On the one-way algebraic homomorphism

Eikoh Chida, Takao Nishizeki, Motoji Ohmori, Hiroki Shizuya

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    In this paper we discuss the relation between a one-way group homomorphism and a one-way ring homomorphism. Let U, V be finite abelian groups with #U = n. We show that if there exists a one-way group homomorphism f: U → V, then there exists a one-way ring homomorphism F: Zn ⊕ U → Zn ⊕ Im f. We also give examples of such ring homomorphisms which are one-way under a standard cryptographic assumption. This implies that there is an affirmative solution to an extended version of the open question raised by Feigenbaum and Merrit: Is there an encryption function f such that both f(x + y) and f(x · y) can be efficiently computed from f(x) and f(y) ? A multiple signature scheme is also given as an application of one-way ring homomorphisms.

    Original languageEnglish
    Pages (from-to)54-60
    Number of pages7
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    VolumeE79-A
    Issue number1
    Publication statusPublished - 1996 Jan 1

    Keywords

    • Cryptography
    • Homomorphism
    • One-way function

    ASJC Scopus subject areas

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

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