Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Journal of Cryptology
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Mathematics of Computation
On the discrete logarithm in the divisor class group of curves
Mathematics of Computation
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Counting Rational Points on Curves and Abelian Varieties over Finite Fields
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Counting Points on Hyperelliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
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
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To achieve the same level of security, hyperelliptic curve cryptosystems (HCC) use a smaller field than elliptic curve cryptosystems (ECC). HCC has a more potential application to the product that has limited memory and computing power, for instance Smart cards. We discussed how to represent the domain parameters of HCC in a compact way. The domain parameters include the field over which the curve is defined, the curve itself, the order of the Jocobian and the base point. In our method, the representation of HCC with genus g=4 over F241 (It can provide the same level of security with 164 bits ECC) only uses 339 bits.