Impossibility of the provable security of the schnorr signature from the one-more DL assumption in the non-programmable random oracle model

Masayuki Fukumitsu, Shingo Hasegawa

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    1 Citation (Scopus)

    Abstract

    The security of the Schnorr signature was widely discussed. In the random oracle model (ROM), it is provable from the DL assumption, whereas there is a negative circumstantial evidence in the standard model. Fleischhacker, Jager and Schröder showed that the tight security of the Schnorr signature is unprovable from a strong cryptographic assumption, such as the One-more DL (OM-DL) assumption and the computational and decisional Diffie-Hellman assumption, in the ROM via a generic reduction as long as the underlying cryptographic assumption holds. However, it remains open whether or not the impossibility of the provable security of the Schnorr signature from a strong assumption via a non-tight and reasonable reduction. In this paper, we show that the security of the Schnorr signature is unprovable from the OM-DL assumption in the non-programmable ROM as long as the OM-DL assumption holds. Our impossibility result is proven via a non-tight and non-restricted Turing reduction.

    Original languageEnglish
    Title of host publicationProvable Security - 11th International Conference, ProvSec 2017, Proceedings
    EditorsTatsuaki Okamoto, Yong Yu, Man Ho Au, Yannan Li
    PublisherSpringer Verlag
    Pages201-218
    Number of pages18
    ISBN (Print)9783319686363
    DOIs
    Publication statusPublished - 2017
    Event11th International Conference on Provable Security, ProvSec 2017 - Xi'an, China
    Duration: 2017 Oct 232017 Oct 25

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume10592 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other11th International Conference on Provable Security, ProvSec 2017
    CountryChina
    CityXi'an
    Period17/10/2317/10/25

    Keywords

    • Impossibility result
    • Non-programmable random oracle model
    • One-more DL assumption
    • Schnorr signature

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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