Generating elements of orders dividing p6 ± p5 + p4 ± p3 + p2 + p ± 1

In this paper we propose an algorithm for computing large primes p and q such that q divides p6 + p5 + p4 + p3 + p2 + p + 1 or p6 - p5 + p4 - p3 + p2 - p + 1. Such primes are the key parameters for the cryptosystem based on the 7th order characteristic sequences