Applied Algebra and Number Theory

doi:10.1017/CBO9781139696456

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Ni, Jianqiang Zhang, Jianhui Wang, Gaoli Li, Rui and Shen, Yanzhao 2023. Algebraic Attacks against Grendel: An Arithmetization-Oriented Primitive with the Legendre Symbol. Symmetry, Vol. 15, Issue. 8, p. 1563.

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Edited by Gerhard Larcher, Johannes Kepler Universität Linz, Friedrich Pillichshammer, Johannes Kepler Universität Linz, Arne Winterhof, Austrian Academy of Sciences, Linz, Chaoping Xing, Nanyang Technological University, Singapore

Publisher:: Cambridge University Press
Online publication date:: December 2014
Print publication year:: 2014
Online ISBN:: 9781139696456
DOI:: https://doi.org/10.1017/CBO9781139696456

Subjects:: Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Discrete Mathematics Information Theory and Coding

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Harald Niederreiter's pioneering research in the field of applied algebra and number theory has led to important and substantial breakthroughs in many areas. This collection of survey articles has been authored by close colleagues and leading experts to mark the occasion of his 70th birthday. The book provides a modern overview of different research areas, covering uniform distribution and quasi-Monte Carlo methods as well as finite fields and their applications, in particular, cryptography and pseudorandom number generation. Many results are published here for the first time. The book serves as a useful starting point for graduate students new to these areas or as a refresher for researchers wanting to follow recent trends.

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Applied Algebra and Number Theory

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Frontmatter
pp i-iv

Contents
pp v-x

Preface
pp xi-xii

1 - Some highlights of Harald Niederreiter's work
pp 1-21

2 - Partially bent functions and their properties
pp 22-38

3 - Applications of geometric discrepancy in numerical analysis and statistics
pp 39-57

4 - Discrepancy bounds for low-dimensional point sets
pp 58-90

5 - On the linear complexity and lattice test of nonlinear pseudorandom number generators
pp 91-101

6 - A heuristic formula estimating the keystream length for the general combination generator with respect to a correlation attack
pp 102-108

7 - Point sets of minimal energy
pp 109-125

8 - The cross-correlation measure for families of binary sequences
pp 126-143

9 - On an important family of inequalities of Niederreiter involving exponential sums
pp 144-163

10 - Controlling the shape of generating matrices in global function field constructions of digital sequences
pp 164-189

11 - Periodic structure of the exponential pseudorandom number generator
pp 190-203

12 - Construction of a rank-1 lattice sequence based on primitive polynomials
pp 204-215

13 - A quasi-Monte Carlo method for the coagulation equation
pp 216-234

14 - Asymptotic formulas for partitions with bounded multiplicity
pp 235-254

15 - A trigonometric approach for Chebyshev polynomials over finite fields
pp 255-279

16 - Index bounds for value sets of polynomials over finite fields
pp 280-296

17 - Rational points of the curve over
pp 297-306

18 - On the linear complexity of multisequences, bijections between ℤahlen and ℕumber tuples, and partitions
pp 307-335

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Applied Algebra and Number Theory

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