Statistical Methods for Cryptography

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,..., m - 1) with probability 1/m and let the second s.v. Y assume the value i with probability (pi : Sigma(m-1)(i=1)Pi = 1, pi >= 0). If the s.v. Z = X + Y (mod in) is uniformly distributed and m is a prime number, at least one of the two s. v. X and Y is uniformly distributed.