Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003
Association of Mizar Users
Magnitude Relation Properties of Radix$2^k$ SD Number

Masaaki Niimura

Shinshu University, Nagano

Yasushi Fuwa

Shinshu University, Nagano
Summary.

In this article, magnitude relation properties of Radix$2^k$ SD number
are discussed.\par
Until now, the Radix$2^k$ SD Number is proposed for the highspeed
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 discussed about a magnitude relation of Radix$2^k$
SD Number. In the first section, we prepared some useful theorems for
operations of Radix$2^k$ SD Number. In the second section, we proved some
properties about the primary numbers expressed by Radix$2^k$ SD Number
such as 0, 1, and Radix(k). In the third section, we proved primary
magnitude relations between two Radix$2^k$ SD Numbers. In the fourth
section, we defined Max/Min numbers in some cases. And in the last section,
we proved some relations about the addition of Max/Min numbers.
MML Identifier:
RADIX_5
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[8]
[1]
[6]
[4]
[2]
[3]
[5]

Some Useful Theorems

Properties of Primary Radix$2^k$ SD Number

Primary Magnitude Relation of Radix$2^k$ SD Number

Definition of Max/Min Radix$2^k$ SD Numbers in Some Digits

Properties of Max/Min Radix$2^k$ SD Numbers
Bibliography
 [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Yoshinori Fujisawa and Yasushi Fuwa.
Definitions of radix$2^k$ signeddigit number and its adder algorithm.
Journal of Formalized Mathematics,
11, 1999.
 [5]
Andrzej Kondracki.
The Chinese Remainder Theorem.
Journal of Formalized Mathematics,
9, 1997.
 [6]
Takaya Nishiyama and Yasuho Mizuhara.
Binary arithmetics.
Journal of Formalized Mathematics,
5, 1993.
 [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [8]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
Received November 7, 2003
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