Abstract
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 IFp 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.
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© 2000 Springer-Verlag Berlin Heidelberg
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Buchmann, J., Baier, H. (2000). Efficient Construction of Cryptographically Strong Elliptic Curves. In: Roy, B., Okamoto, E. (eds) Progress in Cryptology —INDOCRYPT 2000. INDOCRYPT 2000. Lecture Notes in Computer Science, vol 1977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44495-5_17
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DOI: https://doi.org/10.1007/3-540-44495-5_17
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