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In practical quantum cryptography, the source sometimes produces multi-photonpulses, thus enabling the eavesdropper Eve to perform the powerfulphoton-number-splitting (PNS) attack. Recently, it was shown by Curty andLutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not alwaysthe optimal attack when two photons are present: if errors are present in thecorrelations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Evegains a larger amount of information using another attack based on a 2->3cloning machine. In this work, we extend this analysis to all distancesAlice-Bob. We identify a new incoherent 2->3 cloning attack which performsbetter than those described before. Using it, we confirm that, in the presenceof errors, Eve's better strategy uses 2->3 cloning attacks instead of the PNS.However, this improvement is very small for the implementations of theBennett-Brassard 1984 (BB84) protocol. Thus, the existence of these new attacksis conceptually interesting but basically does not change the value of thesecurity parameters of BB84. The main results are valid both for Poissonian andsub-Poissonian sources.Comment: 11 pages, 5 figures; "intuitive" formula (31) adde

Photon-number-splitting versus cloning attacks in practical implementations of the Bennett-Brassard 1984 protocol for quantum cryptography