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Lower Bounds of Shortest Vector Lengths in Random NTRU Lattices

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7287))

Abstract

Finding the shortest vector of a lattice is one of the most important problems in computational lattice theory. For a random lattice, one can estimate the length of the shortest vector using the Gaussian heuristic. However, no rigorous proof can be provided for some classes of lattices, as the Gaussian heuristic may not hold for them. In this paper, we propose a general method to estimate lower bounds of the shortest vector lengths for random integral lattices in certain classes, which is based on the incompressibility method from the theory of Kolmogorov complexity. As an application, we can prove that for a random NTRU lattice, with an overwhelming probability, the ratio between the length of the shortest vector and the length of the target vector, which corresponds to the secret key, is at least a constant, independent of the rank of the lattice.

Partially supported by NSF of China Projects (No.61133013 and No.60931160442), GIIFSDU Project (No. 11140070613184) and Tsinghua University Initiative Scientific Research Program (No.2009THZ01002).

Partially supported by NSF under grants CCF-0830522 and CCF-0830524.

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Author information

Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, P.R. China

    Jingguo Bi

  2. School of Computer Science, University of Oklahoma, Norman, OK, 73019, USA

    Jingguo Bi & Qi Cheng

Authors
  1. Jingguo Bi
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  2. Qi Cheng
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Resource Planning and Generation, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Manindra Agrawal

  2. Department of Pure Mathematics, Leeds, University of Leeds, LS2 9JT, UK

    S. Barry Cooper

  3. Institute of Software, Chinese Academy of Sciences, P.O. Box 8718, 100190, Beijing, P.R. China

    Angsheng Li

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Bi, J., Cheng, Q. (2012). Lower Bounds of Shortest Vector Lengths in Random NTRU Lattices. In: Agrawal, M., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2012. Lecture Notes in Computer Science, vol 7287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29952-0_18

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  • DOI: https://doi.org/10.1007/978-3-642-29952-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29951-3

  • Online ISBN: 978-3-642-29952-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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