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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.

Computer science --- Financial engineering. --- Social sciences --- Mathematics. --- Computational finance --- Engineering, Financial --- Finance --- Computer mathematics --- Electronic data processing --- Mathematics --- Modern Cryptography --- Computational Complexity --- Hamming Distance --- Shannon Theorem --- Source Coding Theorem --- Optimal Code Theory --- Statistical Characteristics of Cryptosystem --- Elliptic Curve Public Key Cryptosystem --- Integer Lattice and Q-ary Lattice --- NTRU Cryptosystem and Ajtai/Dwork Cryptosystem