A simple method for obtaining relations among factor basis elements for special hyperelliptic curves

P Sarkar, S Singh - Applicable Algebra in Engineering, Communication …, 2017 - Springer
Nagao proposed a decomposition method for divisors of hyperelliptic curves defined over a
field F _ q^ n F qn with n ≥ 2 n≥ 2. Joux and Vitse later proposed a variant which provided …

Attacking a binary GLS elliptic curve with magma

JJ Chi, T Oliveira - Progress in Cryptology--LATINCRYPT 2015: 4th …, 2015 - Springer
In this paper we present a complete Magma implementation for solving the discrete
logarithm problem (DLP) on a binary GLS curve defined over the field F _ 2^ 62 F 2 62. For …

Improved sieving on algebraic curves

V Vitse, A Wallet - Progress in Cryptology--LATINCRYPT 2015: 4th …, 2015 - Springer
The best algorithms for discrete logarithms in Jacobians of algebraic curves of small genus
are based on index calculus methods coupled with large prime variations. For hyperelliptic …

Field extensions and index calculus on algebraic curves

V Vitse - Arithmetic, Geometry, Cryptography and Coding …, 2017 - books.google.com
Discrete logarithm index calculus algorithms are usually more efficient for non-hyperelliptic
curves (Diem's method) than for hyperelliptic curves (Gaudry's method). However when the …

The point decomposition problem in Jacobian varieties

A Wallet - 2016 - theses.hal.science
The discrete logarithm problem is a fundamental brick for several protocols for secured
communications. Its instantiation over elliptic curves allows the deployment of efficient …

[PDF][PDF] Cryptography in small-characteristic finite fields= Criptografía en campos finitos de característica chica

TE Figueiredo Oliveira - 2016 - repositorio.cinvestav.mx
Desde el inicio de la criptografıa de llave pública, los campos finitos de caracterıstica chica
han sido propuestos como estructuras matemáticas en implementación de protocolos de …