New Methods in Cryptography

This project surveys the development of quantum computers and their usability in decrypting prevalently used cryptosystems such as the RSA, based on the hardness of integer factoring, and Diffie-Hellman, based on the hardness of discrete logarithms. It then proceeds to discuss Peter Shor's contributions to developing such algorithms, and gives an overview of common post-quantum cryptosystems under active research and development in the field of cryptanalysis. We assume basic knowledge of number theory and quantum mechanics, but we detail the necessary information and principles used in quantum computers and Shor's algorithm for factoring large integers and solving the discrete log problem.