[图书][B] Handbook of finite fields
GL Mullen, D Panario - 2013 - api.taylorfrancis.com
The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …
book for the theory and applications of finite fields. It is not intended to be an introductory …
A simple provably secure key exchange scheme based on the learning with errors problem
We use the learning with errors (LWE) problem to build a new simple and provably secure
key exchange scheme. The basic idea of the construction can be viewed as certain …
key exchange scheme. The basic idea of the construction can be viewed as certain …
Fast exhaustive search for polynomial systems in
We analyze how fast we can solve general systems of multivariate equations of various low
degrees over F_2; this is a well known hard problem which is important both in itself and as …
degrees over F_2; this is a well known hard problem which is important both in itself and as …
A new incremental algorithm for computing Gröbner bases
S Gao, Y Guan, F Volny IV - … of the 2010 International Symposium on …, 2010 - dl.acm.org
In this paper, we present a new algorithm for computing Gröbner bases. Our algorithm is
incremental in the same fashion as F5 and F5C. At a typical step, one is given a Gröbner …
incremental in the same fashion as F5 and F5C. At a typical step, one is given a Gröbner …
SoK: Gröbner basis algorithms for arithmetization oriented ciphers
JF Sauer, A Szepieniec - Cryptology ePrint Archive, 2021 - eprint.iacr.org
Many new ciphers target a concise algebraic description for efficient evaluation in a proof
system or a multi-party computation. This new target for optimization introduces algebraic …
system or a multi-party computation. This new target for optimization introduces algebraic …
On the relation between the MXL family of algorithms and Gröbner basis algorithms
The computation of Gröbner bases remains one of the most powerful methods for tackling
the Polynomial System Solving (PoSSo) problem. The most efficient known algorithms …
the Polynomial System Solving (PoSSo) problem. The most efficient known algorithms …
Solving LWE problem with bounded errors in polynomial time
J Ding - Cryptology ePrint Archive, 2010 - eprint.iacr.org
In this paper, we present a new algorithm, such that, for the learning with errors (LWE)
problems, if the errors are bounded--the errors do not span the whole prime finite field $ F_q …
problems, if the errors are bounded--the errors do not span the whole prime finite field $ F_q …
Linear algebra to compute syzygies and Gröbner bases
D Cabarcas, J Ding - Proceedings of the 36th international symposium …, 2011 - dl.acm.org
In this paper, we introduce a new method to avoid zero reductions in Gröbner basis
computation. We call this method LASyz, which stands for Lineal Algebra to compute …
computation. We call this method LASyz, which stands for Lineal Algebra to compute …
An algebraic broadcast attack against NTRU
J Ding, Y Pan, Y Deng - … and Privacy: 17th Australasian Conference, ACISP …, 2012 - Springer
In this paper, we propose an algebraic broadcast attack against NTRU, which recovers a
single message encrypted multiple times using different NTRU public keys. Namely, when a …
single message encrypted multiple times using different NTRU public keys. Namely, when a …
[PDF][PDF] On the Relation Between the Mutant Strategy and the Normal Selection Strategy in Gröbner Basis Algorithms.
MR Albrecht, C Cid, JC Faugere… - IACR Cryptol. ePrint …, 2011 - marekrychlik.com
The computation of Gröbner bases remains one of the most powerful methods for tackling
the Polynomial System Solving (PoSSo) problem. The most efficient known algorithms …
the Polynomial System Solving (PoSSo) problem. The most efficient known algorithms …