Post-quantum cryptography

TL;DR: Post-quantum cryptography is necessary to secure against large-scale quantum computers, with lattice-based cryptography emerging as a prominent area, including LWE and AGCD problems, to standardize public-key encryption and digital signatures.

Abstract: Abstract The need for developing post-quantum cryptography, that is to say cryptographic schemes that are believed to remain secure if large-scale quantum computers are developed, is demonstrated by a discussion of the classical and the quantum algorithms for solving the factorization problem. The ongoing process by the US standards body NIST to standardize post-quantum public-key encryption and digital signatures is described. Lattice-based cryptography is introduced as a prominent area of post-quantum cryptography. Lattice problems, including the Learning with Errors (LWE) problem, are introduced. The AGCD cryptosystem, based on the approximate greatest common divisor (AGCD) problem, is described.