@inproceedings{729508698fbe40ad8ba550653a914466,

title = "Random permutations from logarithmic signatures",

abstract = "A cryptographle system, called PGM, was invented in the late 1970{\textquoteleft}s by S. Magiiveras. PGM iS based on the prolific existence of certain kinds of factorizatlon sets, called logarithmic signatures, for finite permutation groups. Logarithmic signatures were initially motivated by C. Sims{\textquoteright} bases and strong generators. A logarithmic signature α, for a given group G, induces a mapping {\^a} from ZG to G. Hence it would be natural to use logarithmic signatures for generating random elements in a group. In this paper we focus on generating random permutations in the symmetric group Sn. Random permutations find applications in design of experiments simulation cryptology, voice-encryption etc. Given a logarithmic signature α for sn and a seed s0, we could efficiently compute the following sequence : ᾶ(s0), ᾶ(s0 + 1),…,ᾶ(s0 + r - 1) of r permutations. We claim that this sequence behaves llke a sequence of random permutations. We undertake statistical tests to substantiate our claim.",

author = "Magliveras, {Spyros S.} and Memon, {Nasir D.}",

year = "1991",

doi = "10.1007/BFb0038493",

language = "English (US)",

isbn = "9780387976280",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "199--205",

editor = "Sherwani, {Naveed A.} and {de Doncker}, Elise and Kapenga, {John A.}",

booktitle = "Computing in the 1990's - 1st Great Lakes Computer Science Conference, Proceedings",

note = "1st Great Lakes Computer Science Conference, 1989 ; Conference date: 18-10-1989 Through 20-10-1989",

}