ABSTRACT
Elliptic Curve cryptosystems were independently proposed by Vic-
tor Miller of IBM in 1985 [209] and Neal Koblitz in 1987 [167].
Elliptic Curve cryptosystems are believed to be as secure as RSA
and the Discrete Logarithm problem in Z∗p . Moreover, as will be
discussed in Section 9.5, because the Index Calculus Method has
not been successfully applied to the Discrete Logarithm problem
in the Group of an Elliptic Curve, such cryptosystems require sig-
nificantly smaller operands to achieve equivalent security versus
cryptosystems such as RSA and the Discrete Logarithm problem
in Z∗p .
