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.

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Zhiyong Zheng is Dean of School of Mathematics, Renmin University of China. He got Ph.D from Shandong University in 1991 and was awarded as Distinguished Paper Award (ICCM 2018), Qiu Shi Outstanding Young Scholar Award (1997), Distinguished Young Scholars (NSF, 1996). His research areas include Diophantine approximation, character sum, cryptography.

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