Finding vulnerable curves over finite fields of characteristic 2 by pairing reduction

2017 ◽  
Author(s):  
Yuhong Zhang ◽  
Meng Zhang ◽  
Maozhi Xu
Keyword(s):  
Finite Fields ◽  
Curves Over Finite Fields ◽  
Characteristic 2

scholarly journals Computing Zeta Functions of Artin–schreier Curves over Finite Fields

2002 ◽  
Vol 5 ◽  
pp. 34-55 ◽  
Author(s):  
Alan G. B. Lauder ◽  
Daqing Wan
Keyword(s):  
Finite Fields ◽  
Hyperelliptic Curve ◽  
Exponential Sums ◽  
Reduction Method ◽  
Zeta Functions ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Efficient Reduction ◽  
Curves Over Finite Fields ◽  
Characteristic 2

AbstractThe authors present a practical polynomial-time algorithm for computing the zeta function of certain Artin–Schreier curves over finite fields. This yields a method for computing the order of the Jacobian of an elliptic curve in characteristic 2, and more generally, any hyperelliptic curve in characteristic 2 whose affine equation is of a particular form. The algorithm is based upon an efficient reduction method for the Dwork cohomology of one-variable exponential sums.

scholarly journals On the existence of some specific elements in finite fields of characteristic 2

2012 ◽  
Vol 18 (4) ◽  
pp. 800-813 ◽  
Author(s):  
Peipei Wang ◽  
Xiwang Cao ◽  
Rongquan Feng
Keyword(s):  
Finite Fields ◽  
Characteristic 2
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