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
