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The Closest Vector Problem on Some Lattices

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Grid and Cooperative Computing (GCC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3033))

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Abstract

The closest vector problem for general lattices is NP-hard. However, we can efficiently find the closest lattice points for some special lattices, such as root lattices (A n , D n and some E n ). In this paper, we discuss the closest vector problem on more general lattices than root lattices.

This work is supported by NSF of China (No.60003007) and by Japan Society for Promotion of Science (JSPS) Research Grant (No. 14380139)

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References

  1. Babai, L.: On Lovasz lattice reduction and the nearest lattice point problem. Combinatorica 6, 1–13 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Van Emde, B.: Another NP-complete problem and the complexity of computing short vectors in a lattice, Report 81-04, University of Amsterdam

    Google Scholar 

  3. Conway, J.H., Sloane, N.J.A.: Fast quantizing and decoding algorithms for lattice quantizers and codes. IEEE Transactions on Information Theory 28, 227–232 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  4. Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1998)

    Google Scholar 

  5. Lenstra, A.K., Lenstra Jr., H.W., Lovasz, L.: Factoring polynomials with rational coefficients. Math. Ann. 261, 513–534 (1982)

    Article  MathSciNet  Google Scholar 

  6. Micciancio, D., Goldwasser, S.: Complexity of Lattice Problems: a Cryptographic Perspective. Kluwer Academic Publishers, Dordrecht (2002)

    MATH  Google Scholar 

  7. Schnorr, C.P.: A hierarchy of polynomial time lattice basis reduction algorithms. Theoret. Comput. Sci. 53, 201–224 (1987)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. The Department of Computer Science & Engineering, Fudan University, Shanghai, P.R. China

    Haibin Kan & Hong Zhu

  2. Graduate School and Information Science, Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Tatsunokuchi, Ishikawa, 923-1292, Japan

    Haibin Kan & Hong Shen

Authors
  1. Haibin Kan
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  2. Hong Shen
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  3. Hong Zhu
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiatong University, 80 Dongcuan Road, 200240, Shanghai, China

    Minglu Li

  2. Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA

    Xian-He Sun

  3. Department. of Computer Science, Shanghai Jiaotong University, 1954 HuaShan Road, 200030, Shanghai, P.R. China

    Qianni Deng

  4. Department of Computer Science, College of Liberal Arts and Science, University of Iowa, IA 52242, Iowa City, USA

    Jun Ni

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© 2004 Springer-Verlag Berlin Heidelberg

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Kan, H., Shen, H., Zhu, H. (2004). The Closest Vector Problem on Some Lattices. In: Li, M., Sun, XH., Deng, Q., Ni, J. (eds) Grid and Cooperative Computing. GCC 2003. Lecture Notes in Computer Science, vol 3033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24680-0_76

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  • DOI: https://doi.org/10.1007/978-3-540-24680-0_76

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21993-4

  • Online ISBN: 978-3-540-24680-0

  • eBook Packages: Springer Book Archive

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