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

Masayuki Fukumitsu, Shingo Hasegawa

Research output: Contribution to journalArticlepeer-review

Abstract

The Schnorr signature is one of the representative signature schemes and its security was widely discussed. In the random oracle model (ROM), it is provable from the DL assumption, whereas there is 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 Turing reduction.

Original languageEnglish
Pages (from-to)1163-1174
Number of pages12
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE104A
Issue number9
DOIs
Publication statusPublished - 2021

Keywords

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

ASJC Scopus subject areas

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

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