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

3 Citations (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
Externally publishedYes
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
Country/TerritoryChina
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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