A Cryptosystem Analogous to LUCELG and a Digital Signature Scheme

ElGamal 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 ElGamal 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.