Primality Testing Using Complex Integers and Pythagorean Triplets

Autor:	Boris S. Verkhovsky
Rok vydání:	2012
Předmět:	Discrete mathematics Fermat primality test Fermat's little theorem Carmichael number Miller–Rabin primality test Mathematics::Number Theory Primality certificate Arithmetic Primality test Solovay–Strassen primality test Mathematics Industrial-grade prime
Zdroj:	International Journal of Communications, Network and System Sciences. :513-519
ISSN:	1913-3723 1913-3715
Popis:	Prime integers and their generalizations play important roles in protocols for secure transmission of information via open channels of telecommunication networks. Generation of multidigit large primes in the design stage of a cryptographic system is a formidable task. Fermat primality checking is one of the simplest of all tests. Unfortunately, there are composite integers (called Carmichael numbers) that are not detectable by the Fermat test. In this paper we consider modular arithmetic based on complex integers; and provide several tests that verify the primality of real integers. Although the new tests detect most Carmichael numbers, there are a small percentage of them that escape these tests.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e04458491536b4506effce446d901955 https://doi.org/10.4236/ijcns.2012.59062 Zobrazit plný text záznamu