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An Experiment of Number Field Sieve over GF(p) of Low Hamming Weight Characteristic

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Coding and Cryptology (IWCC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6639))

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Abstract

The security of the digital signature algorithm (DSA) and Diffie-Hellman key exchange is based on the difficulty of the discrete logarithm problems (DLP) over prime field GF(p), and thus it is important to evaluate the difficulty of the DLP over GF(p) for discussing the security of these protocols. The number field sieve (NFS) is asymptotically the fastest algorithm to solve the DLP over GF(p). NFS was first proposed by Gordon and then it was improved by Schirokauer and Joux-Lercier. On the other hand, Schirokauer presented a new variant of NFS, which is particularly efficient for the characteristic p with low weight (p has a signed binary representation of low Hamming weight). In this paper, we implement the NFS proposed by Joux-Lercier and Schirokauer, and then we compare the running time of the NFS using the polynomials by Joux-Lercier and Schirokauer with respect to low weight primes of 100 bits or 110 bits.

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Author information

Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Kenichiro Hayasaka

  2. Institute of Mathematics for Industry, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Tsuyoshi Takagi

Authors
  1. Kenichiro Hayasaka
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  2. Tsuyoshi Takagi
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Editor information

Editors and Affiliations

  1. School of Physical and Mathematical Sciences, Division of Mathematical Sciences, Nanyang Technological University, 637371, Singapore

    Yeow Meng Chee , San Ling , Huaxiong Wang  & Chaoping Xing , ,  & 

  2. College of Information Engineering, Qingdao University, 266071, Shandong, P.R. China

    Zhenbo Guo

  3. Qingdao University, 266071, Shandong, P.R. China

    Fengjing Shao

  4. School of Mathematical Sciences, Yangzhou University, 225002, Jiangsu, P.R. China

    Yuansheng Tang

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Hayasaka, K., Takagi, T. (2011). An Experiment of Number Field Sieve over GF(p) of Low Hamming Weight Characteristic. In: Chee, Y.M., et al. Coding and Cryptology. IWCC 2011. Lecture Notes in Computer Science, vol 6639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20901-7_11

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  • DOI: https://doi.org/10.1007/978-3-642-20901-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20900-0

  • Online ISBN: 978-3-642-20901-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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