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In this paper, a new algorithm to solve the discrete logarithm problem ispresented which is similar to the usual baby-step giant-step algorithm. Ouralgorithm exploits the order of the discrete logarithm in the multiplicativegroup of a finite field. Using randomization with parallelized collisionsearch, our algorithm indicates some weakness in NIST curves over prime fieldswhich are considered to be the most conservative and safest curves among allNIST curves.

A Probabilistic Baby-Step Giant-Step Algorithm