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oapen-20.500.12657-601952024-03-27T14:14:53Z Modern Cryptography Volume 2 Zheng, Zhiyong Tian, Kun Liu, Fengxia Post-Quantum Cryptography Gauss Lattice Reduction Learning With Errors FHE Fourier transform Ideal lattice NTRU Smoothing parameters Discrete Gaussian measure thema EDItEUR::K Economics, Finance, Business and Management::KC Economics::KCB Macroeconomics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics 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. 2022-12-13T12:41:03Z 2022-12-13T12:41:03Z 2023 book ONIX_20221213_9789811976445_48 9789811976445 https://library.oapen.org/handle/20.500.12657/60195 eng Financial Mathematics and Fintech application/pdf n/a 978-981-19-7644-5.pdf https://link.springer.com/978-981-19-7644-5 Springer Nature Springer 10.1007/978-981-19-7644-5 10.1007/978-981-19-7644-5 6c6992af-b843-4f46-859c-f6e9998e40d5 e6574b1a-f99f-4ac4-8c3f-0aa4c3d0c4f6 9789811976445 Springer 191 Singapore [...] Renmin University of China RUC open access
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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.
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