Efficient computation of Cantor's division polynomials of hyperelliptic curves over finite fields. (July 2023)

• Record Type: Journal Article
• Authors: Eid, Elie
• Is Part Of: Journal of symbolic computation. Volume 117(2023)
• Page Start: 68
• Page End: 100
• Publication Date: 2023-07
• Subjects: p-adic differential equations -- Newton scheme -- Arithmetic geometry -- Isogenies -- Cantor's polynomials; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.10.006
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Let p be an odd prime number. We propose an algorithm for computing rational representations of isogenies between Jacobians of hyperelliptic curves via p -adic differential equations with a sharp analysis of the loss of precision. Consequently, after having possibly lifted the problem in the p -adics, we derive fast algorithms for computing explicitly Cantor's division polynomials of hyperelliptic curves defined over finite fields.