A Rapid Procedure of Creating Elliptic Curves Applying to Cryptography
Wang Xiang-hui · Journal of North University of China · 2006
When complex multiplication(CM) is used to create elliptic curves over F_p,the ring of complex quadratic field is only used.The authors propose to use sub-ring of complex quadratic field to create elliptic curves over F_p.Since the Pell equation u~2+dv~2=4p exists root over Z/2p,Z/3p,more elliptic curves can then be created at the same range of discriminant.With the computation of Mathematica programming,the number of created curves increases significantly.