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MPFR: A multiple-precision binary floating-point library with correct rounding
TLDR
This article presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Expand
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
TLDR
In this work, we show that BKZ can be terminated long before its completion, while still providing bases of excellent quality. Expand
Improved Analysis of Kannan's Shortest Lattice Vector Algorithm
TLDR
Kannan's algorithm for solving the shortest vector problem (SVP) is in particular crucial in Schnorr's celebrated block reduction algorithm, on which rely the best known generic attacks against the lattice-based encryption schemes mentioned above. Expand
Algorithms for the Shortest and Closest Lattice Vector Problems
TLDR
We present the state of the art solvers of the Shortest and Closest Lattice Vector Problems in the Euclidean norm. Expand
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 theoryExpand
The Middle Product Algorithm I
TLDR
We present new algorithms for the inverse, division, and square root of power series. Expand
Accelerating Lattice Reduction with FPGAs
TLDR
We describe an FPGA accelerator for the Kannan-Fincke-Pohst enumeration algorithm (KFP) solving the Shortest Lattice Vector Problem (SVP). Expand
Terminating BKZ
TLDR
In this work, we show that BKZ can be terminated long before its completion, while still providing bases of excellent quality. Expand
Worst Cases of a Periodic Function for Large Arguments
TLDR
The first non-naive algorithm for finding hard to round cases of a periodic function for large floating-point inputs, more precisely when the function cannot be efficiently approximated by a polynomial. Expand
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