Application of Algorithms on Lattices in Post-Quantum Cryptography

Abstract

The article analyzes approaches to the development of post-quantum algorithms, reviews progress in the field of quantum computers and post-quantum cryptographic encryption systems. One of the most promising approaches is considered, which is based on the theory of lattices. Difficult-to-solve problems are presented, on the basis of which cryptographic primitives of lattice theory are constructed. The article discusses in more detail the Goldreich Goldwasser Halevi encryption scheme based on the theory of lattices. The article presents a software package that allows the user to study the main functions of the GGH scheme: key generation algorithms, encryption algorithms and message decryption. The article specifies the main purposes of the modules of the software package, and describes the user interface of the program. Also, the software package makes it possible to carry out an attack on the encryption scheme using the Lenstra-Lenstra-Lovasz algorithm. This application can be used as part of a laboratory complex when studying.

Keywords

• post-quantum encryption algorithms
• cryptosystem
• qubit
• goldreich goldwasser halevi scheme
• lattice-based cryptography