It has been shown [2, 3, 4] that in ElGamal public key encryption scheme [6, 7, 8] working over SM G(pm ), the need of nding primitive elements of GF (pm ), necessary if the system works traditionally but unfeasible in the case of huge elds, is eliminated. Thus, the discussed system is user-friendly, giving the possibility of very strong encryption with the key of order 10.000 bits and more. The construction of such cryptosystem is of great practical importance, therefore, the paper informs the reader in detail how to resolve this problem using Maple.