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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.
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Keywords
- applied mathematics
- Computational complexity
- Computer science
- Computing & information technology
- Economics, finance, business & management
- Elliptic Curve Public Key Cryptosystem
- Finance
- Finance & accounting
- Hamming distance
- Integer Lattice and Q-ary Lattice
- Mathematical theory of computation
- Mathematics
- Mathematics & science
- Modern Cryptography
- NTRU Cryptosystem and Ajtai/Dwork Cryptosystem
- Optimal Code Theory
- Shannon Theorem
- Source Coding Theorem
- Statistical Characteristics of Cryptosystem
- thema EDItEUR::K Economics, Finance, Business and Management::KF Finance and accounting::KFF Finance and the finance industry
- thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics
- thema EDItEUR::U Computing and Information Technology::UY Computer science::UYA Mathematical theory of computation
Links
DOI: 10.1007/978-981-19-0920-7Editions