A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Constructing elliptic curves with given group order over large finite fields
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Generating Class Fields using Shimura Reciprocity
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Comparing Invariants for Class Fields of Imaginary Quadratic Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Generating More MNT Elliptic Curves
Designs, Codes and Cryptography
A comparison of MNT curves and supersingular curves
Applicable Algebra in Engineering, Communication and Computing
A method for distinguishing the two candidate elliptic curves in CM method
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
An improved algorithm for computing logarithms over and its cryptographic significance (Corresp.)
IEEE Transactions on Information Theory
Reducing elliptic curve logarithms to logarithms in a finite field
IEEE Transactions on Information Theory
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
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The Complex Multiplication (CM) method is a method frequently used for the generation of elliptic curves (ECs) over a prime field F"p. The most demanding and complex step of this method is the computation of the roots of a special type of class polynomials, called Hilbert polynomials. However, there are several polynomials, called class polynomials, which can be used in the CM method, having much smaller coefficients, and fulfilling the prerequisite that their roots can be easily transformed to the roots of the corresponding Hilbert polynomials. In this paper, we propose the use of a new class of polynomials which are derived from Ramanujan's class invariants t"n. We explicitly describe the algorithm for the construction of the new polynomials and give the necessary transformation of their roots to the roots of the corresponding Hilbert polynomials. We provide a theoretical asymptotic bound for the bit precision requirements of all class polynomials and, also using extensive experimental assessments, we compare the efficiency of using the new polynomials against the use of the other class polynomials. Our comparison shows that the new class of polynomials clearly surpass all of the previously used polynomials when they are used in the generation of prime order elliptic curves.