Suitable Curves for Genus-4 HCC over Prime Fields: Point Counting Formulae for Hyperelliptic Curves of Type y 2=x $^{\rm 2{\it k}+1}$ +ax

2005 ◽  
pp. 539-550 ◽  
Author(s):  
Mitsuhiro Haneda ◽  
Mitsuru Kawazoe ◽  
Tetsuya Takahashi
Keyword(s):  
Hyperelliptic Curves ◽  
Point Counting ◽  
Prime Fields

scholarly journals Isogenies for Point Counting on Genus Two Hyperelliptic Curves with Maximal Real Multiplication

2017 ◽  
pp. 63-94 ◽  
Author(s):  
Sean Ballentine ◽  
Aurore Guillevic ◽  
Elisa Lorenzo García ◽  
Chloe Martindale ◽  
Maike Massierer ◽  
...  
Keyword(s):  
Hyperelliptic Curves ◽  
Point Counting ◽  
Real Multiplication ◽  
Genus Two

scholarly journals Point Counting in Families of Hyperelliptic Curves in Characteristic 2

2007 ◽  
Vol 10 ◽  
pp. 207-234 ◽  
Author(s):  
Hendrik Hubrechts
Keyword(s):  
Zeta Function ◽  
Polynomial Time ◽  
Time Complexity ◽  
Hyperelliptic Curves ◽  
Small Field ◽  
Extension Field ◽  
Point Counting ◽  
The Family ◽  
Characteristic 2 ◽  
Weierstrass Equation

AbstractLet EΓ be a family of hyperelliptic curves over F2alg cl with general Weierstrass equation given over a very small field F. The author of this paper describes an algorithm for computing the zeta function of Eγ, with γ in a degree n extension field of F, which has time complexity O(n3 + ε) bit operations and memory requirements O(n2) bits. Using a slightly different algorithm, one can get time O(n2.667) and memory O(n2.5), and the computation for n curves of the family can be done in time O(n3.376). All of these algorithms are polynomial-time in the genus.

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