results on Bent–Negabent Boolean Functions

Bent functions from nonlinear permutations and conversely ...

WebNov 1, 2024 · A new secondary construction of generalized bent functions from four initial functions is also investigated. We demonstrate that many known constructions can be … Webstudied bent functions in the 1960s. His pioneering work was published in the open literature ten years later[2]. And during the last four decades, bent functions have been intensively studied, see Refs.[3,4]. To design new bent functions is an eternal theme for researchers. There are direct and indirect ways for construction of bent functions. full form of tsrtcWebMar 25, 2024 · Under labels like »AI« or »Machine Learning«, adaptive systems using methods of function approximation for adapting their performance to given sets of data from the environment are increasingly being deployed in the domain of knowledge work. Their design and effective use raise new questions with respect to their … full form of tslc

"WebMar 1, 2024 · Bent functions are optimal combinatorial objects and have been attracted their research for four decades. Secondary constructions play a central role in … " - Four decades of research on bent functions

Four decades of research on bent functions

On constructions of bent functions from involutions - IEEE Xplore

WebA new secondary construction of generalized bent functions from four initial functions is also investigated. We demonstrate that many known constructions can be derived from … WebFeb 9, 2024 · to new bent functions which are provably outside the completed Mclass. Moreover, we consider the so-called 4-bent concatenation (using four di erent bent functions on the same variable space) of the (non)modi ed bent functions in Mand show that we can generate new bent functions in this way which do not belong to the …

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WebNov 27, 2024 · Introduced by Rothaus and first examined by Dillon, these important functions have subsequently been studied by many researchers over the last four … WebJan 31, 2016 · We investigate explicit constructions of bent functions which are linear on elements of spreads. Our constructions are obtained from symplectic presemifields which are associated to pseudo-planar functions. ... Four decades of research on bent functions, J. Des. Codes Crypt., 78 (2016) , 5-50. doi: 10.1007/s10623-015-0145-8. A. …

WebJul 1, 2016 · Bent functions have attracted a lot of research for four decades because of their relation to coding theory (in particular, as explained by Ding in the two nice papers [ 11, 12 ], bent functions give rise automatically to linear codes), sequences, applications in cryptography and other domains such as combinatorics and design theory. WebBent functions are optimal combinatorial objects having a lot of applications, in particular, in cryptography. Since their introduction, substantial efforts have been directed toward their study in the last three decades. In this paper, we investigate two families of functions possessing properties related to bentness: the so-called negabent ...

WebIn this survey, we revisit the Rothaus paper and the chapter of Dillon’s thesis dedicated to bent functions, and we describe the main results obtained on these functions during … WebThe Path to Power читать онлайн. In her international bestseller, The Downing Street Years, Margaret Thatcher provided an acclaimed account of her years as Prime Minister. This second volume reflects

WebDec 31, 2015 · Abstract: This book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, variations and applications, considers open problems in classification and systematization of bent functions, and discusses proofs of several results.

Webof stream ciphers and of S-boxes for block ciphers), bent functions have attracted a lot of research for four decades. Despite their simple and natural de nition, bent functions turned out to admit a very complicated structure in general. Since the complete classi- cation of bent functions seems elusive, many researchers turn to design ... gingerbread story printableWebFeb 22, 2024 · Much research has been conducted in an attempt to decrease skeletal injuries in athletic horses. The objective of this literature review is to compile the findings of over three decades of research in this area, make practical recommendations, and describe how research can develop over the years. An initial study investigating the role … gingerbread story youtubeWebNov 30, 2024 · In this paper, we propose a generic construction of rotation symmetric bent functions by modifying the support of a known class of quadratic rotation symmetric bent functions, which generalizes some earlier works. gingerbread stitchWebDec 31, 2015 · Abstract: This book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, … full form of trisWebNov 1, 2024 · They were introduced by Rothaus in the mid-sixties (The same combinatorial object, under different name, appears to be considered even earlier in Russian mathematical articles.), whereas a decade later, one of the most general secondary construction of bent functions was given by Rothaus [ 1 ]. full form of ttmmWebJul 1, 2016 · Bent functions are maximally nonlinear Boolean functions. They are important functions introduced by Rothaus and studied firstly by Dillon and next by … gingerbread storytimeWebNov 30, 2024 · Abstract. Rotation symmetric bent functions are a special class of Boolean functions, and their construction is of theoretical and practical interest. In this paper, we … gingerbread story online