http://hdl.handle.net/11320/21431 2026-11-05T13:28:03Z 2026-11-05T13:28:03Z Niimura, Masaaki Yasushi, Fuwa http://hdl.handle.net/11320/21443 2026-11-05T12:20:36Z 2004-01-01T00:00:00Z

Tytuł: High Speed Modulo Calculation Algorithm with Radix-2ᵏ SD Number Autorzy: Niimura, Masaaki; Yasushi, Fuwa Abstrakt: 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-2ᵏ SD numbers are enough to specify the answer. In the first section, we present some useful theorems for operations of Radix-2ᵏ SD Number. In the second section, we define Upper 3 Digits of Radix-2ᵏ SD number and prove that property. In the third section, we prove some property connected with the minimum digits of Radix-2ᵏ 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.

2004-01-01T00:00:00Z Niimura, Masaaki Fuwa, Yasushi http://hdl.handle.net/11320/21438 2026-11-05T09:52:41Z 2004-01-01T00:00:00Z

Tytuł: Magnitude Relation Properties of Radix-2ᵏ SD Number Autorzy: Niimura, Masaaki; Fuwa, Yasushi Abstrakt: In this article, magnitude relation properties of Radix-2ᵏ SD number are discussed. Until now, the Radix-2ᵏ 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. In this article, we discuss magnitude relation of Radix-2ᵏ SD Number. In the first section, we present some useful theorems for operations of Radix-2ᵏ SD Number. In the second section, we prove some properties of the primary numbers expressed by Radix-2ᵏ SD Number such as 0, 1, and Radix(k). In the third section, we prove primary magnitude relations between two Radix-2ᵏ 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.

2004-01-01T00:00:00Z Nakamura, Yatsuka http://hdl.handle.net/11320/21434 2026-11-05T08:55:11Z 2004-01-01T00:00:00Z

Tytuł: Sorting Operators for Finite Sequences Autorzy: Nakamura, Yatsuka Abstrakt: Two kinds of sorting operators, descendent one and ascendent one are introduced for finite sequences of reals. They are also called rearrangement of finite sequences of reals. Maximum and minimum values of finite sequences of reals are also defined. We also discuss relations between these concepts.

2004-01-01T00:00:00Z