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Fast 2Variable Integer Programming
 Integer Programming and Combinatorial Optimization, IPCO 2001, volume 2081 of LNCS
, 2001
"... We show that a 2variable integer program defined by m constraints involving coefficients with at most s bits can be solved with O(m+s log m) arithmetic operations or with O(m+logm log s)M(s) bit operations, where M(s) is the time needed for sbit integer multiplication. ..."
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We show that a 2variable integer program defined by m constraints involving coefficients with at most s bits can be solved with O(m+s log m) arithmetic operations or with O(m+logm log s)M(s) bit operations, where M(s) is the time needed for sbit integer multiplication.
Fast Reduction of Ternary Quadratic Forms
"... We show that a positive definite integral ternary form can be reduced with O(M(s)log s) bit operations, where s is the binary encoding length of the form and M(s) is the bitcomplexity of sbit integer multiplication. ..."
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We show that a positive definite integral ternary form can be reduced with O(M(s)log s) bit operations, where s is the binary encoding length of the form and M(s) is the bitcomplexity of sbit integer multiplication.
A Survey on IQ Cryptography
 In Proceedings of Public Key Cryptography and Computational Number Theory
, 2001
"... This paper gives a survey on cryptographic primitives based on class groups of imaginary quadratic orders (IQ cryptography, IQC). We present IQC versions of several well known cryptographic primitives, and we explain, why these primitives are secure if one assumes the hardness of the underlying p ..."
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This paper gives a survey on cryptographic primitives based on class groups of imaginary quadratic orders (IQ cryptography, IQC). We present IQC versions of several well known cryptographic primitives, and we explain, why these primitives are secure if one assumes the hardness of the underlying problems. We give advice on the selection of the cryptographic parameters and show the impact of this advice on the eciency of some IQ cryptosystems.
Short Vectors of Planar Lattices Via Continued Fractions
 Information Processing Letters
, 2001
"... We show that a shortest vector of a 2dimensional integral lattice with respect to the ` norm can be computed with a constant number of extendedgcd computations, one commonconvergent computation and a constant number of arithmetic operations. It follows that in two dimensions, a fast basisredu ..."
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We show that a shortest vector of a 2dimensional integral lattice with respect to the ` norm can be computed with a constant number of extendedgcd computations, one commonconvergent computation and a constant number of arithmetic operations. It follows that in two dimensions, a fast basisreduction algorithm can be solely based on Schnhage's classical algorithm on the fast computation of continued fractions and the reduction algorithm of Gau. Keywords: Algorithms, computational geometry, number theoretic algorithms 1