In 1986, Fiat and Shamir suggested a general method for transforming secure 3-round public-coin identification schemes into digital signature schemes. The significant contribution of this method is a means for designing efficient digital signatures, while hopefully achieving security against chosen message attacks. All other known constructions which achieve such security are substantially more inefficient and complicated in design.

In 1996, Pointcheval and Stern proved that the signature schemes
obtained by the Fiat-Shamir transformation are secure in the so called `Random Oracle Model'. The question is: does the proof of the security of the Fiat-Shamir transformation in the Random Oracle Model, imply
that the transformation yields secure signature schemes in the ``real-world''?

In this paper we answer this question negatively. We show that there exist secure 3-round public-coin identification schemes for which the Fiat-Shamir methodology produces {\bf insecure} digital signature schemes for {\bf any} implementation of the `Random Oracle Model' in the `real-world' by a function ensemble.