Journal ArticleDOI
Gauss' algorithm revisited
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TLDR
An algorithm which reduces integer lattices in the two-dimensional case and finds a basis of a lattice consisting of its two successive minima and generalizes the worst-case input configuration of the centered Euclidean algorithm to dimension two is exhibited.About:
This article is published in Journal of Algorithms.The article was published on 1991-12-01. It has received 61 citations till now. The article focuses on the topics: Gauss & Euclidean algorithm.read more
Citations
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Book ChapterDOI
Mixed Integer Linear Models
TL;DR: In this article, the authors provide a tutorial on mixed integer linear models and define the corresponding conventional and mixed integer least squares (ILS) problems, and obtain lower and upper probabilistic bounds for the probability with which the integers are correctly estimated.
Posted Content
Computing Jacobi's \theta in quasi-linear time.
TL;DR: In this paper, an algorithm for computing the theta-constants in O(M(P) \log P) bit operations was proposed, where P is the number of operations needed to multiply two complex $P$-bit numbers.
Proceedings ArticleDOI
Attacks on Low Private Exponent RSA: An Experimental Study
TL;DR: Attacks on low private exponent RSA are considered and lattice attack using Gauss lattice reduction algorithm is more effective than Wiener attack, and it is not always to recover decryption exponent even if its bit-length is less than one-quarter bit- length of the modulus.
Book ChapterDOI
Another View of the Gaussian Algorithm
TL;DR: In this article, a rewrite system in the group of unimodular matrices with integer entries and determinant equal to ± 1 is introduced, and a worst-case analysis of the Gaussian algorithm is proposed.
References
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Journal ArticleDOI
Factoring Polynomials with Rational Coefficients
TL;DR: This paper presents a polynomial-time algorithm to solve the following problem: given a non-zeroPolynomial fe Q(X) in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q (X).
Factoring polynomials with rational coeficients
TL;DR: In this paper, a polynomial-time algorithm was proposed to decompose a primitive polynomials into irreducible factors in Z(X) if the greatest common divisor of its coefficients is 1.
Journal ArticleDOI
Integer Programming with a Fixed Number of Variables
TL;DR: It is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable.
Proceedings ArticleDOI
Improved algorithms for integer programming and related lattice problems
TL;DR: The proposed algorithm first finds a “more orthogonal” basis for a lattice than those of Lenstra (1981) and Lenstra, Lenstra and Lovasz (1982), but in time 0(ndn poly (length of input)).
Journal ArticleDOI
Solving low-density subset sum problems
TL;DR: This method gives a polynomial time attack on knapsack public key cryptosystems that can be expected to break them if they transmit information at rates below dc (n), as n → ∞.