On the pseudo-freeness and the CDH assumption

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    7 Citations (Scopus)


    The notion of pseudo-free group was first introduced by Hohenberger (Master's thesis, EECS Dept., MIT, 2003). Rivest (TCC 2004. LNCS 2951, 505-521, 2004) formalized it and showed that several standard cryptographic assumptions hold on pseudo-free groups, such as the RSA assumption, the strong RSA assumption and the discrete logarithm assumption. Rivest (TCC 2004. LNCS 2951, 505-521, 2004) also proposed some variations of pseudo-free group, and those were formalized by Hirano and Tanaka (Research Reports, Series C: Computer Science, C-239, Tokyo Institute of Technology, 2007). In this paper, we study the relationships among such variations of pseudo-free group. We show that the pseudo-freeness implies the weak pseudo-freeness, and that the pseudo- freeness is equivalent to the pseudo-freeness with generalized exponential expressions. We also show that the computational Diffie-Hellman assumption holds on pseudo-free groups in a slightly varied form.

    Original languageEnglish
    Pages (from-to)347-355
    Number of pages9
    JournalInternational Journal of Information Security
    Issue number5
    Publication statusPublished - 2009 Jun 23


    • CDH assumption
    • Pseudo-free group
    • Pseudo-free group with generalized exponential expressions
    • Weak pseudo-free group

    ASJC Scopus subject areas

    • Software
    • Information Systems
    • Safety, Risk, Reliability and Quality
    • Computer Networks and Communications


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