Implementations of extended LLL In systems like GP/PARI one uses an implementation of the LLL lattice reduction algorithm which allows dependent vectors and which also returns a transformation matrix. However, no complexity analysis is possible for their qflll algorithm (and similar algorithms), at least not in the manner of the original LLL paper. When we speak of extended LLL, we refer to the ...

Computational projects Introduction Projects Contact Introduction Long ago, I decided to find interesting problems, usually requiring extensive verifications and/or enumerations, to occupy the idle CPU time of most workstations and personal computers in my working environment. This page presents links to short descriptions of ongoing or finished computational projects I have found interesting ...

1.2 Numerical Problems Specific Algorithms 1.2.1 Solving Linear Equations 1.2.2 Bandwidth Reduction 1.2.3 Matrix Multiplication 1.2.4 Determinants and Permanents 1.2.5 Constrained and Unconstrained Optimization 1.2.6 Linear Programming 1.2.7 Random Number Generation 1.2.8 Factoring and Primality Testing 1.2.9 Arbitrary Precision Arithmetic 1.2.10 Knapsack Problem 1.2.11 Discrete Fourier ...

Basics of Computational Number Theory Robert Campbell Contents Introduction Modular Arithmetic GCD - The Euclidean Algorithm Exponentiation - The Russian Peasant Algorithm Prime Numbers Finding Primes Element Orders Factoring Other Fields Gaussian Integers Galois Fields Appendices Programming Notes References Glossary 1. Introduction This document is a gentle introduction to computational number ...

A list of interesting papers on the LLL algorithm and its applications to cryptology.

Computational Number Theory Robert Campbell This is a short collection of documents which provides an introduction to computational number theory. The first text provides a simple gloss of the subject, emphasizing results at the expense of theory, what instead of why. The second text will cover the same topic in greater depth and then will continue on to cover more topics. Basic Introduction ...

Suggested readings in Algorithmic number theory This list was provided by the organizers of the Fall 2000 program in Algorithmic number theory. Editor: Adleman, Leonard M. / Huang, Ming-Deh A. Title: Algorithmic number theory : first international symposium, ANTS-I, Ithaca, NY, USA, May 6-9, 1994 : proceedings Publ: Springer-Verlag Year: c1994 Series: Lecture notes in computer science SerNo: 877 ...