Complexity analysis of the cryptographic primitive problems through square-root exponent

Chisato Konoma, Masahiro Mambo, Hiroki Shizuya

    Research output: Contribution to journalReview articlepeer-review

    9 Citations (Scopus)


    To examine the computational complexity of cryptographic primitives such as the discrete logarithm problem, the factoring problem and the Diffle-Hellman problem, we define a new problem called square-root exponent, which is a problem to compute a value whose discrete logarithm is a square root of the discrete logarithm of a given value. We analyze reduction between the discrete logarithm problem modulo a prime and the factoring problem through the square-root exponent. We also examine reductions among the computational version and the decisional version of the square-root exponent and the Diffie-Hellman problem and show that the gap between the computational square-root exponent and the decisional square-root exponent partially overlaps with the gap between the computational Diffie-Hellman and the decisional Diffie-Hellman under some condition.

    Original languageEnglish
    Pages (from-to)1083-1091
    Number of pages9
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    Issue number5
    Publication statusPublished - 2004 May


    • Computing problem
    • Decision problem
    • Diffie-Hellman problem
    • Discrete logarithm problem
    • Factoring problem
    • Square-root exponent

    ASJC Scopus subject areas

    • Signal Processing
    • Computer Graphics and Computer-Aided Design
    • Electrical and Electronic Engineering
    • Applied Mathematics


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