Public Key Security for Quantum Key Distribution

This paper explores the intersection of Quantum Key Distribution (QKD) and Lattice Cryptography, two innovative fields in modern cryptography. The quantum realm provides unique opportunities for secure communication through principles like superposition and entanglement, while lattice-based cryptography offers promising post-quantum secure solutions. We delve into three prominent QKD protocols—BB84, B92, and EPR—and examine foundational aspects of Lattice Cryptography, including Learning With Errors (LWE) and the Shortest Vector Problem (SVP). By bridging quantum and classical cryptographic concepts, this paper contributes to the evolving landscape of secure communication in an era where the threat of quantum computing looms. This paper will further discuss how to make a QKD work along with SVP, so that we can convert a shared key algorithm(QKD) to a Public Key Cryptography for more safety. This paper will mostly deal with QKD protocol-BB84 and Shortest Vector Problems along with some basic requirements to understand these two algorithms.