Post-Quantum Cryptography: An Analysis of Code-Based and Lattice-Based Cryptosystems

TL;DR

This paper analyzes code-based and lattice-based cryptosystems as promising quantum-resistant alternatives, focusing on McEliece and NTRU, and explores their security foundations against quantum attacks.

Contribution

It provides a comparative analysis of McEliece and NTRU cryptosystems, highlighting their structural security assumptions and potential as post-quantum cryptographic solutions.

Findings

McEliece is believed to be secure against quantum attacks due to code hardness.

NTRU's security relies on the difficulty of the Shortest Vector Problem.

Connections between the structural foundations of both systems are established.

Abstract

Most modern cryptographic systems, such as RSA and the Diffie-Hellman Key Exchange, rely on "trapdoor" mathematical functions that are presumed to be computationally difficult with existing tools. However, quantum computers will be able to break these systems using Shor's Algorithm, necessitating the development of quantum-resistant alternatives. We first examine the McEliece cryptosystem, a code-based scheme believed to be secure against quantum attacks due to the hardness of decoding arbitrary linear codes. We then explore NTRU, a lattice-based system grounded in the difficulty of solving the Shortest Vector Problem. Finally, we establish connections between the structural foundations and security of the two systems.