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INDOCRYPT
2003
Springer

On the Construction of Prime Order Elliptic Curves

13 years 8 months ago
On the Construction of Prime Order Elliptic Curves
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.
Elisavet Konstantinou, Yannis C. Stamatiou, Christ
Added 07 Jul 2010
Updated 07 Jul 2010
Type Conference
Year 2003
Where INDOCRYPT
Authors Elisavet Konstantinou, Yannis C. Stamatiou, Christos D. Zaroliagis
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