Random permutations from logarithmic signatures

Spyros S. Magliveras, Nasir D. Memon

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    A cryptographle system, called PGM, was invented in the late 1970‘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’ bases and strong generators. A logarithmic signature α, for a given group G, induces a mapping â 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.

    Original languageEnglish (US)
    Title of host publicationComputing in the 1990's - 1st Great Lakes Computer Science Conference, Proceedings
    PublisherSpringer Verlag
    Pages199-205
    Number of pages7
    Volume507 LNCS
    ISBN (Print)9780387976280
    DOIs
    StatePublished - 1991
    Event1st Great Lakes Computer Science Conference, 1989 - Kalamazoo, United States
    Duration: Oct 18 1989Oct 20 1989

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume507 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other1st Great Lakes Computer Science Conference, 1989
    CountryUnited States
    CityKalamazoo
    Period10/18/8910/20/89

    Fingerprint

    Random Permutation
    Statistical tests
    Design of experiments
    Cryptography
    Seed
    Logarithmic
    Signature
    Cryptology
    Random Element
    Design of Experiments
    Permutation group
    Statistical test
    Symmetric group
    Encryption
    Permutation
    Finite Group
    Generator
    Simulation

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Magliveras, S. S., & Memon, N. D. (1991). Random permutations from logarithmic signatures. In Computing in the 1990's - 1st Great Lakes Computer Science Conference, Proceedings (Vol. 507 LNCS, pp. 199-205). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 507 LNCS). Springer Verlag. https://doi.org/10.1007/BFb0038493

    Random permutations from logarithmic signatures. / Magliveras, Spyros S.; Memon, Nasir D.

    Computing in the 1990's - 1st Great Lakes Computer Science Conference, Proceedings. Vol. 507 LNCS Springer Verlag, 1991. p. 199-205 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 507 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Magliveras, SS & Memon, ND 1991, Random permutations from logarithmic signatures. in Computing in the 1990's - 1st Great Lakes Computer Science Conference, Proceedings. vol. 507 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 507 LNCS, Springer Verlag, pp. 199-205, 1st Great Lakes Computer Science Conference, 1989, Kalamazoo, United States, 10/18/89. https://doi.org/10.1007/BFb0038493
    Magliveras SS, Memon ND. Random permutations from logarithmic signatures. In Computing in the 1990's - 1st Great Lakes Computer Science Conference, Proceedings. Vol. 507 LNCS. Springer Verlag. 1991. p. 199-205. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/BFb0038493
    Magliveras, Spyros S. ; Memon, Nasir D. / Random permutations from logarithmic signatures. Computing in the 1990's - 1st Great Lakes Computer Science Conference, Proceedings. Vol. 507 LNCS Springer Verlag, 1991. pp. 199-205 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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