On the singular values of Weber modular functions
Mathematics of Computation
Solvability by radicals from an algorithmic point of view
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Generating Class Fields using Shimura Reciprocity
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Primality Proving Using Elliptic Curves: An Update
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Ramanujan's class invariants and their use in elliptic curve cryptography
Computers & Mathematics with Applications
Fast decomposition of polynomials with known Galois group
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Generating prime order elliptic curves: difficulties and efficiency considerations
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
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Class fields of imaginary quadratic number fields can be constructed from singular values of modular functions, called class invariants. From a computational point of view, it is desirable that the associated minimal polynomials be small. We examine different approaches to measure the size of the polynomials. Based on experimental evidence, we compare two families of class invariants suggested in the literature with respect to these criteria. Our results lead to more efficient constructions of elliptic curves for cryptography or in the context of elliptic curve primality proving (ECPP).