  Quantum key distribution based on encoding in three dimensional systems in
the presence of several eavesdroppers is proposed. This extends the BB84
protocol in the presence of many eavesdroppers where two-level quantum systems
(qubits) are replaced by three-level systems (qutrits). We discuss the
scenarios involving two, three and four complementary bases. We derive the
explicit form of Alice and Bob mutual information and the information gained by
each eavesdropper. In particular, we show that, in the presence of only one
eavesdropper, the protocol involving four bases is safer than the other ones.
However, for two eavesdroppers, the security is strongly dependent on the
attack probabilities. The effect of a large number of eavesdroppers is also
investigated.
