Efficient Construction of Cryptographically Strong Elliptic Curves
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
Constructing elliptic curves with given group order over large finite fields
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
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
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We present an implementation that turns out to be most efficient in practice to compute singular moduli within a fixed floating point precision. First, we show how to efficiently determine the Fourier coefficients of the modular function j and related functions γ2, f2, and η. Comparing several alternative methods for computing singular moduli, we show that in practice the computation via the η-function turns out to be the most efficient one. An important application with respect to cryptography is that we can speed up the generation of cryptographically strong elliptic curves using the Complex Multiplication Approach.