Journal of Cryptology
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Algebraic aspects of cryptography
Algebraic aspects of cryptography
Mathematics of Computation
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Efficient construction of secure hyperelliptic discrete logarithm problems
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
A Family of Jacobians Suitable for Discrete Log Cryptosystems
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Design of Elliptic Curves with Controllable Lower Boundary of Extension Degree for Reduction Attacks
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
A Fast Software Implementation for Arithmetic Operations in GF(2n)
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Secure Hyperelliptic Cryptosystems and Their Performances
PKC '98 Proceedings of the First International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Non supersingular elliptic curves for public key cryptosystems
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Fast Scalar Multiplication on the Jacobian of a Family of Hyperelliptic Curves
ICICS '01 Proceedings of the Third International Conference on Information and Communications Security
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We investigate the discrete logarithm problem over jacobians of hyperelliptic curves suitable for public-key cryptosystems. We focus on the case when the definition field has small characteristic 2, 3, 5 and 7, then we present hyperelliptic cryptosystems that resist against all known attacks. We further implement our designed hyperelliptic cryptosystems over finite fields F2n in software on Alpha and Pentium-II computers. Our results indicate that if we choose curves carefully, hyperelliptic cryptosystems do have practical performance.