Constructing Order-2 Carmichael Numbers with non-rigid factors
Submission Type
Pre-recorded Research Talk
Area of Study or Work
Computer Science, Mathematics
Faculty Advisor
ashallue@iwu.edu
Expected Graduation Date
2022
Start Date
4-10-2021 8:00 AM
End Date
4-11-2021 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.
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.