In Mathematical Foundations of Public Key Cryptography, the authors combine the result of greater than twenty years of study and instructing adventure to assist scholars bridge the distance among math conception and crypto perform. The ebook presents a theoretical constitution of primary quantity idea and algebra wisdom helping public-key cryptography.
Rather than just combining quantity idea and smooth algebra, this textbook positive factors the interdisciplinary features of cryptography―revealing the integrations of mathematical theories and public-key cryptographic purposes. Incorporating the complexity concept of algorithms all through, it introduces the fundamental quantity theoretic and algebraic algorithms and their complexities to supply a initial figuring out of the purposes of mathematical theories in cryptographic algorithms.
Supplying a continuing integration of cryptography and arithmetic, the ebook contains insurance of basic quantity thought; algebraic constitution and attributes of staff, ring, and box; cryptography-related computing complexity and easy algorithms, in addition to lattice and primary equipment of lattice cryptanalysis.
The textual content comprises eleven chapters. uncomplicated concept and instruments of trouble-free quantity concept, akin to congruences, primitive roots, residue sessions, and endured fractions, are lined in Chapters 1-6. the fundamental options of summary algebra are brought in Chapters 7-9, the place 3 easy algebraic constructions of teams, jewelry, and fields and their houses are defined.
Chapter 10 is ready computational complexities of a number of comparable mathematical algorithms, and tough difficulties resembling integer factorization and discrete logarithm. bankruptcy eleven provides the fundamentals of lattice idea and the lattice foundation aid algorithm―the LLL set of rules and its software within the cryptanalysis of the RSA algorithm.
Containing a few workouts on key algorithms, the ebook is acceptable to be used as a textbook for undergraduate scholars and first-year graduate scholars in details defense courses. it's also an incredible reference ebook for cryptography execs seeking to grasp public-key cryptography.
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