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 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 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

Contents (PDF format)

1. Some Useful Theorems
2. Properties of Primary Radix-$2^k$ SD Number
3. Primary Magnitude Relation of Radix-$2^k$ SD Number
4. Definition of Max/Min Radix-$2^k$ SD Numbers in Some Digits
5. Properties of Max/Min Radix-$2^k$ SD Numbers

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