By Xiaoyun Wang,Guangwu Xu,Mingqiang Wang,Xianmeng Meng
In Mathematical Foundations of Public Key Cryptography, the authors combine the result of greater than two decades of study and educating adventure to assist scholars bridge the space among math conception and crypto perform. The e-book presents a theoretical constitution of basic quantity concept and algebra wisdom helping public-key cryptography.
Rather than just combining quantity conception and glossy algebra, this textbook positive factors the interdisciplinary features of cryptography—revealing the integrations of mathematical theories and public-key cryptographic functions. Incorporating the complexity thought of algorithms all through, it introduces the fundamental quantity theoretic and algebraic algorithms and their complexities to supply a initial figuring out of the functions of mathematical theories in cryptographic algorithms.
Supplying a unbroken integration of cryptography and arithmetic, the publication contains assurance of hassle-free quantity conception; algebraic constitution and attributes of workforce, ring, and box; cryptography-related computing complexity and uncomplicated algorithms, in addition to lattice and basic tools of lattice cryptanalysis.
The textual content contains eleven chapters. uncomplicated concept and instruments of simple quantity concept, equivalent to congruences, primitive roots, residue periods, and persevered fractions, are coated in Chapters 1-6. the fundamental strategies of summary algebra are brought in Chapters 7-9, the place 3 uncomplicated algebraic constructions of teams, earrings, and fields and their houses are defined.
Chapter 10 is ready computational complexities of a number of comparable mathematical algorithms, and difficult difficulties similar to integer factorization and discrete logarithm. bankruptcy eleven offers the fundamentals of lattice concept and the lattice foundation aid algorithm—the LLL set of rules and its software within the cryptanalysis of the RSA algorithm.
Containing a few routines on key algorithms, the e-book is appropriate to be used as a textbook for undergraduate scholars and first-year graduate scholars in details safety courses. it's also a great reference ebook for cryptography pros seeking to grasp public-key cryptography.
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Additional resources for Mathematical Foundations of Public Key Cryptography
Mathematical Foundations of Public Key Cryptography by Xiaoyun Wang,Guangwu Xu,Mingqiang Wang,Xianmeng Meng