  The machinery of industrial environments was connected to the Internet years
ago with the scope of increasing their performance. However, this change made
such environments vulnerable against cyber-attacks that can compromise their
correct functioning resulting in economic or social problems. Moreover,
implementing cryptosystems in the communications between operational technology
(OT) devices is a more challenging task than for information technology (IT)
environments since the OT networks are generally composed of legacy elements,
characterized by low-computational capabilities. Consequently, implementing
cryptosystems in industrial communication networks faces a trade-off between
the security of the communications and the amortization of the industrial
infrastructure. Critical Infrastructure (CI) refers to the industries which
provide key resources for the daily social and economical development, e.g.
electricity. Furthermore, a new threat to cybersecurity has arisen with the
theoretical proposal of quantum computers, due to their potential ability of
breaking state-of-the-art cryptography protocols, such as RSA or ECC. Many
global agents have become aware that transitioning their secure communications
to a quantum secure paradigm is a priority that should be established before
the arrival of fault-tolerance. In this paper, we aim to describe the
problematic of implementing post-quantum cryptography (PQC) to CI environments.
For doing so, we describe the requirements for these scenarios and how they
differ against IT. We also introduce classical cryptography and how quantum
computers pose a threat to such security protocols. Furthermore, we introduce
state-of-the-art proposals of PQC protocols and present their characteristics.
We conclude by discussing the problematic of integrating PQC in industrial
environments.
