@MISC{RADIX_6.MIZ,
  AUTHOR = {Niimura, Masaaki and Fuwa, Yasushi},
  TITLE = {High Speed Modulo Calculation Algorithm with Radix-$2^k$ {SD} Number},
  SECTION1 = {Some Useful Theorems},
  SECTION2 = {Definitions of Upper 3 Digits of Radix-$2^k$ SD Number and Its Property},
  SECTION3 = {Properties of Minimum Digits of Radix-$2^k$ SD Number},
  SECTION4 = {Modulo Calculation Algorithm Using Upper 3 Digits of Radix-$2^k$ SD Number},
  SECTION5 = {How to Identify the Range of Modulo Arithmetic Result},
  DAY = {07},
  MONTH = {November},
  YEAR = {2003},
  ADDRESS1 = {Shinshu University\\Nagano},
  ADDRESS2 = {Shinshu University\\Nagano},
  SUMMARY = {In RSA Cryptograms, many modulo calculations are used, but modulo calculation is
 based on many subtractions and it takes long a time to calculate it. In this article,
 we explain a new modulo calculation algorithm using a table. And we prove
 that upper 3 digits of Radix-$2^k$ SD numbers are enough to specify the answer.
  \par
 In the first section, we present some useful theorems for operations of
 Radix-$2^k$ SD Number. In the second section, we define Upper 3 Digits of
 Radix-$2^k$ SD number and prove that property. In the third section, we prove
 some property connected with the minimum digits of Radix-$2^k$ SD number. In the fourth
 section, we identify the range of modulo arithmetic result and prove that the
 Upper 3 Digits indicate two possible answers. And in the last section, we define
 a function to select true answer from the results of Upper 3 Digits.}}

