@MISC{RADIX_5.MIZ,
  AUTHOR = {Niimura, Masaaki and Fuwa, Yasushi},
  TITLE = {Magnitude Relation Properties of Radix-$2^k$ {SD} Number},
  SECTION1 = {Some Useful Theorems},
  SECTION2 = {Properties of Primary Radix-$2^k$ SD Number},
  SECTION3 = {Primary Magnitude Relation of Radix-$2^k$ SD Number},
  SECTION4 = {Definition of Max/Min Radix-$2^k$ SD Numbers in Some Digits},
  SECTION5 = {Properties of Max/Min Radix-$2^k$ SD Numbers},
  DAY = {07},
  MONTH = {November},
  YEAR = {2003},
  ADDRESS1 = {Shinshu University\\Nagano},
  ADDRESS2 = {Shinshu University\\Nagano},
  SUMMARY = {In this article, magnitude relation properties of Radix-$2^k$ SD number
  are discussed.
  Until now, the Radix-$2^k$ SD Number has been proposed for the high-speed
  calculations for RSA Cryptograms. In RSA Cryptograms, many modulo calculations
  are used, and modulo calculations need a comparison between two numbers.\par
  In this article, we discuss magnitude relation of Radix-$2^k$
  SD Number. In the first section, we present some useful theorems for
  operations of Radix-$2^k$ SD Number. In the second section, we prove some
  properties of the primary numbers expressed by Radix-$2^k$ SD Number
  such as 0, 1, and Radix(k). In the third section, we prove primary
  magnitude relations between two Radix-$2^k$ SD Numbers. In the fourth
  section, we define Max/Min numbers in some cases. And in the last section,
  we prove some relations between the addition of Max/Min numbers.}}

