Recovering the Tight Security Proof of SPHINCS+

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

4 Citations (Scopus)

Abstract

In 2020, Kudinov, Kiktenko, and Fedorov pointed out a flaw in the tight security proof of the SPHINCS+ construction. This work gives a new tight security proof for SPHINCS+. The flaw can be traced back to the security proof for the Winternitz one-time signature scheme (WOTS) used within SPHINCS+. In this work, we give a stand-alone description of the WOTS variant used in SPHINCS+ that we call WOTS-TW. We provide a security proof for WOTS-TW and multi-instance WOTS-TW against non-adaptive chosen message attacks where the adversary only learns the public key after it made its signature query. Afterwards, we show that this is sufficient to give a tight security proof for SPHINCS+. We recover almost the same bound for the security of SPHINCS+, with only a factor w loss compared to the previously claimed bound, where w is the Winternitz parameter that is commonly set to 16. On a more technical level, we introduce new lower bounds on the quantum query complexity for generic attacks against properties of cryptographic hash functions and analyse the constructions of tweakable hash functions used in SPHINCS+ with regard to further security properties.
Original languageEnglish
Title of host publicationAdvances in Cryptology – ASIACRYPT 2022
Subtitle of host publication28th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, December 5–9, 2022, Proceedings, Part IV
EditorsShweta Agrawal, Dongdai Lin
Place of PublicationCham
PublisherSpringer Nature
Chapter1
Pages3-33
Number of pages31
ISBN (Electronic)978-3-031-22972-5
ISBN (Print)978-3-031-22971-8
DOIs
Publication statusPublished - Jan 2023
Event28th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2022 - Taipei, Taiwan
Duration: 5 Dec 20229 Dec 2022

Publication series

NameLecture Notes in Computer Science (LNCS)
PublisherSpringer
Volume13794
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference28th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2022
Country/TerritoryTaiwan
CityTaipei
Period5/12/229/12/22

Funding

This work was funded by an NWO VIDI grant (Project No. VI.Vidi.193.066). Part of this work was done while M.K. was still affiliated with the Russian Quantum Center, QApp. Date: November 19, 2022.

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk OnderzoekVI.Vidi.193.066

    Keywords

    • hash functions
    • hash-based signatures
    • Post-quantum cryptography
    • PRF
    • SPHINCS
    • undetectability
    • W-OTS
    • WOTS-TW

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