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Since its foundation as an application of algebra, coding theory is obtaining a day by day increasing importance. For instance, any communication system needs the concepts of coding theory to function efficiently. In this thesis, reader will find an introductory explanation to linear codes and binary hamming codes including some of the algebraic tools devised in their applications. All the described software applications are verified using SageMath 9.0 using Hochschule Mittweida’s JupyterHub.
Developing computer processors and quantum computers requires continuous development of cryptographic algorithms. Researchers in standardization organizations keep experimenting with cryptographic algorithms and the related key sizes to recommend best practices for secure cryptography implementation [SE16]. The goal of researching Post Quantum Cryptography (PQC) is to develop cryptographic algorithms that are implemented in classic computers and secure against both quantum and classic computers [NIS16].
In this writing, we will have a primary introduction to lattices. Further, we will discuss the encryption and decryption functions of two lattice-based public key cryptography algorithms. The Sagemath codes are all experimented with using the JupyterHub server of the University of Applied Sciences Mittweida (Hochschule Mittweida).
