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Load Balanced Block Lanczos Algorithm over GF(2) for Factorization of Large Keys

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High Performance Computing - HiPC 2006 (HiPC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4297))

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Abstract

Researchers use NFS (Number Field Sieve) method with Lanczos algorithm to analyze big-sized RSA keys. NFS method includes the integer factorization process and nullspace computation of huge sparse matrices. Parallel processing is indispensible since sequential computation requires weeks (even months) of CPU time with supercomputers even for 150-digit RSA keys. This paper presents details of improved block Lanczos algorithm based on previous implementation[4,10]. It includes a new load balancing scheme by partitioning the matrix such that the numbers of nonzero components in the submatrices become equal. Experimentally, a speedup up to 6 and the maximum of efficiency of 0.74 have been achieved using an 8-node cluster with Myrinet interconnection.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Korea University, Seoul, Rep. of Korea

    Wontae Hwang & Dongseung Kim

Authors
  1. Wontae Hwang
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  2. Dongseung Kim
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Editor information

Editors and Affiliations

  1.  ,  

    Yves Robert

  2. Department of Electrical and Computer Engineering, Rutgers, the State University of New Jersey, 94 Brett Road, NJ 08854, Piscataway, USA

    Manish Parashar

  3. Hewlett-Packard ISO, Sy 192, Whitefield Road, Mahadevapura Post, 560048, Bangalore, India

    Ramamurthy Badrinath

  4. Department of Electrical Engineering, University of Southern California, 90089-2562, Los Angeles, CA, USA

    Viktor K. Prasanna

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© 2006 Springer-Verlag Berlin Heidelberg

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Hwang, W., Kim, D. (2006). Load Balanced Block Lanczos Algorithm over GF(2) for Factorization of Large Keys. In: Robert, Y., Parashar, M., Badrinath, R., Prasanna, V.K. (eds) High Performance Computing - HiPC 2006. HiPC 2006. Lecture Notes in Computer Science, vol 4297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11945918_38

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  • DOI: https://doi.org/10.1007/11945918_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68039-0

  • Online ISBN: 978-3-540-68040-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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