ABSTRACT
This chapter introduces post-quantum cryptography. It describes lattice-based cryptographic constructions of post-quantum cryptography. Lattice-based cryptographic constructions are one of candidates of post-quantum cryptography, which are believed to be secure against quantum computers. Learning with errors (LWE) is one of the most promising primitives in many usages due to its lightweight operation and rigorous security reduction against the worst-case of the lattice problems that are considered to be hard to solve even after the advance of quantum computers. After the research about the connection between the LWE problem and some lattice problems, some variants of LWE, of which the secret distributions are modified from the uniform distribution, were proposed. Due to the efficiency and compactness of ring-LWE, many lattice-based cryptosystems are constructed as ring-LWE based, rather than LWE-based. The chapter explains a ring variant of Lizard scheme, called RLizard, IND-CCA secure encryption scheme.
