This open access book systematically explores the statistical characteristics of cryptographic
systems the computational complexity theory of cryptographic algorithms and the mathematical
principles behind various encryption and decryption algorithms. The theory stems from
technology. Based on Shannon's information theory this book systematically introduces the
information theory statistical characteristics and computational complexity theory of public
key cryptography focusing on the three main algorithms of public key cryptography RSA
discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it
is. It systematically simplifies and combs the theory and technology of lattice cryptography
which is the greatest feature of this book. It requires a good knowledge in algebra number
theory and probability statistics for readers to read this book. The senior students majoring
in mathematics compulsory for cryptography and science and engineering postgraduates will find
this book helpful. It can also be used as the main reference book for researchers in
cryptography and cryptographic engineering areas.
