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International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2003: Advances in Cryptology — EUROCRYPT 2003 pp 433–448Cite as

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Hypercubic Lattice Reduction and Analysis of GGH and NTRU Signatures

Hypercubic Lattice Reduction and Analysis of GGH and NTRU Signatures

  • Michael Szydlo5 
  • Conference paper
  • First Online: 01 January 2003
  • 3637 Accesses

  • 13 Citations

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2656)

Abstract

In this paper, we introduce a new lattice reduction technique applicable to the narrow, but important class of Hypercubic lattices, (L ≅ ℤN). Hypercubic lattices arise during transcript analysis of certain GGH, and NTRUSign signature schemes. After a few thousand signatures, key recovery amounts to discovering a hidden unitary matrix U, from its Gram matrix G = UU T. This case of the Gram Matrix Factorization Problem is equivalent to finding the shortest vectors in the hypercubic lattice, L G , defined by the quadratic form G. Our main result is a polynomial-time reduction to a conjecturally easier problem: the Lattice Distinguishing Problem. Additionally, we propose a heuristic solution to this distinguishing problem with a distributed computation of many “relatively short” vectors.

Keywords

  • Lattice Isomorphism
  • Lattice Distinguishing Oracle
  • Distributed Lattice Reduction
  • Decisional Lattice Problem
  • Gram Matrix Factorization
  • Integral Lattice Embedding Orthogonal Lattice
  • GGH Cryptanalysis
  • NTRUSign

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Author information

Authors and Affiliations

  1. RSA Laboratories, Bedford, MA, USA

    Michael Szydlo

Authors
  1. Michael Szydlo
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Editor information

Editors and Affiliations

  1. Computer Science Department, Technion — Israel Institute of Technology, Haifa, 32000, Israel

    Eli Biham

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© 2003 International Association for Cryptologic Research

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Cite this paper

Szydlo, M. (2003). Hypercubic Lattice Reduction and Analysis of GGH and NTRU Signatures. In: Biham, E. (eds) Advances in Cryptology — EUROCRYPT 2003. EUROCRYPT 2003. Lecture Notes in Computer Science, vol 2656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39200-9_27

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  • DOI: https://doi.org/10.1007/3-540-39200-9_27

  • Published: 13 May 2003

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-14039-9

  • Online ISBN: 978-3-540-39200-2

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