A structural comparison of the computational difficulty of breaking discrete log cryptosystems

Kouichi Sakurai, Hiroki Shizuya

    Research output: Contribution to journalArticle

    18 Citations (Scopus)

    Abstract

    The complexity of breaking cryptosystems of which security is based on the discrete logarithm problem is explored. The cryptosystems mainly discussed are the Diffie-Hellman key exchange scheme (DH), the Bellare-Micali noninteractive oblivious transfer scheme (EM), the ElGamal public-key cryptosystem (EG), the Okamoto conference-key sharing scheme (CONF), and the Shamir 3-pass key-transmission scheme (3PASS). The obtained relation among these cryptosystems is that 3 PASS < CONF < EG =£" BM s DH, where <JJdenotes the polynomial-time functionally many-to-one reducibility, i.e., a function version of the <£ -reducibility. We further give some condition in which these algorithms have equivalent difficulty. One of such conditions suggest another advantage of the discrete logarithm associated with ordinary elliptic curves.

    Original languageEnglish
    Pages (from-to)29-43
    Number of pages15
    JournalJournal of Cryptology
    Volume11
    Issue number1
    DOIs
    Publication statusPublished - 1998 Jan 1

    Keywords

    • Computational number theory
    • Cryptosystem
    • Discrete logarithm
    • Elliptic curves
    • Key exchange
    • Public-key cryptography
    • Randomness
    • Security

    ASJC Scopus subject areas

    • Software
    • Computer Science Applications
    • Applied Mathematics

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