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.