A new efficient algorithm for computing Gröbner bases (F4)
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TLDR
In this paper, the Buchberger algorithm is replaced by the simultaneous reduction of several polynomials, which is achieved by means of a symbolic precomputation and by extensive use of sparse linear algebra methods.About:
This article is published in Journal of Pure and Applied Algebra.The article was published on 1999-06-01 and is currently open access. It has received 1089 citations till now. The article focuses on the topics: Faugère's F4 and F5 algorithms & Buchberger's algorithm.read more
Citations
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Journal ArticleDOI
SymPy: Symbolic Computing in Python
Aaron Meurer,Christopher Smith,Mateusz Paprocki,Ondřej Čertík,Sergey B Kirpichev,Matthew Rocklin,Amit Kumar,Sergiu Ivanov,Jason K. Moore,Sartaj Singh,Thilina Rathnayake,Sean Vig,Brian E. Granger,Richard P. Muller,Francesco Bonazzi,Harsh Gupta,Shivam Vats,Fredrik Johansson,Fabian Pedregosa,Matthew Curry,Matthew Curry,Andy R. Terrel,Štěpán Roučka,Ashutosh Saboo,Isuru Dilanka Fernando,Sumith Kulal,Robert Cimrman,Anthony Scopatz +27 more
TL;DR: The architecture of SymPy is presented, a description of its features, and a discussion of select domain specific submodules are discussed, to become the standard symbolic library for the scientific Python ecosystem.
Book ChapterDOI
Efficient algorithms for solving overdefined systems of multivariate polynomial equations
TL;DR: It is provided strong evidence that relinearization and XL can solve randomly generated systems of polynomial equations in subexponential time when m exceeds n by a number that increases slowly with n.
Proceedings ArticleDOI
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
TL;DR: In this article, the Buchberger criteria were replaced by an optimal criteria and the resulting algorithm (called F5) was shown to generate no useless critical pairs if the input is a regular sequence.
Book ChapterDOI
PRINCE: a low-latency block cipher for pervasive computing applications
Julia Borghoff,Anne Canteaut,Tim Güneysu,Elif Bilge Kavun,Miroslav Knezevic,Lars R. Knudsen,Gregor Leander,Ventzislav Nikov,Christof Paar,Christian Rechberger,Peter Maria Franciscus Rombouts,Søren S. Thomsen,Tolga Yalcin +12 more
TL;DR: In this paper, a block cipher called PRINCE is proposed that allows encryption of data within one clock cycle with a very competitive chip area compared to known solutions. But it does not have the α-reflection property, which holds that decryption for one key corresponds to encryption with another key.
Posted Content
PRINCE – A Low-latency Block Cipher for Pervasive Computing Applications
Julia Borghoff,Anne Canteaut,Tim Güneysu,Elif Bilge Kavun,Miroslav Knežević,Lars R. Knudsen,Gregor Leander,Ventzislav Nikov,Christof Paar,Christian Rechberger,Peter Maria Franciscus Rombouts,Søren S. Thomsen,Tolga Yalcin +12 more
TL;DR: This paper presents a block cipher that is optimized with respect to latency when implemented in hardware and holds that decryption for one key corresponds to encryption with a related key, which is of independent interest and proves its soundness against generic attacks.
References
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Book
The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Journal ArticleDOI
Shift-register synthesis and BCH decoding
TL;DR: It is shown in this paper that the iterative algorithm introduced by Berlekamp for decoding BCH codes actually provides a general solution to the problem of synthesizing the shortest linear feedback shift register capable of generating a prescribed finite sequence of digits.
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Computer solution of large sparse positive definite systems
Book
Gröbner Bases: A Computational Approach to Commutative Algebra
TL;DR: This chapter discusses linear algebra in Residue Class Rings in Vector Spaces and Modules, and first applications of Gr bner Bases.