Hash function requirements for Schnorr signatures
We provide two necessary conditions on hash functions for the Schnorr signature scheme to be secure, assuming compact group representations such as those which occur in elliptic curve groups. We also show, via an argument in the generic group model, that these conditions are sufficient. Our hash fun...
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doaj-fdf85a8449784c57a46380147126f5822021-09-06T19:39:36ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842009-05-0131698710.1515/JMC.2009.004Hash function requirements for Schnorr signaturesNeven Gregory0Smart Nigel P.1Warinschi Bogdan2IBM Research, Zurich Research Laboratory, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland, and Department of Electrical Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001 Heverlee, Belgium. Email: nev@zurich.ibm.comDepartment of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom. Email: nigel@cs.bris.ac.ukDepartment of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom. Email: bogdan@cs.bris.ac.ukWe provide two necessary conditions on hash functions for the Schnorr signature scheme to be secure, assuming compact group representations such as those which occur in elliptic curve groups. We also show, via an argument in the generic group model, that these conditions are sufficient. Our hash function security requirements are variants of the standard notions of preimage and second preimage resistance. One of them is in fact equivalent to the Nostradamus attack by Kelsey and Kohno (Eurocrypt, Lecture Notes in Computer Science 4004: 183–200, 2006), and, when considering keyed compression functions, both are closely related to the ePre and eSec notions by Rogaway and Shrimpton (FSE, Lecture Notes in Computer Science 3017: 371–388, 2004).https://doi.org/10.1515/JMC.2009.004schnorr signaturesgeneric group modelhash function |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Neven Gregory Smart Nigel P. Warinschi Bogdan |
spellingShingle |
Neven Gregory Smart Nigel P. Warinschi Bogdan Hash function requirements for Schnorr signatures Journal of Mathematical Cryptology schnorr signatures generic group model hash function |
author_facet |
Neven Gregory Smart Nigel P. Warinschi Bogdan |
author_sort |
Neven Gregory |
title |
Hash function requirements for Schnorr signatures |
title_short |
Hash function requirements for Schnorr signatures |
title_full |
Hash function requirements for Schnorr signatures |
title_fullStr |
Hash function requirements for Schnorr signatures |
title_full_unstemmed |
Hash function requirements for Schnorr signatures |
title_sort |
hash function requirements for schnorr signatures |
publisher |
De Gruyter |
series |
Journal of Mathematical Cryptology |
issn |
1862-2976 1862-2984 |
publishDate |
2009-05-01 |
description |
We provide two necessary conditions on hash functions for the Schnorr signature scheme to be secure, assuming compact group representations such as those which occur in elliptic curve groups. We also show, via an argument in the generic group model, that these conditions are sufficient. Our hash function security requirements are variants of the standard notions of preimage and second preimage resistance. One of them is in fact equivalent to the Nostradamus attack by Kelsey and Kohno (Eurocrypt, Lecture Notes in Computer Science 4004: 183–200, 2006), and, when considering keyed compression functions, both are closely related to the ePre and eSec notions by Rogaway and Shrimpton (FSE, Lecture Notes in Computer Science 3017: 371–388, 2004). |
topic |
schnorr signatures generic group model hash function |
url |
https://doi.org/10.1515/JMC.2009.004 |
work_keys_str_mv |
AT nevengregory hashfunctionrequirementsforschnorrsignatures AT smartnigelp hashfunctionrequirementsforschnorrsignatures AT warinschibogdan hashfunctionrequirementsforschnorrsignatures |
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1717770407679885312 |