Comparative Analysis of Elliptic Curve and Lattice Based Cryptography

In this paper, we provide a mathematical background and analysis of Lattice Based Cryptography for the less mathematically mature reader. Discussing the benefits and constraints of Lattice Based Crypto, we compare and contrast with Elliptic Curve Cryptography to provide an understanding of what the limitations of Lattice Based Cryptography are, and what needs to be achieved for the quantum resistant protocols to be deploy-able to any and all devices.