Patent•
Prime number generating apparatus
08 Jan 2003-
TL;DR: In this article, a candidate of the prime number is divided by a known prime number, and then the candidate is determined to be a multiple number of the known prime numbers based on the updated number of times of the candidate.
Abstract: PROBLEM TO BE SOLVED: To obtain an apparatus and a method for generating a prime number which can quickly generate the prime number SOLUTION: A candidate of the prime number is divided by a known prime number The first prime number determination is performed based on the existence of a residue The second prime number determination is performed by determining whether the candidate of the prime number is a multiple number of the known prime number based on the updated number of times of the candidate of the prime number When there is the possibility that the candidate of the prime number is the prime number based on the first and second prime number determination, the third prime number determination for the candidate of the prime number is performed The number of times of the first and third prime number determination can be reduced The time required for generating the prime number can be shortened
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Patent•
27 Dec 2007
TL;DR: In this paper, the authors propose a program to carry out the Miller-Rabin test on one base, in order to increase the speed of full-scale prime number judgment after trial division.
Abstract: PROBLEM TO BE SOLVED: To increase speed of full-scale prime number judgment after trial division of each prime number candidate. SOLUTION: In a "Miller-Rabin test" used for full-scale prime number judgment, when a candidate passes the prime number judgment on one base, the candidate is a strong probable prime number. In other words, when the candidate fails in the test, the candidate tends to fail in the prime number judgment on one base. Hence, by configuring a program to carry out the "Miller-Rabin test" on one base, in general, "the full-scale prime number judgment of p (up to the midway)" on ahead, when the candidate fails in the "Miller-Rabin test (a test on one base) (ST4)", in general, "the full-scale prime number judgment of p (up to the midway) (ST4')", it is not required to perform the following processing (steps ST5 to ST9 or ST5' to ST9'). Hence, the speed of the full-scale prime number judgment after the trial division of each prime number candidate can be increased by the portion of the following processing (ST5 to ST9 or steps ST5' to ST9'). COPYRIGHT: (C)2008,JPO&INPIT
1 citations