ABSTRACT
In this chapter, the authors discuss several techniques for creating public-key cryptosystems and signature schemes in the setting of post-quantum cryptography. They include lattice-based cryptography, code-based cryptography, multivariate cryptography, and hash-based signature schemes. There have been several interesting approaches to post-quantum cryptography that have been investigated in recent years. In particular, National Institute of Standards and Technology is giving a high priority to quantum cryptography, sponsoring the first standardization conference for post-quantum cryptography in 2018. It turns out that it is possible to identify an "easy" special case of the decoding problem and then disguise it so that it looks like a "difficult" general case of the problem. The McEliece Cryptosystem has received much more attention since the advent of post-quantum cryptography. Merkle invented a useful method of extending a one-time scheme so it could be used for a large number of signatures, without increasing the size of the public key.
