A Note on the Relationships among Certified Discrete Log Cryptosystems

Eikoh Chida, Toshiya Itoh, Hiroki Shizuya

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)


    The certified discrete logarithm problem modulo p prime is a discrete logarithm problem under the conditions that the complete factorization of p-1 is given and by which the base g is certified to be a primitive root mod p. For the cryptosystems based on the intractability of certified discrete logarithm problem, Sakurai-Shizuya showed that breaking the Diffie-Hellman key exchange scheme reduces to breaking the Shamir 3-pass key transmission scheme with respect to the expected polynomial-time Turing reducibility. In this paper, we show that we can remove randomness from the reduction above, and replace the reducibility with the polynomial-time many-one. Since the converse reduction is known to hold with respect to the polynomial-time many-one reducibility, our result gives a stronger evidence for that the two schemes are completely equivalent as certified discrete log cryptosystems.

    Original languageEnglish
    Pages (from-to)1198-1202
    Number of pages5
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    Issue number5
    Publication statusPublished - 2003 May


    • Certified discrete logarithm problem
    • Deterministic reducibility
    • Order
    • Primitive root
    • Probabilistic reducibility

    ASJC Scopus subject areas

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


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