Bose–Einstein Statistics, Random Block Ciphers, and the One-Time Notepad in Quantum Cryptography

Abstract

Many problems in statistical physics, as well as in classical and quantum information theory including quantum cryptography, have much in common, since they are reduced to the processing of exponentially large sets. It has been shown that there is a deep relationship between the distribution of bosons over energy levels and the number of collisions of a random block cipher. It has been shown that the number of collisions is equal to the number of empty levels in the distribution of bosons over levels. The number of collisions is of practical interest, since it determines the complexity of search for keys transmitted through a quantum network.