  Consider the classical ElGamal digital signature scheme based on the modular
relation $\alpha^m\equiv y^r\, r^s\ [p]$. In this work, we prove that if we can
compute a natural integer $i$ such that $\alpha^i\ mod\ p$ is smooth and
divides $p-1$, then it is possible to sign any given document without knowing
the secret key. Therefore we extend and reinforce Bleichenbacher's attack
presented at Eurocrypt'96.

Cryptography and Security