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A new efficient algorithm for computing Gröbner bases (F4)
This paper introduces a new efficient algorithm for computing Grobner bases. To avoid as much intermediate computation as possible, the algorithm computes successive truncated Grobner bases and itExpand
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Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering
TLDR
We present an efficient algorithm for the transformation of a Grobner basis of a zero-dimensional ideal with respect to any given ordering into a GroBner basis withrespect to any other ordering. Expand
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Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases
TLDR
In this paper, we present a new and efficient attack of this cryptosystem based on fast algorithms for computing Grobner basis. Expand
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On the complexity of the BKW algorithm on LWE
TLDR
This work presents a study of the complexity of the Blum–Kalai–Wasserman (BKW) algorithm when applied to the Learning with Errors (LWE) problem, by providing refined estimates for the data and computational effort requirements for solving concrete instances of the LWE problem. Expand
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Algebraic Cryptanalysis of McEliece Variants with Compact Keys
TLDR
We prove that the private key of the McEliece Cryptosystem satisfies a system of bi-homogeneous polynomial equations. Expand
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Hybrid approach for solving multivariate systems over finite fields
TLDR
We present an improved approach to solve multivariate polynomial systems over finite fields. Expand
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FGb: A Library for Computing Gröbner Bases
TLDR
FGb is a high-performance, portable, C library for computing Grobner bases over the integers and over finite fields. Expand
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Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic
TLDR
We investigate in this paper the security of HFE and Multi-HFE schemes as well as their minus and embedding variants. Expand
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On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations
We extend the notion of regular sequence ([Mac16]) to overdetermined system of algebraic equations. We study generic properties of Grobner bases and analyse precisely the behavior of the F5 [Fau02]Expand
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A new efficient algorithm for computing Gr öbner bases without reduction to zero ( F 5 ) ( 15 / 6 / 2004 )
This paper introduces a new efficient algorithm for computin g Gröbner bases. We replace the Buchberger criteria by an optimal crit eria. We give a proof that the resulting algorithm (called F5)Expand
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