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Attempting to reach a minimal number of moves in cryptographic protocols is a quite classical issue. Besides the theoretical interests, minimizing the number of moves can clearly facilitate practical implementations in environments with communication constraints. In this paper, we offer a solution to this problem in the context of undeniable signatures with interactive verification protocols by proposing a way to achieve these protocols in 2 moves. To this goal, we review a scheme we proposed at Asiacrypt 2004 whose property is the full scalability of the signature length against security. We slightly modify (to make it non-transferable) a 2-move version of this scheme which was mentioned in the original article without a proof of security. In the random oracle model, we prove the security of the modified version against an active adversary and precisely assess the security in terms of the signature length. To the best of our knowledge, this scheme is the first 2-move undeniable signature scheme with a security proof.