scholarly journals Improved Complexity Bounds for Counting Points on Hyperelliptic Curves

2018 ◽  
Vol 19 (3) ◽  
pp. 591-621 ◽  
Author(s):  
Simon Abelard ◽  
Pierrick Gaudry ◽  
Pierre-Jean Spaenlehauer
Keyword(s):  
Hyperelliptic Curves ◽  
Complexity Bounds ◽  
Counting Points

scholarly journals Counting points on genus-3 hyperelliptic curves with explicit real multiplication

2019 ◽  
Vol 2 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Simon Abelard ◽  
Pierrick Gaudry ◽  
Pierre-Jean Spaenlehauer
Keyword(s):  
Hyperelliptic Curves ◽  
Real Multiplication ◽  
Counting Points

scholarly journals Coleman integration for even-degree models of hyperelliptic curves

2015 ◽  
Vol 18 (1) ◽  
pp. 258-265 ◽  
Author(s):  
Jennifer S. Balakrishnan
Keyword(s):  
Number Theory ◽  
Computer Science ◽  
Hyperelliptic Curves ◽  
Open Book ◽  
Line Integral ◽  
Book Series ◽  
Numerical Examples ◽  
Lecture Notes ◽  
Integration Algorithms ◽  
Mathematical Sciences

The Coleman integral is a $p$-adic line integral that encapsulates various quantities of number theoretic interest. Building on the work of Harrison [J. Symbolic Comput. 47 (2012) no. 1, 89–101], we extend the Coleman integration algorithms in Balakrishnan et al. [Algorithmic number theory, Lecture Notes in Computer Science 6197 (Springer, 2010) 16–31] and Balakrishnan [ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Series 1 (Mathematical Sciences Publishers, 2013) 41–61] to even-degree models of hyperelliptic curves. We illustrate our methods with numerical examples computed in Sage.

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