An Improved Algorithm for Iterative Matrix-Vector Multiplications over Finite Fields

2019 ◽  
pp. 358-367
Author(s):  
Ceyda Mangır ◽  
Murat Cenk ◽  
Murat Manguoğlu
Keyword(s):  
Finite Fields ◽  
Matrix Vector ◽  
Improved Algorithm

scholarly journals The multiple number field sieve for medium- and high-characteristic finite fields

2014 ◽  
Vol 17 (A) ◽  
pp. 230-246 ◽  
Author(s):  
Razvan Barbulescu ◽  
Cécile Pierrot
Keyword(s):  
Number Field ◽  
Finite Fields ◽  
Discrete Logarithm ◽  
Number Fields ◽  
Discrete Logarithm Problem ◽  
Discrete Logarithms ◽  
Number Field Sieve ◽  
Characteristic Case ◽  
Asymptotic Complexity ◽  
Improved Algorithm

AbstractIn this paper we study the discrete logarithm problem in medium- and high-characteristic finite fields. We propose a variant of the number field sieve (NFS) based on numerous number fields. Our improved algorithm computes discrete logarithms in $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathbb{F}_{p^n}$ for the whole range of applicability of the NFS and lowers the asymptotic complexity from $L_{p^n}({1/3},({128/9})^{1/3})$ to $L_{p^n}({1/3},(2^{13}/3^6)^{1/3})$ in the medium-characteristic case, and from $L_{p^n}({1/3},({64/9})^{1/3})$ to $L_{p^n}({1/3},((92 + 26 \sqrt{13})/27)^{1/3})$ in the high-characteristic case.

Finite Fields

1996 ◽  
Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  
Finite Fields

Maximum Distance Separable Hankel Rhotrices over Finite Fields

2018 ◽  
Vol 43 (1-4) ◽  
pp. 13-45
Author(s):  
Prof. P. L. Sharma ◽  
◽  
Mr. Arun Kumar ◽  
Mrs. Shalini Gupta ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Maximum Distance ◽  
Maximum Distance Separable
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