Statistical Methods for Cryptography

  • Alfredo RizziEmail author
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


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.


Prime Number Composite Number Modular Arithmetic Stock Holding Deterministic Test 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Dipartimento di Statistica, Probabilità e Statistiche ApplicateUniversità di Roma “La Sapienza”RomaItaly

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