  We present in this paper an algorithm for exchanging session keys, coupled
with a hashing encryption module. We show schemes designed for their potential
invulnerability to classical and quantum attacks. In turn, if the parameters
included were appropriate, brute-force attacks exceed the (five) security
levels used in the NIST competition of new post-quantum standards. The original
idea consists of products of rectangular matrices in Zp as public values and
whose factorization is proved to be an NP-complete problem. We present running
times as a function of the explored parameters and their link with operational
safety. To our knowledge there are no classical and quantum attacks of
polynomial complexity available at hand, remaining only the systematic
exploration of the private-key space.
