@MISC{RLVECT_X.MIZ,
  AUTHOR = {Futa, Yuichi and Okazaki, Hiroyuki and Shidama, Yasunari},
  TITLE = {Formalization of Integral Linear Space},
  SECTION1 = {Preliminaries},
  SECTION2 = {Integral Linear Space},
  DAY = {17},
  MONTH = {August},
  YEAR = {2010},
  ADDRESS1 = {Shinshu University, Nagano, Japan},
  ADDRESS2 = {Shinshu University, Nagano, Japan},
  ADDRESS3 = {Shinshu University, Nagano, Japan},
  SUMMARY = {In this article, we formalize
  integral linear spaces, that is a linear space with
  integer coefficients.
  Integral linear spaces are necessary for lattice problems,
  LLL base reduction algorithm and cryptographic systems with
  lattice \cite{Micci:2002}.}
  ACKNOWLEDGMENT = {This work was supported by JSPS KAKENHI 22300285.}}

@ARTICLE{Micci:2002,
      AUTHOR  = {Daniele Micciancio and Shafi Goldwasser},
      TITLE   = {Complexity of Lattice Problems:
      A Cryptographic Perspective (The International Series
      in Engineering and Computer Science)},
      PUBLISHER={Springer},
      YEAR    = 2002}
