An experiment of number field sieve over GF(p) of low hamming weight characteristic

Kenichiro Hayasaka, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationCoding and Cryptology - Third International Workshop, IWCC 2011, Proceedings
Pages191-200
Number of pages10
DOIs
Publication statusPublished - Jun 23 2011
Event3rd International Workshop on Coding and Cryptology, IWCC 2011 - Qingdao, China
Duration: May 30 2011Jun 3 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6639 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd International Workshop on Coding and Cryptology, IWCC 2011
CountryChina
CityQingdao
Period5/30/116/3/11

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Hayasaka, K., & Takagi, T. (2011). An experiment of number field sieve over GF(p) of low hamming weight characteristic. In Coding and Cryptology - Third International Workshop, IWCC 2011, Proceedings (pp. 191-200). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6639 LNCS). https://doi.org/10.1007/978-3-642-20901-7_11