Data Analysis and Classification pp 13-21 | Cite as

# Statistical Methods for Cryptography

Conference paper

First Online:

## 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.

## Keywords

Prime Number Composite Number Modular Arithmetic Stock Holding Deterministic Test
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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