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METHOD FOR THE CONSTRUCTION OF ELLIPTIC CURVES OVER FINITE FIELDS
METHOD FOR THE CONSTRUCTION OF ELLIPTIC CURVES OVER FINITE FIELDS
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机译：有限域上椭圆曲线的构造方法
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摘要
The invention relates to a method for constructing elliptic curves E over finite fields based on the equation M = P + 1 + x (where ||x|| = 2√P; P represents a prime power while E represents an elliptic curve over the field Fp comprising P elements), accordingly 4P = x2 + y2||D|| (where y ϵ N and the discriminant D = f2D0 of the order of conductor f in the imaginary quadratic number field K of discriminant D0), by using module functions g so as to have access to large discriminant values ||D||. According to the invention, the module functions g are characterized in that the degree of g(alpha) is a real divisor of h (h being the ideal class number of the order of K to the discriminant D) while the coefficients of the associated minimal polynomials are small.
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机译：本发明涉及一种基于等式M ＝ P + 1 + x（其中|| x || ＜＝ 2＆radic; P; P表示素数幂，而E表示椭圆曲线E上的椭圆曲线）在有限域上构造椭圆曲线E的方法。字段Fp包含P个元素），因此4P = x 2 + y 2 ||| D || （其中，y和N且判别式D =判别式D0的虚二次数字段K中导体f的阶的判别式D = f 2 D0），通过使用模块函数g可以访问大的判别式值||。 D ||。根据本发明，模块函数g的特征在于，g（α）的度是h的实数除数（h是从K到判别式D的理想分类数），而相关的极小系数多项式很小。
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