Causality in cryptography

Abstract

Pseudo-random numbers play an important role for the security of a message in a cryptographic system based on a non reutilizable key code. The coded sequences of length n appear at the decoder like one of the possible sets of values that can be taken by a sequence of independent and uniformly distributed random variables. In this paper the problem of randomness in Cryptography is discussed, in connection with the security of a cryptographic message. Randomness is firstly discussed as to its different meanings like, for instance, the ones connected with Knuth's definition or with de Finetti's definition or with Baldessari's definition. Secondly a new meaning of randomness is suggested in the cryptographic context: it is the one defined with respect to a set of statistical tests. This because every statistical test considers a particular aspect of randomness. For this reason some of the most important tests utilized in cryptography to prove the hypothesis of independence and uniform distribution are also dealt with. Furthermore a test based on an order statistic is suggested. The concept of uncertainty based on entropy and the analysis of the main characteristics of the most known pseudo-random numbers generators are also discussed.