Studying the efficiency of the Frobenius primality test

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dc.contributor.authorGheisari, Hiva
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorFiori, Andrew
dc.contributor.supervisorKadiri, Habiba
dc.date.accessioned2024-11-15T19:26:21Z
dc.date.available2024-11-15T19:26:21Z
dc.date.issued2024
dc.degree.levelMasters
dc.description.abstractIn mathematics, especially number theory, prime numbers are essential concepts. Prime numbers are used in cryptography as one application. Finding large prime numbers is crucial for cryptographic protocols; to do this, we must be able to tell whether a given number is prime or not. To test whether a number is a prime number, we require a computationally efficient primality testing algorithm. The primary objective of my research is to evaluate how well the tests work. Especially, in my research our main focus is on Grantham’s primality test. Grantham’s test is probabilistic and fast, but it comes with the risk of false positives. To determine how ‘good’ a test is, one must be aware of the possibility of false positives because in our development, deterministic tests are slower than false positive ones. In this thesis, we will explain the definitions of ‘probable prime numbers’, such as ‘Frobenius pseudoprime’, as given by Jon Grantham. Our research goal is to find upper and lower bounds for the number of probable prime numbers by generalizing the work of Paul Erdös and Carl Pomerance on Fermat pseudoprimes, and Jon Grantham on Frobenius pseudoprimes.
dc.embargoNo
dc.identifier.urihttps://hdl.handle.net/10133/6952
dc.language.isoen
dc.publisherLethbridge, Alta. : University of Health, Dept. of Mathematics and Computer Science
dc.publisher.departmentDepartment of Mathematics and Computer Science
dc.publisher.facultyArts and Science
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)
dc.subjectPrime numbers
dc.subjectProbable prime numbers
dc.subjectPrimality test
dc.subjectPseudoprimes
dc.subjectGrantham
dc.subjectFrobenius
dc.subjectFermat
dc.subject.lcshNumbers, Prime
dc.subject.lcshErdos, Paul, 1913-1996
dc.subject.lcshPomerance, Carl
dc.subject.lcshGrantham, Jon
dc.subject.lcshDissertations, Academic
dc.titleStudying the efficiency of the Frobenius primality test
dc.typeThesis
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