We give an efficient explicit algorithm to find the structure and generators of the maximal 2-
subgroup of the Jacobian of a genus 2 curve over a finite field of odd characteristic. We use …

Integer multiplication in Jacobians of genus $2 $ curves over a finite field $\mathbb {F} _q $
is a fundamental operation for hyperelliptic curve cryptography. Algorithmically, the result of …

We study division by 3 in Jacobians of genus 2 curves over binary fields with a 2-torsion
subgroup of rank 1 or 2. We characterize the 3-torsion divisors and provide, for every D∈ …

We provide trisection (division by 3) algorithms for Jacobians of genus 2 curves over finite
fields F _q F q of odd characteristic which rely on the factorization of a polynomial whose …

We show how to compute the pre-images of multiplication-by-2 in Jacobians of genus 2
curves C: y 2= f (x) over F q with q odd. We characterize D=[u (x), v (x)]∈ 2 Jac (C)(F q) in …

For any prime i, it is possible to construct global function fields whose Jacobians have high i-
rank by moving to a sufficiently large constant field extension. This was investigated in some …

Given a genus 2 curve C defined over a finite field 𝔽 q of odd characteristic such that 2|# Jac
(C)(𝔽 q), we study the growth of the 2-adic valuation of the cardinality of the Jacobian over a …

We study l-section algorithms for Jacobian of genus two over finite fields. We provide
trisection (division by l= 3) algorithms for Jacobians of genus 2 curves over finite fields Fq of …

Given a genus 2 curve C defined over a finite field Fq of odd characteristic such that 2|# Jac
(C)(Fq), we study the growth of the 2-adic valuation of the cardinality of the Jacobian over a …

Symbolic Trisection Polynomials for Genus 2 Curves in Odd Characteristic Page 1 Copyright ©
by SIAM. Unauthorized reproduction of this article is prohibited. SIAM J. DISCRETE MATH. c …