This book constitutes the refereed proceedings of the 5th International Conference on Sequences and Their Applications, SETA 2008, held in Lexington, KY, USA in September 2008. The 32 revised full papers presented were carefully reviewed and selected. The papers are organized in topical sections on probabilistic methods and randomness properties of sequences; correlation; combinatorial and algebraic foundations; security aspects of sequences; algorithms; correlation of sequences over rings; nonlinear functions over finite fields.
This book constitutes the refereed proceedings of the 8th International Conference on Sequences and Their Applications, SETA 2014, held in Melbourne, VIC, Australia, in November 2014. The 24 full papers presented together with 2 invited papers were carefully reviewed and selected from 36 submissions. The papers have been organized in topical sections on Boolean functions, perfect sequences, correlation of arrays, relative difference sets, aperiodic correlation, pseudorandom sequences and stream ciphers, crosscorrelation of sequences, prime numbers in sequences, OFDM and CDMA, and frequency-hopping sequences.
This volumecontainstherefereedproceedingsoftheSixth International Conf- ence on Sequences and Their Applications (SETA 2010), held in Paris, France, September 13-17, 2010. The previous ?ve conferences were held in Singapore (RepublicofSingapore),Bergen(Norway),Seoul(SouthKorea),Beijing(China) and Lexington (USA). Topics of SETA include: – Randomness of sequences – Correlation (periodic and aperiodic types) and combinatorial aspects of - quences (di?erence sets) – Sequences with applications in coding theory and cryptography – Sequences over ?nite ?elds/rings/function ?elds – Linear and nonlinear feedback shift register sequences – Sequences for radar distance ranging, synchronization, identi?cation, and hardware testing – Sequences for wireless communication – Pseudorandom sequence generators – Boolean and vectorial functions for sequences, coding and/or cryptography – Multidimensional sequences and their correlation properties – Linear and nonlinear complexity of sequences The Technical Program Committee of SETA 2010 refereed 56 submitted - pers. Each paper was reviewed by at least 2 referees (at least 3 when an author was a TPC member) and the TPC selected 33 papers to be presented at the conference. In addition, we had 4 invited papers, byRobert Calderbank(Prin- ton University, USA), James Massey (retired from ETH Zurich, Switzerland), Jong-Seon No (Seoul National University, South Korea) and Arne Winterhof ¨ (Osterreichische Akademie der Wissenschaften, Austria). TheCo-chairsoftheTPCwereClaudeCarlet(Universit´ eParis8,France)and Alexander Pott (Otto-von-Guericke-Universit¨ at, Magdeburg, Germany). They wish to thank the other members of the ProgramCommittee: Thierry P.
This volume is dedicated to Robert F. Tichy on the occasion of his 60th birthday. Presenting 22 research and survey papers written by leading experts in their respective fields, it focuses on areas that align with Tichy’s research interests and which he significantly shaped, including Diophantine problems, asymptotic counting, uniform distribution and discrepancy of sequences (in theory and application), dynamical systems, prime numbers, and actuarial mathematics. Offering valuable insights into recent developments in these areas, the book will be of interest to researchers and graduate students engaged in number theory and its applications.
This book constitutes the refereed proceedings of the 7th International Conference on Sequences and Their Applications, SETA 2012, held in Waterloo, Canada, in June 2012. The 28 full papers presented together with 2 invited papers in this volume were carefully reviewed and selected from 48 submissions. The papers are grouped in topical sections on perfect sequences; finite fields; boolean functions; Golomb 80th birthday session; linear complexity; frequency hopping; correlation of sequences; bounds on sequences, cryptography; aperiodic correlation; and Walsh transform.
This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.
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.
