Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm
نویسندگان
چکیده
In this paper, we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Our new, multi-threaded algorithm is the first to provide an efficient, parallel implementation of the Schorr-Euchner algorithm for today’s multi-processor, multi-core computer architectures. Experiments with sparse and dense lattice bases show a speed-up factor of about 1.8 for the 2-thread and about factor 3.2 for the 4-thread version of our new parallel lattice basis reduction algorithm in comparison to the traditional non-parallel algorithm.
منابع مشابه
A Parallel LLL using POSIX Threads
In this paper we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Lattice theory and in particular lattice basis reduction continues to play an integral role in cryptography. Not only does it provide effective cryptanalysis tools but it is also believed to bring about new cryptographic primitives that exhibit strong security even in the presence of quantum computer...
متن کاملImproving the Parallel Schnorr-Euchner LLL Algorithm
This paper introduces a number of modifications that allow for significant improvements of parallel LLL reduction. Experiments show that these modifications result in an increase of the speed-up by a factor of more than 1.35 for SVP challenge type lattice bases in comparing the new algorithm with the state-of-the-art parallel LLL algorithm.
متن کاملAn Efficient LLL Gram Using Buffered Transformations
In this paper we introduce an improved variant of the LLL algorithm. Using the Gram matrix to avoid expensive correction steps necessary in the Schnorr-Euchner algorithm and introducing the use of buffered transformations allows us to obtain a major improvement in reduction time. Unlike previous work, we are able to achieve the improvement while obtaining a strong reduction result and maintaini...
متن کاملA KZ Reduction Algorithm
The Korkine-Zolotareff (KZ) reduction is one of the often used reduction strategies for decoding lattices. A KZ reduction algorithm involves solving shortest vector problems (SVPs) and basis expansion. In this paper, first we improve the commonly used Schnorr-Euchner search strategy for solving SVPs. Then, we derive upper bounds on the magnitudes of the entries of any solution of a SVP when its...
متن کاملParallel Complexitiy of Lattice Basis Reduction and a Floating-Point Parallel Algorithm
Lattice basis reduction is an important problem in the areas of computer algebra and geometry of numbers There are several e cient sequential algorithms for lattice basis reduction e g the well known LLL algorithm and a variant of Schnorr and Euchner which uses fast oating point arithmetic Recently parallel algorithms were developed but they use slow exact integer arithmetic and until now a for...
متن کامل