Error correcting codes, block designs, perfect secrecy and finite fields (Q850774)

This paper addresses a solution to the necessity of key exchange prior to a cryptographic communication between two parties. An algorithm to establish a common key through public discussion under the assumption that the communicants posses keys of a common length \(N\) which are not necessarily equal but whose mutual information is non-zero is analyzed. The algorithm in question was originally introduced by \textit{C. H. Bennett, F. Bessette, G. Brassard, L. Salvail} and \textit{J. Smolin} [Experimental quantum cryptography. J. Cryptol. 5, No. 1, 3--28 (1992; Zbl 1114.94005)] a preliminary version was given in [Advances in Cryptology-- Eurocrypt '90 Proceedings, Berlin-Heidelberg-New York: Springer, Lect. Notes Comput. Sci. 473, 253--265 (1991)]. In the paper under review, it is shown that under modest assumptions the algorithm does indeed converge to a non-empty key. In fact, the paper includes a method to calculate a good choice of \(N\) in order to efficiently arrive at a common key of a prefixed desired length \(n\).