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AAECC
2003
Springer
165views Algorithms» more  AAECC 2003»
13 years 7 months ago
Fast Point Multiplication on Elliptic Curves through Isogenies
Elliptic curve cryptosystems are usually implemented over fields of characteristic two or over (large) prime fields. For large prime fields, projective coordinates are more suitabl...
Eric Brier, Marc Joye
FDTC
2006
Springer
106views Cryptology» more  FDTC 2006»
13 years 7 months ago
Sign Change Fault Attacks on Elliptic Curve Cryptosystems
We present a new type of fault attacks on elliptic curve scalar multiplications: Sign Change Attacks. These attacks exploit different number representations as they are often emplo...
Johannes Blömer, Martin Otto 0002, Jean-Pierr...
ANTS
2006
Springer
73views Algorithms» more  ANTS 2006»
13 years 7 months ago
The Elliptic Curve Database for Conductors to 130000
Abstract. Tabulating elliptic curves has been carried out since the earliest days of machine computation in number theory. After some historical remarks, we report on significant r...
John Cremona
ANTS
2006
Springer
95views Algorithms» more  ANTS 2006»
13 years 7 months ago
Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10
We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with ...
David Freeman
ANTS
2010
Springer
250views Algorithms» more  ANTS 2010»
13 years 7 months ago
A Subexponential Algorithm for Evaluating Large Degree Isogenies
An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between ellip...
David Jao, Vladimir Soukharev
ANTS
1998
Springer
123views Algorithms» more  ANTS 1998»
13 years 7 months ago
Primality Proving Using Elliptic Curves: An Update
In 1986, following the work of Schoof on counting points on elliptic curves over finite fields, new algorithms for primality proving emerged, due to Goldwasser and Kilian on the on...
François Morain
ANTS
1998
Springer
93views Algorithms» more  ANTS 1998»
13 years 7 months ago
The Decision Diffie-Hellman Problem
The decision Diffie
Dan Boneh
EUROCRYPT
1999
Springer
13 years 8 months ago
Comparing the MOV and FR Reductions in Elliptic Curve Cryptography
Abstract. This paper addresses the discrete logarithm problem in elliptic curve cryptography. In particular, we generalize the Menezes, Okamoto, and Vanstone (MOV) reduction so tha...
Ryuichi Harasawa, Junji Shikata, Joe Suzuki, Hidek...
ANTS
2000
Springer
133views Algorithms» more  ANTS 2000»
13 years 8 months ago
Lifting Elliptic Curves and Solving the Elliptic Curve Discrete Logarithm Problem
Abstract. Essentially all subexponential time algorithms for the discrete logarithm problem over nite elds are based on the index calculus idea. In proposing cryptosystems based on...
Ming-Deh A. Huang, Ka Lam Kueh, Ki-Seng Tan
INDOCRYPT
2001
Springer
13 years 8 months ago
Elliptic Curves of Prime Order over Optimal Extension Fields for Use in Cryptography
We present an algorithm for generating elliptic curves of prime order over Optimal Extension Fields suitable for use in cryptography. The algorithm is based on the theory of Comple...
Harald Baier