Algorithms for Generation of a Common Key Using a Quantum Communication Channel

Subscribers $A$ and $B$, with the help of a quantum communication channel, obtain binary sequences $a$ and $b$ close in Hamming metric. The channel is eavesdropped by a subscriber $E$. Each of $A$ and $B$ must generate a common secret key $k$, which should be inaccessible to $E$. In this paper, on the basis of error-correcting codes, we propose an original algorithm for generating $k$, which requires only one round of exchange over a noiseless public communication channel. Using the physical assumptions about the possibilities of intercepting information in a quantum channel, we can prove rigorously that the eavesdropper $E$ will be able to obtain almost no information about the common key $k$ if a “good” error-correcting code is exploited with the algorithm proposed.