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Paper: Some Easy Instances of Ideal-SVP and Implications to the Partial Vandermonde Knapsack Problem

Authors:
Katharina Boudgoust , Aarhus University
Erell Gachon , Université de Bordeaux
Alice Pellet-Mary , CNRS and Université de Bordeaux
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Presentation: Slides
Conference: CRYPTO 2022
Abstract: In this article, we generalize the works of Pan et al. (Eurocrypt'21) and Porter et al. (ArXiv'21) and provide a simple condition under which an ideal lattice defines an easy instance of the shortest vector problem. Namely, we show that the more automorphisms stabilize the ideal, the easier it is to find a short vector in it. This observation was already made for prime ideals in Galois fields, and we generalize it to any ideal (whose prime factors are not ramified) of any number field. We then provide a cryptographic application of this result by showing that particular instances of the partial Vandermonde knapsack problem, also known as partial Fourier recovery problem, can be solved classically in polynomial time. As a proof of concept, we implemented our attack and managed to solve those particular instances for concrete parameter settings proposed in the literature. For random instances, we can halve the lattice dimension with non-negligible probability.
Video from CRYPTO 2022
BibTeX
@inproceedings{crypto-2022-32098,
  title={Some Easy Instances of Ideal-SVP and Implications to the Partial Vandermonde Knapsack Problem},
  publisher={Springer-Verlag},
  author={Katharina Boudgoust and Erell Gachon and Alice Pellet-Mary},
  year=2022
}