Comment. Remarks on the LUC public key system

The authors of [Remarks on the LUC public key system, see ibid., vol. 30, p. 123, 1994] consider the Lucas function on which the public cryptosystem LUC proposed by Smith and Lennon [1993] is based. For a finite field G with m∈G, the Lucas function V_n(m) is defined by the second order linear recurrence relation V_n(m)=mV_n-1(m)-V_n-2(m) where V_o (m)=2, V₁(m)=m. The characteristic polynomial f of the Lucas function is f(x)=x²-mx+1, and V_x(m)=α ^x+α^-x where α is a root of f. We now consider some of the results of and give concise proofs