Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Mathematics of Computation
Remarks on the Schoof-Elkies-Atkin algorithm
Mathematics of Computation
Elliptic curves in cryptography
Elliptic curves in cryptography
Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Use of Elliptic Curves in Cryptography
CRYPTO '85 Advances in Cryptology
Efficient Implementation of Schoof's Algorithm
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances 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
Selecting Cryptographic Key Sizes
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Computing l-Isogenies Using the p-Torsion
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Finding good random elliptic curves for cryptosystems defined over IF2n
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Counting the number of points on elliptic curves over finite fields: strategies and performances
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Elliptic Curves of Prime Order over Optimal Extension Fields for Use in Cryptography
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
An Extension of Kedlaya's Point-Counting Algorithm to Superelliptic Curves
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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The use of elliptic curves in cryptography relies on the ability to count the number of points on a given curve. Before 1999, the SEA algorithm was the only efficient method known for random curves. Then Satoh proposed a new algorithm based on the canonical p-adic lift of the curve for p ≥ 5. In an earlier paper, the authors extended Satoh's method to the case of characteristics two and three. This paper presents an implementation of the Satoh-FGH algorithm and its application to the problem of finding curves suitable for cryptography. By combining Satoh-FGH and an early-abort strategy based on SEA, we are able to find secure random curves in characteristic two in much less time than previously reported. In particular we can generate curves widely considered to be as secure as RSA-1024 in less than one minute each on a fast workstation.