On the Success Probability of Solving Unique SVP via BKZ

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.