This paper introduces an improvement to a currently published algorithm to compute both Lucas " sister " sequences V k and U k. The proposed algorithm uses Lucas sequence properties to improve the running time by about 20% over the algorithm published in .
In this paper we analyze the extended RSA algorithm into the field of Gaussian integers. We examine in depth the perceived advantages of this extension, such as security and efficiency. We found that the extended RSA is slightly less efficient and could be more secure only if RSA is not as strong as factoring (even in this case it is not guaranteed to add… (More)
This paper introduces an extension of Rabin cryptosystem into the domain of complex integers. The extended cryptosystem employs a new square root algorithm for complex integers that is presented. The extended Rabin cryptosystem is efficient, provably secure and has certain advantages over the real- integer Rabin cryptosystem.
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… (More)