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MPFR: A multiple-precision binary floating-point library with correct rounding
This article presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitrary-precision, ideas…
Existence of Primitive Divisors of Lucas and Lehmer Numbers
We prove that for n > 30, every n-th Lucas and Lehmer number has a primitive divisor. This allows us to list all Lucas and Lehmer numbers without a primitive divisor.
Analyzing Blockwise Lattice Algorithms Using Dynamical Systems
This work shows that BKZ can be terminated long before its completion, while still providing bases of excellent quality and develops a completely new elementary technique based on discrete-time affine dynamical systems, which could lead to the design of improved lattice reduction algorithms.
Improved Analysis of Kannan's Shortest Lattice Vector Algorithm
This paper improves the complexity upper-bounds of Kannan's algorithms, and provides new insight on the practical cost of solving SVP, and helps progressing towards providing meaningful key-sizes.
Algorithms for the Shortest and Closest Lattice Vector Problems
The theoretical worst-case complexity bounds of the state of the art solvers of the Shortest and Closest Lattice Vector Problems in the Euclidean norm are concentrated on, but also consider some practical facets of these algorithms.
Solving Thue Equations of High Degree
Abstract We propose a general method for numerical solution of Thue equations, which allows one to solve in reasonable time Thue equations of high degree (provided necessary algebraic number theory…
Solving Thue equations without the full unit group
- G. Hanrot
- Computer Science, MathematicsMath. Comput.
It is shown that the knowledge of a subgroup of finite index is in fact sufficient and two examples linked with the primitive divisor problem for Lucas and Lehmer sequences are given.
The Middle Product Algorithm I
- G. Hanrot, Michel Quercia, P. Zimmermann
- Computer ScienceApplicable Algebra in Engineering, Communication…
- 1 March 2004
A new algorithm is presented – MiddleProduct or, for short, MP – computing the n middle coefficients of a (2n−1)×n full product in the same number of multiplications as a full n×n product.
Accelerating Lattice Reduction with FPGAs
This is the first FPGA implementation of KFP specifically targeting cryptographically relevant dimensions, and it is claimed that this implementation is faster than a multi-core CPU implementation by a factor around 2.12.