A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
An Application of Sieve Methods to Elliptic Curves
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Counting Points on Hyperelliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Refinements of Miller's algorithm for computing the Weil/Tate pairing
Journal of Algorithms
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Let A be an Abelian variety over a finite field $\mathbb{F}$. The possibility of using the group $A(\mathbb{F})$ of points on A in $\mathbb{F}$ as the basis of a public-key cryptography scheme is still at an early stage of exploration. In this article, we will discuss some of the issues and their current staus. In particular, we will discuss arithmetic on Abelian varieties, methods for point counting, and attacks on the Discrete Logarithm Problem, especially those that are peculiar to higher-dimensional varieties.