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BKZ 2.0: Better lattice security estimates. (English) Zbl 1227.94037
Lee, Dong Hoon (ed.) et al., Advances in cryptology – ASIACRYPT 2011. 17th international conference on the theory and application of cryptology and information security, Seoul, South Korea, December 4–8, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-25384-3/pbk). Lecture Notes in Computer Science 7073, 1-20 (2011).
Summary: The best lattice reduction algorithm known in practice for high dimension is Schnorr-Euchner’s BKZ: all security estimates of lattice cryptosystems are based on NTL’s old implementation of BKZ. However, recent progress on lattice enumeration suggests that BKZ and its NTL implementation are no longer optimal, but the precise impact on security estimates was unclear. We assess this impact thanks to extensive experiments with BKZ 2.0, the first state-of-the-art implementation of BKZ incorporating recent improvements, such as Gama-Nguyen-Regev pruning. We propose an efficient simulation algorithm to model the behaviour of BKZ in high dimension with high blocksize $$\geq 50$$, which can predict approximately both the output quality and the running time, thereby revising lattice security estimates. For instance, our simulation suggests that the smallest NTRUSign parameter set, which was claimed to provide at least 93-bit security against key-recovery lattice attacks, actually offers at most 65-bit security.
For the entire collection see [Zbl 1227.94002].

MSC:
 94A60 Cryptography
NTRU; BKZ
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