International Association for Cryptologic Research

International Association
for Cryptologic Research


Fast Practical Lattice Reduction through Iterated Compression

Keegan Ryan , UC San Diego
Nadia Heninger , UC San Diego
DOI: 10.1007/978-3-031-38548-3_1 (login may be required)
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Presentation: Slides
Conference: CRYPTO 2023
Award: Best Paper Award
Abstract: We introduce a new lattice basis reduction algorithm with approximation guarantees analogous to the LLL algorithm and practical performance that far exceeds the current state of the art. We achieve these results by iteratively applying precision management techniques within a recursive algorithm structure and show the stability of this approach. We analyze the asymptotic behavior of our algorithm, and show that the heuristic running time is $O(n^{\omega}(C+n)^{1+\varepsilon})$ for lattices of dimension $n$, $\omega\in (2,3]$ bounding the cost of size reduction, matrix multiplication, and QR factorization, and $C$ bounding the log of the condition number of the input basis $B$. This yields a running time of $O\left(n^\omega (p + n)^{1 + \varepsilon}\right)$ for precision $p = O(\log \|B\|_{max})$ in common applications. Our algorithm is fully practical, and we have published our implementation. We experimentally validate our heuristic, give extensive benchmarks against numerous classes of cryptographic lattices, and show that our algorithm significantly outperforms existing implementations.
  title={Fast Practical Lattice Reduction through Iterated Compression},
  author={Keegan Ryan and Nadia Heninger},