On the Strength of the Strong RSA Assumption

Shintaro Itagaki, Masahiro Mambo, Hiroki Shizuya

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    The strong RSA assumption is an assumption that the following problem is hard to solve: Given an RSA modulus and a ciphertext, find a pair of plaintext and exponent corresponding to them. It differs from the standard RSA assumption in a sense that in the strong version, no exponent is given as an input. The strong RSA assumption is considered to be stronger than the RSA assumption, but their exact relationship is not known. We investigate the strength of the strong RSA assumption and show that the strong RSA assumption restricted to low exponents is equivalent to the assumption that RSA problem is intractable for any low exponent. We also show that in terms of algebraic computation, the strong RSA assumption is properly stronger than the RSA assumption if there exists an RSA modulus n such that gcd(φ(n), 3) = 1 and RSA problem is intractable.

    Original languageEnglish
    Pages (from-to)1164-1170
    Number of pages7
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    Issue number5
    Publication statusPublished - 2003 May


    • Algebraic computation
    • RSA
    • Straight-line program
    • Strong RSA assumption

    ASJC Scopus subject areas

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


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