Paper 2025/087
On Gaussian Sampling for $q$-ary Lattices and Linear Codes with Lee Weight
Abstract
We show that discrete Gaussian sampling for a $q$-ary lattice is equivalent to codeword sampling for a linear code over $\mathbb{Z}_q$ with the Lee weight. This insight allows us to derive the theta series of a $q$-ary lattice from the Lee weight distribution of the associated code. We design a novel Gaussian sampler for $q$-ary lattices assuming an oracle that computes the symmetrized weight enumerator of the associated code. We apply this sampler to well-known lattices, such as the $E_8$, Barnes-Wall, and Leech lattice, highlighting both its advantages and limitations, which depend on the underlying code properties. For certain root lattices, we show that the sampler is indeed efficient, forgoing the need to assume an oracle. We also discuss applications of our results in digital signature schemes and the Lattice Isomorphism Problem. In many cases, our sampler achieves a significant speed-up compared to state-of-the-art sampling algorithms in cryptographic applications.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Lattice Gaussian samplingLee weightq-ary latticeSchur productTheta series
- Contact author(s)
-
maiarabollauf @ gmail com
m lie22 @ imperial ac uk
c ling @ imperial ac uk - History
- 2025-01-22: revised
- 2025-01-20: received
- See all versions
- Short URL
- https://ia.cr/2025/087
- License
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CC BY
BibTeX
@misc{cryptoeprint:2025/087, author = {Maiara F. Bollauf and Maja Lie and Cong Ling}, title = {On Gaussian Sampling for $q$-ary Lattices and Linear Codes with Lee Weight}, howpublished = {Cryptology {ePrint} Archive, Paper 2025/087}, year = {2025}, url = {https://eprint.iacr.org/2025/087} }