This open access book covers the most cutting-edge and hot research topics and fields of
post-quantum cryptography. The main purpose of this book is to focus on the computational
complexity theory of lattice ciphers especially the reduction principle of Ajtai in order to
fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption
algorithms but the theoretical proof is insufficient. In Chapter 3 Chapter 4 and Chapter 6
author introduces the theory and technology of LWE distribution LWE cipher and homomorphic
encryption in detail. When using random analysis tools there is a problem of ambiguity in both
definition and algorithm. The greatest feature of this book is to use probability distribution
to carry out rigorous mathematical definition and mathematical demonstration for various
unclear or imprecise expressions so as to make it a rigorous theoretical system for classroom
teaching and dissemination. Chapters 5 and 7 further expand and improve the theory of cyclic
lattice ideal lattice and generalized NTRU cryptography. This book is used as a professional
book for graduate students majoring in mathematics and cryptography as well as a reference
book for scientific and technological personnel engaged in cryptography research.
