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