Modern computer algebra
Elliptic curves in cryptography
Elliptic curves in cryptography
Satoh's algorithm in characteristic 2
Mathematics of Computation
Finding Secure Curves with the Satoh-FGH Algorithm and an Early-Abort Strategy
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
A Memory Efficient Version of Satoh's Algorithm
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Fast Elliptic Curve Point Counting Using Gaussian Normal Basis
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
A Timing-Resistant Elliptic Curve Backdoor in RSA
Information Security and Cryptology
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
A p-adic point counting algorithm for elliptic curves on legendre form
Finite Fields and Their Applications
Algebraic curves and cryptography
Finite Fields and Their Applications
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Since the first use of a p-adic method for counting points of elliptic curves, by Satoh in 1999, several variants of his algorithm have been proposed. In the current state, the AGM algorithm, proposed by Mestre is thought to be the fastest in practice, and the algorithm by Satoh-Skjernaa-Taguchi has the best asymptotic complexity but requires precomputations. We present an amelioration of the SST algorithm, borrowing ideas from the AGM. We make a precise comparison between this modified SST algorithm and the AGM, thus demonstrating that the former is faster by a significant factor, even for small cryptographic sizes.