  We present security proofs for a protocol for Quantum Key Distribution (QKD)
based on encoding in finite high-dimensional Hilbert spaces. This protocol is
an extension of Bennett's and Brassard's basic protocol from two bases, two
state encoding to a multi bases, multi state encoding. We analyze the mutual
information between the legitimate parties and the eavesdropper, and the error
rate, as function of the dimension of the Hilbert space, while considering
optimal incoherent and coherent eavesdropping attacks. We obtain the upper
limit for the legitimate party error rate to ensure unconditional security when
the eavesdropper uses incoherent and coherent eavesdropping strategies. We have
also consider realistic noise caused by detector's noise.
