Properties of cryptosystem PGM

Spyros S. Magliveras, Nasir D. Memon

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

    Abstract

    A cryptographic system, called PGM, was invented in the late 1970’s by S. Magliveras. PGM is based on the prolific existence of certain kinds of factorization sets, called logarithmic signatures, for finite permutation groups. Logarithmic signatures were initially motivated by C. Sims’ bases and strong generators. Statistical properties of random number generators based on PGM have been investigated in [7], [8] and show PGM to be statistically robust. In this paper we present recent results on the algebraic properties of PGM. PGM is an endomorphic cryptosystem in which the message space is Z|G|, for a given finite permutation group G. We show that the set of PGM transformations TG is not closed under functional composition and hence not a group. This set is 2-transitive on Z|G| if the underlying group G is not hamiltonian. Moreover, if |G| ≠ 2a, then the set of transformations contains an odd permutation. An important consequence of the above results is that the group generated by the set of transformations is nearly always the full symmetric group.

    Original languageEnglish (US)
    Title of host publicationAdvances in Cryptology — CRYPTO 1989, Proceedings
    PublisherSpringer Verlag
    Pages447-460
    Number of pages14
    Volume435 LNCS
    ISBN (Print)9780387973173
    DOIs
    StatePublished - 1990
    EventConference on the Theory and Applications of Cryptology, CRYPTO 1989 - Santa Barbara, United States
    Duration: Aug 20 1989Aug 24 1989

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume435 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    OtherConference on the Theory and Applications of Cryptology, CRYPTO 1989
    CountryUnited States
    CitySanta Barbara
    Period8/20/898/24/89

    Fingerprint

    Hamiltonians
    Cryptosystem
    Factorization
    Cryptography
    Chemical analysis
    Permutation group
    Logarithmic
    Odd permutation
    Finite Group
    Signature
    Random number Generator
    Symmetric group
    Statistical property
    Generator
    Closed

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Magliveras, S. S., & Memon, N. D. (1990). Properties of cryptosystem PGM. In Advances in Cryptology — CRYPTO 1989, Proceedings (Vol. 435 LNCS, pp. 447-460). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 435 LNCS). Springer Verlag. https://doi.org/10.1007/0-387-34805-0_41

    Properties of cryptosystem PGM. / Magliveras, Spyros S.; Memon, Nasir D.

    Advances in Cryptology — CRYPTO 1989, Proceedings. Vol. 435 LNCS Springer Verlag, 1990. p. 447-460 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 435 LNCS).

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

    Magliveras, SS & Memon, ND 1990, Properties of cryptosystem PGM. in Advances in Cryptology — CRYPTO 1989, Proceedings. vol. 435 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 435 LNCS, Springer Verlag, pp. 447-460, Conference on the Theory and Applications of Cryptology, CRYPTO 1989, Santa Barbara, United States, 8/20/89. https://doi.org/10.1007/0-387-34805-0_41
    Magliveras SS, Memon ND. Properties of cryptosystem PGM. In Advances in Cryptology — CRYPTO 1989, Proceedings. Vol. 435 LNCS. Springer Verlag. 1990. p. 447-460. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/0-387-34805-0_41
    Magliveras, Spyros S. ; Memon, Nasir D. / Properties of cryptosystem PGM. Advances in Cryptology — CRYPTO 1989, Proceedings. Vol. 435 LNCS Springer Verlag, 1990. pp. 447-460 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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