Classical key distribution is only secure if the adversary is bounded  
in some way, e.g., computationally. But if Alice and Bob use a  
quantum channel to communicate they can achieve unconditional  
security: eavesdropping cannot be performed on a quantum channel  
without modifying the states being transmitted, so Alice and Bob can  
detect the noise introduced, and take the necessary steps.

BB84 is one of the simplest and probably most well known QKD
protocols. It is a so-called ``prepare-and-measure'' protocol, which
doesn't need a complete quantum computer to be performed, but can be
realized with today's technology. We present a new prepare-and-measure
protocol for quantum key distribution using two-way communication,
achieving a tolerable error rate of $16.9\%$. We combine error
detection instead of correction as proposed by Gottesman and Lo
\cite{GL03} and classical privacy amplification, which has been proven
secure against a quantum adversary by Renner and K\"onig
\cite{KMR03,RK05}. We prove the security of our protocol using EPR
pairs and the result from \cite{KMR03,RK05}, and then derive our
prepare-and-measure version from the EPR one as in the Shor and
Preskill security proof of BB84 \cite{SP00}.

Our result is slightly worse than Gottesman and Lo's, which achieves
18.9\% but is much simpler and only makes use of error correcting
codes for a very small number of errors, which otherwise could require
exponential time, making practical realizations impossible.