Journal of Cryptology
The implementation of elliptic curve cryptosystems
AUSCRYPT '90 Proceedings of the international conference on cryptology on Advances in cryptology
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Improved low-density subset sum algorithms
Computational Complexity
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Lattice Attacks on Digital Signature Schemes
Designs, Codes and Cryptography
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Faster Attacks on Elliptic Curve Cryptosystems
SAC '98 Proceedings of the Selected Areas in 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
The Hardness of the Hidden Subset Sum Problem and Its Cryptographic Implications
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Efficient Multiplication on Certain Nonsupersingular Elliptic Curves
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes
CRYPTO '96 Proceedings of the 16th 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
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
Speeding up the Scalar Multiplication in the Jacobians of Hyperelliptic Curves Using Frobenius Map
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Speeding up the Discrete Log Computation on Curves with Automorphisms
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Supersingular Curves in Cryptography
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Two Topics in Hyperelliptic Cryptography
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
Designs, Codes and Cryptography
New directions in cryptography
IEEE Transactions on Information Theory
A public key cryptosystem and a signature scheme based on discrete logarithms
IEEE Transactions on Information Theory
Reducing elliptic curve logarithms to logarithms in a finite field
IEEE Transactions on Information Theory
Skew-Frobenius Maps on Hyperelliptic Curves
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Koblitz curves and integer equivalents of frobenius expansions
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
On the distribution of the coefficients of normal forms for Frobenius expansions
Designs, Codes and Cryptography
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Efficient scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
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Hyperelliptic curves over finite fields are used in cryptosystems. To reach better performance, Koblitz curves, i.e. subfield curves, have been proposed. We present fast scalar multiplication methods for Koblitz curve cryptosystems for hyperelliptic curves enhancing the techniques published so far. For hyperelliptic curves, this paper is the first to give a proof on the finiteness of the Frobenius-expansions involved, to deal with periodic expansions, and to give a sound complexity estimate. As a second topic we consider a different, even faster set-up. The idea is to use a @t-adic expansion as the key instead of starting with an integer which is then expanded. We show that this approach has similar security and is especially suited for restricted devices as the requirements to perform the operations are reduced to a minimum.