  In this paper, a new algorithm to solve the discrete logarithm problem is
presented which is similar to the usual baby-step giant-step algorithm. Our
algorithm exploits the order of the discrete logarithm in the multiplicative
group of a finite field. Using randomization with parallelized collision
search, our algorithm indicates some weakness in NIST curves over prime fields
which are considered to be the most conservative and safest curves among all
NIST curves.
