Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A course in computational algebraic number theory
A course in computational algebraic number theory
A new polynomial factorization algorithm and its implementation
Journal of Symbolic Computation
On the singular values of Weber modular functions
Mathematics of Computation
Elliptic curves in cryptography
Elliptic curves in cryptography
Constructing elliptic curves with given group order over large finite fields
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Elliptic Curves of Prime Order over Optimal Extension Fields for Use in Cryptography
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
A Software Library for Elliptic Curve Cryptography
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Efficient Computation of Singular Moduli with Application in Cryptography
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
On the Efficient Generation of Elliptic Curves over Prime Fields
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Elliptic curves cryptosystems for ecommerce applications
MCBE'10/MCBC'10 Proceedings of the 11th WSEAS international conference on mathematics and computers in business and economics and 11th WSEAS international conference on Biology and chemistry
Faster pairings using an elliptic curve with an efficient endomorphism
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
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We present a very efficient algorithm which given a negative integer Δ, Δ = 1 mod 8, Δ not divisible by 3, finds a prime number p and a cryptographically strong elliptic curve E over the prime field Fp whose endomorphism ring is the quadratic order O of discriminant Δ. Our algorithm bases on a variant of the complex multiplication method using Weber functions. We depict our very efficient method to find suitable primes for this method. Furthermore, we show that our algorithm is feasible in reasonable time even for orders O whose class number is in the range 200 up to 1000.