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

In search of CurveSwap: Measuring elliptic curve implementations in the wild Luke Valenta∗ , Nick Sullivan† , Antonio Sanso‡ , Nadia Heninger∗ ∗ University

Source URL: www.seas.upenn.edu

• Cryptography
• Elliptic curve cryptography
• Elliptic-curve DiffieHellman
• DiffieHellman key exchange
• Cryptographic protocols
• Alice and Bob
• Computational hardness assumptions
• Transport Layer Security
• WolfSSH

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

Edwards Curves and the ECM Factorisation Method Peter Birkner Eindhoven University of Technology The 12th Workshop on Elliptic Curve Cryptography

Source URL: www.pbirkner.fastmail.fm

SHADOW LINES IN THE ARITHMETIC OF ELLIPTIC CURVES J. S. BALAKRISHNAN, M. C ¸ IPERIANI, J. LANG, B. MIRZA, AND R. NEWTON Abstract. Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every

Source URL: math.bu.edu