Fast Algorithms for Finding the Characteristic Polynomial of a Rank-2 Drinfeld Module

Drinfeld;Module;Elliptic;Curve;Cryptography;Algorithm;Randomized

Musleh, Yossefadvisor:Schost, Eric ; affiliation1:Faculty of Mathematics ; Schost, Eric ;

University of Waterloo

关键词: Randomized;    Master Thesis;    Curve;    Drinfeld;    Elliptic;    Module;    Cryptography;    Algorithm;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/13889/3/Musleh_Yossef.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

This thesis introduces a new Monte Carlo randomized algorithm for computing the characteristic polynomial of a rank-2 Drinfeld module. We also introduce a deterministic algorithm that uses some ideas seen in Schoof's algorithm for counting points on elliptic curves over finite fields. Both approaches are a significant improvement over the current literature.