Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Journal of Cryptology
Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Fast exponentiation with precomputation
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Speeding up the Arithmetic on Koblitz Curves of Genus Two
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
Fast Generation of Pairs (k, [k]P) for Koblitz Elliptic Curves
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Speeding Up Point Multiplication on Hyperelliptic Curves with Efficiently-Computable Endomorphisms
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Compact Encoding of Non-adjacent Forms with Applications to Elliptic Curve Cryptography
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
An Improved Method of Multiplication on Certain Elliptic Curves
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Protections against Differential Analysis for Elliptic Curve Cryptography
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
An Improved Algorithm for uP + vQ on a Family of Elliptic Curves
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 17 - Volume 18
A note on window τ-NAF algorithm
Information Processing Letters
On Τ-adic representations of integers
Designs, Codes and Cryptography
A note on window τ-NAF algorithm
Information Processing Letters
New Frobenius expansions for elliptic curves with efficient endomorphisms
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Koblitz curves and integer equivalents of frobenius expansions
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Designs, Codes and Cryptography
On the distribution of the coefficients of normal forms for Frobenius expansions
Designs, Codes and Cryptography
Efficient countermeasures for thwarting the SCA attacks on the frobenius based methods
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Finite Fields and Their Applications
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Elliptic curves defined over finite fields have been proposed for Diffie-Hellman type crypto systems. Koblitz has suggested to use "anomalous" elliptic curves in characteristic 2, as these are nonsupersingular and allow for efficient multiplication of points by an integer.For anomalous curves E defined over F2 and regarded as curves over the extension field F2n, a new algorithm for computing multiples of arbitrary points on E is developed. The algorithm is shown to be three times faster than double and add, is easy to implement and does not rely on precomputation or additional memory. The algorithm is used to generate efficient one-way permutations involving pairs of twisted elliptic curves by extending a construction of Kaliski to finite fields of characteristic 2.