The Round Functions of Cryptosystem PGM Generate the Symmetric Group

Authors:
A. Caranti;F. Dalla. Volta
Affiliations:
Dipartimento di Matematica, Università degli Studi di Trento, Povo (Trento), Italy I-38050;Dipartimento di Matematica Applicazioni, Edificio U5, Università degli Studi di Milano--Bicocca, Milano, Italy 20125
Venue:
Designs, Codes and Cryptography
Year:
2006

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Abstract

S. S. Magliveras et al. have described symmetric and public key cryptosystems based on logarithmic signatures (also known as group bases) for finite permutation groups.In this paper we show that if G is a nontrivial finite group which is not cyclic of order a prime, or the square of a prime, then the round (or encryption) functions of these systems, that are the permutations of G induced by the exact-transversal logarithmic signatures (also known as transversal group bases), generate the full symmetric group on G.This answers a question of S. S. Magliveras, D. R. Stinson and Tran van Trung.