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.

Caranti, A., & DALLA VOLTA, F. (2006). The round functions of cryptosystem PGM generate the symmetric group. DESIGNS, CODES AND CRYPTOGRAPHY, 38(1), 147-155 [10.1007/s10623-005-5667-z].

The round functions of cryptosystem PGM generate the symmetric group

DALLA VOLTA, FRANCESCA
2006-01

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.
Articolo in rivista - Articolo scientifico
Permutation group mappings (PGM); exact-transversal logarithmic signatures; transversal group bases; primitive permutation groups; symmetric group
English
147
155
Caranti, A., & DALLA VOLTA, F. (2006). The round functions of cryptosystem PGM generate the symmetric group. DESIGNS, CODES AND CRYPTOGRAPHY, 38(1), 147-155 [10.1007/s10623-005-5667-z].
Caranti, A; DALLA VOLTA, F
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/2778
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