| 摘要 |
The present invention is a fast new method for determining whether an arbitrary elliptic curve over a binary field is secure, by using a novel non-converging Arithmetic-Geometric Mean iteration to determine the exact number of points on the curve. This invention is used for the rapid generation of secure curves for Elliptic-Curve Cryptography by selecting a secure curve from among candidate curves with the new method. The secure curve chosen is a curve whose number of points, determined using the invention, is found to be divisible by a large prime number. The number of points on candidate curves is computed by a first phase, which lifts the curve to a certain related curve, followed by a second phase, which computes a certain norm that yields the result. The new Arithmetic-Geometric Mean iteration is used for the lifting phase or for the norm phase or for both.
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