Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Structure of parallel multipliers for a class of fields GF(2m)
Information and Computation
Designs, Codes and Cryptography
Mathematics of Computation
A survey of fast exponentiation methods
Journal of Algorithms
Analysis of the Weil Descent Attack of Gaudry, Hess and Smart
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
How Secure Are Elliptic Curves over Composite Extension Fields?
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Fast Multiplication in Finite Fields GF(2N)
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
An algorithm for solving the discrete log problem on hyperelliptic curves
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Efficient Multiplication Beyond Optimal Normal Bases
IEEE Transactions on Computers
A Redundant Representation of GF(q^n) for Designing Arithmetic Circuits
IEEE Transactions on Computers
Fast Normal Basis Multiplication Using General Purpose Processors
IEEE Transactions on Computers
Low Complexity Word-Level Sequential Normal Basis Multipliers
IEEE Transactions on Computers
IEEE Transactions on Computers
Extractors for binary elliptic curves
Designs, Codes and Cryptography
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Low-complexity multiplier for GF(2m) based on all-one polynomials
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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In 1999 Silverman [21] introduced a family of binary finite fields which are composite extensions of F2 and on which arithmetic operations can be performed more quickly than on prime extensions of F2 of the same size.We present here a fast approach to elliptic curve cryptography using a distinguished subset of the set of Silverman fields F2N = Fhn. This approach leads to a theoretical computation speedup over fields of the same size, using a standard point of view (cf. [7]). We also analyse their security against prime extension fields F2p , where p is prime, following the method of Menezes and Qu [12]. We conclude that our fields do not present any significant weakness towards the solution of the elliptic curve discrete logarithm problem and that often the Weil descent of Galbraith-Gaudry-Hess-Smart (GGHS) does not offer a better attack on elliptic curves defined over F2N than on those defined over F2p, with a prime p of the same size as N.A noteworthy example is provided by F2226 : a generic elliptic curve Y2 + XY = X3 + 驴X2 + 脽 defined over F2226 is as prone to the GGHS Weil descent attack as a generic curve defined on the NIST field F2233.