Skip to main content
SpringerLink
Log in

Computing the M = UU t Integer Matrix Decomposition

  • Conference paper
Book cover Cryptography and Coding (Cryptography and Coding 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2898))

Included in the following conference series:

Abstract

The cryptanalysis of Gentry and Szydlo of the revised NTRU signature scheme requires the computation of the integer matrix decomposition M = UU t. We propose a heuristic algorithm to compute this decomposition and investigate its properties. Our test implementation of this algorithm in Magma is able to deal with matrices up to 158 rows and columns.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I: The user language. J. Symbolic Comput. 24, 235–265 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cohen, H.: A Course in Computational Algebraic Number Theory. Springer, Heidelberg (1996)

    Google Scholar 

  3. Computational algebra group, Uni. Sydney. Magma (2002) see, http://www.maths.usyd.edu.au:8000/u/magma/

  4. Consortium for Efficient Embedded Security. Efficient Embedded Security Standard (EESS), see http://www.ceesstandards.org/

  5. Gentry, C., Szydlo, M.: Cryptanalysis of the Revised NTRU Signature Scheme. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 299–320. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  6. Goldreich, O., Goldwasser, S., Halevi, S.: Public-Key Cryptosystems from Lattice Reduction Problems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 112–131. Springer, Heidelberg (1997)

    Google Scholar 

  7. Hoffstein, J., Howgrave-Graham, N., Pipher, J., Silverman, J.H., Whyte, W.: NTRUSign: Digital Signatures Using the NTRU Lattice (2002), see http://www.ntru.com/

  8. Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: A ring-based public key cryptosystem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 267–288. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  9. Hoffstein, J., Pipher, J., Silverman, J.H.: NSS: The NTRU Signature Scheme. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 211–228. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Lenstra, A.K., Lenstra, H.W., Lovász, L.: Factoring polynomials with rational coefficients. Math. Ann. 261, 515–534 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  11. Stern, J., Nguyen, P.: Lattice reduction in cryptology: an update. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 85–112. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Szydlo, M.: Hypercubic Lattice Reduction and Analysis of GGH and NTRU Signatures. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 433–448. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB

    Katharina Geißler & Nigel P. Smart

Authors
  1. Katharina Geißler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nigel P. Smart
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Information Security Group, Royal Holloway, University of London, TW20 0EX, Egham, Surrey, U.K.

    Kenneth G. Paterson

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Geißler, K., Smart, N.P. (2003). Computing the M = UU t Integer Matrix Decomposition. In: Paterson, K.G. (eds) Cryptography and Coding. Cryptography and Coding 2003. Lecture Notes in Computer Science, vol 2898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40974-8_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-40974-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20663-7

  • Online ISBN: 978-3-540-40974-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation