Implementing the Elliptic Curve Method of Factoring in Reconfigurable Hardware Kris Gaj, Soonhak Kwon, Patrick Baier, Paul Kohlbrenner, Hoang Le, Mohammed Khaleeluddin, Ramakrishna Bachimanchi George Mason University {kg

Source URL: www.hyperelliptic.org

• Algebra
• Abstract algebra
• Mathematics
• Finite fields
• Integer factorization algorithms
• Elliptic curves
• Group theory
• Lenstra elliptic-curve factorization
• Elliptic curve
• Elliptic curve primality
• Factorization of polynomials over finite fields

Hardware for Collision Search on Elliptic Curve over GF(2m) Philippe Bulens∗, Guerric Meurice de Dormale† and Jean-Jacques Quisquater UCL Crypto Group Universit´e Catholique de Louvain

Source URL: www.hyperelliptic.org

• Cryptography
• Abstract algebra
• Algebra
• Finite fields
• Elliptic curve cryptography
• Public-key cryptography
• Group theory
• Elliptic-curve cryptography
• Elliptic curve
• XTR
• Elliptic curve only hash
• Supersingular isogeny key exchange

On the Security of Elliptic Curve Cryptosystems against Attacks with Special-Purpose Hardware Tim G¨ uneysu, Christof Paar, Jan Pelzl Horst G¨ortz Institute for IT Security, Ruhr University Bochum, Germany {gueneysu,cp

Source URL: www.hyperelliptic.org

• Cryptography
• Abstract algebra
• Algebra
• Finite fields
• Elliptic curve cryptography
• Computational hardness assumptions
• Group theory
• Public-key cryptography
• Elliptic-curve cryptography
• Elliptic curve
• Key size
• Discrete logarithm

Hardware for Collision Search m on Elliptic Curve over GF(2 ) Philippe Bulens (S), Guerric Meurice de Dormale and Jean-Jacques Quisquater {bulens, gmeurice, quisquater}@dice.ucl.ac.be

Source URL: www.hyperelliptic.org

• Finite fields
• Algebraic number theory
• Frobenius endomorphism
• Galois theory
• Meurice
• Jean-Jacques Quisquater
• Mathematics

An Efficient Hardware Architecture for Factoring Integers with the Elliptic Curve Method Jens Franke, Thorsten Kleinjung - University of Bonn Christof Paar, Jan Pelzl - University of Bochum Christine Priplata, Colin Stah

Source URL: www.hyperelliptic.org

• Cryptography
• Integer factorization algorithms
• Lenstra elliptic-curve factorization
• Quadratic sieve
• Elliptic-curve cryptography
• Elliptic curve
• Integer factorization
• General number field sieve
• RSA
• Trial division

An Efficient Hardware Architecture for Factoring Integers with the Elliptic Curve Method Jens Franke1 , Thorsten Kleinjung1 , Christof Paar2 , Jan Pelzl2 , 4 ˇ Christine Priplata3 , Martin Simka

Source URL: www.hyperelliptic.org

• Integer factorization algorithms
• Mathematics
• Abstract algebra
• Algebra
• Lenstra elliptic-curve factorization
• Quadratic sieve
• Montgomery modular multiplication
• Elliptic curve
• Exceptional case-marking
• Division algorithm
• General number field sieve

Elliptic Curves over Q Peter Birkner Technische Universiteit Eindhoven DIAMANT Summer School on Elliptic and Hyperelliptic Curve Cryptography

Source URL: www.pbirkner.fastmail.fm

This is Chapter 7 by Gerhard Frey and Tanja Lange of the Handbook of Elliptic and Hyperelliptic Curve Cryptography, Henri Cohen, Christophe Doche, and Gerhard Frey, Editors, CRC PressCRC Press has granted the foll

Source URL: hyperelliptic.org

Ordinary plane models and completely split divisors Claus Diem and Sebastian Kochinke October 22, 2017 Abstract Let C be a smooth, non-hyperelliptic curve over an algebraically

Source URL: www.mathematik.uni-leipzig.de

Hyperelliptic Curves Peter Birkner Technische Universiteit Eindhoven DIAMANT Summer School on Elliptic and Hyperelliptic Curve Cryptography

Source URL: www.pbirkner.fastmail.fm