Abstract
We consider a variant of the Complex Multiplication (CM) method for constructing elliptic curves (ECs) of prime order with additional security properties. Our variant uses Weber polynomials whose discriminant D is congruent to 3 (mod 8), and is based on a new transformation for converting roots of Weber polynomials to their Hilbert counterparts. We also present a new theoretical estimate of the bit precision required for the construction of the Weber polynomials for these values of D. We conduct a comparative experimental study investigating the time and bit precision of using Weber polynomials against the (typical) use of Hilbert polynomials. We further investigate the time efficiency of the new CM variant under four different implementations of a crucial step of the variant and demonstrate the superiority of two of them.
This work was partially supported by the IST Programme of EU under contracts no. IST-1999-14186 (ALCOM-FT) and no. IST-1999-12554 (ASPIS), and by the Human Potential Programme of EU under contract no. HPRN-CT-1999-00104 (AMORE).
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Konstantinou, E., Stamatiou, Y.C., Zaroliagis, C. (2003). On the Construction of Prime Order Elliptic Curves. In: Johansson, T., Maitra, S. (eds) Progress in Cryptology - INDOCRYPT 2003. INDOCRYPT 2003. Lecture Notes in Computer Science, vol 2904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24582-7_23
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DOI: https://doi.org/10.1007/978-3-540-24582-7_23
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