On the Success Probability of Solving Unique SVP via BKZ

Eamonn Postlethwaite, Fernando Virdia

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


As lattice-based key encapsulation, digital signature, and fully homomorphic encryption schemes near standardisation, ever more focus is being directed to the precise estimation of the security of these schemes. The primal attack reduces key recovery against such schemes to instances of the unique Shortest Vector Problem (uSVP). Dachman-Soled et al. (Crypto 2020) recently proposed a new approach for fine-grained estimation of the cost of the primal attack when using Progressive BKZ for lattice reduction. In this paper we review and extend their technique to BKZ 2.0 and provide extensive experimental evidence of its accuracy. Using this technique we also explain results from previous primal attack experiments by Albrecht et al. (Asiacrypt 2017) where attacks succeeded with smaller than expected block sizes. Finally, we use our simulators to reestimate the cost of attacking the three lattice KEM finalists of the NIST Post Quantum Standardisation Process.
Original languageEnglish
Title of host publicationPublic-Key Cryptography – PKC 2021
Subtitle of host publication24th IACR International Conference on Practice and Theory of Public Key CryptographyVirtual Event, May 10–13, 2021 Proceedings, Part I
Number of pages31
ISBN (Electronic)978-3-030-75245-3
ISBN (Print)978-3-030-75244-6
Publication statusPublished - 1 May 2021


  • Cryptanalysis
  • Lattice-based cryptography
  • Lattice reduction

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