A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Dense Linear Algebra over Word-Size Prime Fields: the FFLAS and FFPACK Packages
ACM Transactions on Mathematical Software (TOMS)
Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
FGb: a library for computing Gröbner bases
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
On the relation between the MXL family of algorithms and Gröbner basis algorithms
Journal of Symbolic Computation
A tutorial on high performance computing applied to cryptanalysis
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Parallel reduction of matrices in gröbner bases computations
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
The M4RIE library for dense linear algebra over small fields with even characteristic
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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Polynomial system solving is one of the important area of Computer Algebra with many applications in Robotics, Cryptology, Computational Geometry, etc. To this end computing a Gröbner basis is often a crucial step. The most efficient algorithms [6, 7] for computing Gröbner bases [2] rely heavily on linear algebra techniques. In this paper, we present a new linear algebra package for computing Gaussian elimination of Gröbner bases matrices. The library is written in C and contains specific algorithms [11] to compute Gaussian elimination as well as specific internal representation of matrices (sparse triangular blocks, sparse rectangular blocks and hybrid rectangular blocks). The efficiency of the new software is demonstrated by showing computational results fr well known benchmarks as well as some crypto-challenges. For instance, for a medium size problem such as Katsura 15, it takes 849.7 sec on a PC with 8 cores to compute a DRL Gröbner basis modulo p 16; this is 88 faster than Magma (V2-16-1).