A New Random Number Generator from Permutation Groups

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. 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 group M., in its 5-transitive representation on 24 points.