Title of Presentation

Constructing Order-2 Carmichael Numbers with non-rigid factors

Type of Submission

Pre-recorded Research Talk

Research Field

Computer Science, Mathematics

Faculty Advisor

ashallue@iwu.edu

Graduation Year

2022

Start Date

10-4-2021 8:00 AM

End Date

11-4-2021 5:00 PM

Abstract

A pseudoprime with respect to a primality test is a composite number for which the primality test results are inconclusive. Pseudoprimes and primality tests are of primary importance to public-key cryptography that rely on properties of large prime for their security. A Carmichael number n is a Fermat pseudoprime that passes the Fermat primality test for every base b coprime to n. A Carmichael number of order m is a generalization of a Carmichael number using notions of abstract algebra and, unlike first order Carmichael numbers, can consist of rigid and non-rigid factors. Extending and adapting previous work, we explored possible constructions of order-2 Carmichael numbers that allow for multiple non-rigid factors. An implementation of the construction in C++ is ongoing.

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Apr 10th, 8:00 AM Apr 11th, 5:00 PM

Constructing Order-2 Carmichael Numbers with non-rigid factors

A pseudoprime with respect to a primality test is a composite number for which the primality test results are inconclusive. Pseudoprimes and primality tests are of primary importance to public-key cryptography that rely on properties of large prime for their security. A Carmichael number n is a Fermat pseudoprime that passes the Fermat primality test for every base b coprime to n. A Carmichael number of order m is a generalization of a Carmichael number using notions of abstract algebra and, unlike first order Carmichael numbers, can consist of rigid and non-rigid factors. Extending and adapting previous work, we explored possible constructions of order-2 Carmichael numbers that allow for multiple non-rigid factors. An implementation of the construction in C++ is ongoing.