Landau-Siegel Bound of Post Quantum Cryptography

This code is to simulate and calculate the hacking bound for post quantum cryptography with Yitang Zhang Landau-Siegel zero bound vs others.

The National Institute of Standards and Technology (NIST) has launched a program and competition to standardize one or more post-quantum cryptographic (PQC) algorithms to fight against quantum attacks. In this work, we have conducted the first-ever mathematical analysis of lattice-based and polynomial-based PQC by introducing the relationship between automorphism and homomorphism. This analysis can help enterprises and organizations leverage NIST-selected PQC algorithms to safeguard their digital services from quantum attacks. We performed the simulation to illustrate brute force broken probability for polynomial-based or multivariate-based PQC to validate our mathematical analysis of PQC by using Yitang Zhang's Landau-Siegel zero bound.