Algebraic properties of cryptosystem PGM

Spyros S. Magliveras, Nasir D. Memon

    Research output: Contribution to journalArticle

    Abstract

    In the late 1970s Magliveras invented a private-key cryptographic system called Permutation Group Mappings (PGM). PGM is based on the prolific existence of certain kinds of factorization sets, called logarithmic signatures, for finite permutation groups. PGM is an endomorphic system with message space ℤ|G| for a given finite permutation group G. In this paper we prove several algebraic properties of PGM. We show that the set of PGM transformations ℐ G 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 and not abelian. Moreover, if the order of G is not a power of 2, then the set of transformations contains an odd permutation. An important consequence of these results is that the group generated by the set of transformations is nearly always the symmetric group ℒ|G|. Thus, allowing multiple encryption, any permutation of the message space is attainable. This property is one of the strongest security conditions that can be offered by a private-key encryption system.

    Original languageEnglish (US)
    Pages (from-to)167-183
    Number of pages17
    JournalJournal of Cryptology
    Volume5
    Issue number3
    DOIs
    StatePublished - Oct 1992

    Fingerprint

    Permutation group
    Cryptosystem
    Cryptography
    Encryption
    Hamiltonians
    Odd permutation
    Finite Group
    Factorization
    G-space
    Symmetric group
    Logarithmic
    Permutation
    Signature
    Chemical analysis
    Closed

    Keywords

    • Cryptography
    • Cryptology
    • Finite permutation group
    • Logarithmic signatures
    • Multiple encryption
    • Permutation group mappings (PGM)

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Applied Mathematics
    • Electrical and Electronic Engineering
    • Computational Theory and Mathematics

    Cite this

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

    In: Journal of Cryptology, Vol. 5, No. 3, 10.1992, p. 167-183.

    Research output: Contribution to journalArticle

    Magliveras, SS & Memon, ND 1992, 'Algebraic properties of cryptosystem PGM', Journal of Cryptology, vol. 5, no. 3, pp. 167-183. https://doi.org/10.1007/BF02451113
    Magliveras, Spyros S. ; Memon, Nasir D. / Algebraic properties of cryptosystem PGM. In: Journal of Cryptology. 1992 ; Vol. 5, No. 3. pp. 167-183.
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