Statistical Methods for Cryptography

Abstract

In this note, after recalling certain results regarding prime numbers, we will present the following theorem of interest to cryptography: Let two discrete s.v.’s (statistical variable) X, Y assume the value: 0, 1, 2, …, m − 1. Let X be uniformly distributed, that is, it assumes the value $i(i = 0,1,\ldots ,m - 1)$ with probability 1 ∕ m and let the second s.v. Y assume the value i with probability $({p}_{i}\,:\,\sum\limits_{i=1}^{m-1}{p}_{i} =\ 1,{p}_{i}\,\geq \,0)$. If the s.v. $Z = X + Y$ (mod m) is uniformly distributed and m is a prime number, at least one of the two s. v. X and Y is uniformly distributed.