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The intractability of the traditional discrete logarithm problem (DLP) forms the basis for the design of numerous cryptographic primitives. In \([2]\) M. Sramka et al. generalize the DLP to arbitrary finite groups. One of the reasons mentioned for this generalization is P. Shor’s quantum algorithm \([4]\) which solves efficiently the traditional DLP. The DLP for a non-abelian group is based on a particular representation of the group and a choice of generators. In this paper, we show that care must be taken to ensure that the representation and generators indeed yield an intractable DLP. We show that in \(\text{PSL}(2,p) = \langle \alpha, \beta \rangle\) the generalized discrete logarithm problem with respect to \((\alpha,\beta)\) is easy to solve for a specific representation and choice of generators \(\alpha\) and \(\beta\). As a consequence, such representation of \(\text{PSL}(2,p)\) and generators should not be used to design cryptographic primitives.