From Lucas Sequences to Lucas Groups
College of Arts and Sciences
Marion Scheepers and Liljana Babinkostova
Lucas sequences, which generalize the famous Fibonacci sequence, have been studied extensively in the context of number theory and cryptography. Lucas groups, a more recently defined structure, are less studied. Lucas sequences generate subgroups of Lucas Groups. The research represented in this project clarifies the relationship between the full Lucas groups and their subgroups generated by Lucas sequences. The original application of Lucas sequences was primality testing. Lucas sequences were subsequently also employed for encryption. Lucas groups provide a more diverse platform for cryptographic purposes than the Lucas sequences, and we also show that the Lucas groups provide a finer tool for distinguishing between prime numbers and composite numbers.
Hansen, Kayson, "From Lucas Sequences to Lucas Groups" (2018). 2018 Undergraduate Research and Scholarship Conference. 84.