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Method for generating secure elliptic curves using an arithmetic-geometric mean iteration
Method for generating secure elliptic curves using an arithmetic-geometric mean iteration
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机译:使用算术几何平均迭代生成安全椭圆曲线的方法
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摘要
Methods 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. The methods provide 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, 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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