Part II
Post-quantum Cryptography

This chapter explains lattice-based cryptographic schemes: LWE cryptosystem, RLWE cryptosystem, GLWE cryptosystem, GLev cryptosystem, and GGSW cryptosystem. These are the essential building blocks for FHE schemes.

Required Background


B-1 Lattice-based Cryptography
B-1.1 Overview
B-1.2 LWE Cryptosystem
B-1.3 RLWE Cryptosystem
B-2 LWE Cryptosystem
B-2.1 Setup
B-2.2 Encryption
B-2.3 Decryption
B-3 RLWE Cryptosystem
B-3.1 Setup
B-3.2 Encryption
B-3.3 Decryption
B-4 GLWE Cryptosystem
B-4.1 Setup
B-4.2 Encryption
B-4.3 Decryption
B-4.4 An Alternative Version of GLWE
B-4.5 Public Key Encryption
B-5 GLev
B-5.1 Encryption
B-5.2 Decryption
B-5.3 Lev and RLev
B-6 GGSW
B-6.1 Encryption
B-6.2 Decryption
B-6.3 GSW and RGSW