In this paper, we present an analysis of the CCM mode of operations and of a slight variant. CCM is a simple and efficient encryption scheme which combines a CBC-MAC authentication scheme with the counter mode of encryption. It is used in several standards. Despite some criticisms (mainly this mode is not online, and requires non-repeating nonces), it has nice features that make it worth to study. One important fact is that, while the privacy of CCM is provably garanteed up to the birthday paradox, the authenticity of CCM seems to be garanteed beyond that. There is a proof by Jonsson up to the birthday paradox bound, but going beyond it seems to be out of reach with current techniques. Nevertheless, by using pseudo-random functions and not permutations in the counter mode and an authentication key different from the privacy key, we prove security beyond the birthday paradox. We also wonder if the main criticisms against CCM can be avoided: what is the security of the CCM mode when the...