Cryptography forms the basis for secure communications in networks that provide mechanisms for the assurance of information confidentiality, integrity, authenticity, and non-repudiation. The steady development of quantum computers—those processing powers strong enough to probably compromise the commonly used forms of digital encryption, basically—poses a whole new potential security threat to network infrastructures and their services widely used today. Theoretically, an ideal quantum computer has the power to break majority of the widely utilized encryption services today, including Rivest–Shamir–Adleman (RSA), Diffie-Hellman (DH), Elliptic Curve Cryptography etc. Thus, the security of these systems is based on computational impracticability as it is observed in the modern world. However, a quantum algorithm such as Shor’s or Grover’s would theoretically speed up the search for symmetric and asymmetric encryption keys, respectively. This would prompt a need for a longer key to maintain the current security level. However, the huge difference should be kept in mind—between quantum computers of today and their problems for public key cryptosystems: they are expected on the horizon. And quantum-resistant algorithms should, meanwhile, be tested and assessed in parallel in various domain areas. This research henceforth explores the integration of quantum-resistant cryptographic algorithms in LTE networks. Sensitive data exchange involved in the LTE handover process and ways to protect them using some kind of quantum-resistant algorithms can be explored.