A New "F-Lueg" Cryptosystem and its Security

In this thesis, we present a new public-key cryptosystem and a new digital signature based on the extended Lucas function analogue to EIGamal cryptosystem. We name it" F-LUEG" cryptosystem. Chapter 2, we point out how an extended Lucas function can be used in a cryptosystem, which has been presented Md Said in his thesis [Rus]. This extended Lucas function is an extension from Lucas function. In chapter 3, we provide some explanation about EIGamal cryptosystem, which has been presented by TEl Gamal in 1985. Finally, from these two cryptosystems, this thesis associate the extended Lucas and EIGamal cryptosystems to develop a new cryptosystem, which is the F-LUEG cryptosystem

A Cryptosystem Analogous to LUCELG and a Digital Signature Scheme

EIGamal and LUC are examples of a public-key cryptosystem. Based on these two systems, LUCELG that depends on the strength of the two systems was constructed. The combination of EIGamal and the cubic analogue of the LUC cryptosystem (LUC~) produces a new public-key cryptosystem. Following (Smith94), a new digital signature scheme is proposed. The security aspects of the system are also looked into and although all these systems appear to depend on the intractability of factorization or of the discrete logarithm problem, the systems do not seem to be readily comparable