Relationship between Lucas Sequences and Gaussian Integers in Cryptosystems
Document Type
Conference Proceeding
Publication Date
5-26-2015
Abstract
Both Gaussian integers and Lucas sequences have been applied in cryptography. This paper presents the mathematical relationship between Lucas sequences and Gaussian integers. It also explores the complexity of Discrete Logarithm Problem (DLP) for Gaussian integers modulo prime by reducing it to Lucas Sequences DLP and real integer DLP. We demonstrate that the algorithms based on the Gaussian Integer DLP have advantages over the corresponding algorithms based on real integer DLP or Lucas Sequences DLP. Numerical examples are provided.
Identifier
84936769511 (Scopus)
ISBN
[9781479988273]
Publication Title
Proceedings 12th International Conference on Information Technology New Generations Itng 2015
External Full Text Location
https://doi.org/10.1109/ITNG.2015.43
First Page
229
Last Page
233
Recommended Citation
Koval, Aleksey, "Relationship between Lucas Sequences and Gaussian Integers in Cryptosystems" (2015). Faculty Publications. 6996.
https://digitalcommons.njit.edu/fac_pubs/6996
