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A new random number generator from permutation groups

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Abstract

We describe a new random number generator, RPGM, which is based on the cryptographic system PGM invented by Magliveras in 1976 and subsequently studied by Magliveras and Surkan [10]. PGM relies on a certain method of machine representation for permutation groups. This method allows for encryption and decryption algorithms based on a space-efficient data structure which is called a logarithmic signature for the group. The efficacy of RPGM is studied by means of an extensive analysis of generated data of 100,000 numbers using the Mathieu groupM 24 in its 5-transitive representation on 24 points.

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Descriviamo un nuovo generatore di numeri a caso (RPGM), basato sul sistema crittografico PGM inventato da Magliveras nel 1976 e successivamente studiato da Magliveras e Surkan [10]. PGM si fonda su un certo metodo di rappresentazione in un computer di un gruppo di permutazioni. Questo metodo dà luogo ad algoritmi di incrittazione e decrittazione basati su una struttura di dati efficienti, chiamata segnatura logaritmica del gruppo. L'efficacia di RPGM è studiata ricorrendo ad un'ampia analisi dei dati generati di 100.000 numeri, ottenuti usando il gruppo di Mathieu M24 nella sua rappresentazione 5-transitiva di grado 24.

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(Conferenza tenuta il 10 dicembre 1984) dal Prof. Magliveras

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Magliveras, S.S., Oberg, B.A. & Surkan, A.J. A new random number generator from permutation groups. Seminario Mat. e. Fis. di Milano 54, 203–223 (1985). https://doi.org/10.1007/BF02924858

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