In Mathematical Foundations of Public Key Cryptography, the authors combine the result of greater than two decades of analysis and educating event to assist scholars bridge the space among math thought and crypto perform. The booklet presents a theoretical constitution of primary quantity thought and algebra wisdom helping public-key cryptography.

Rather than just combining quantity idea and glossy algebra, this textbook positive aspects the interdisciplinary features of cryptography―revealing the integrations of mathematical theories and public-key cryptographic functions. 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 functions of mathematical theories in cryptographic algorithms.

Supplying a continuing integration of cryptography and arithmetic, the ebook contains insurance of straight forward quantity concept; algebraic constitution and attributes of workforce, ring, and box; cryptography-related computing complexity and easy algorithms, in addition to lattice and basic equipment of lattice cryptanalysis.

The textual content comprises eleven chapters. easy idea and instruments of simple quantity thought, equivalent to congruences, primitive roots, residue sessions, and endured fractions, are coated in Chapters 1-6. the elemental options of summary algebra are brought in Chapters 7-9, the place 3 easy algebraic buildings of teams, jewelry, and fields and their homes are defined.

Chapter 10 is set computational complexities of numerous similar mathematical algorithms, and tough difficulties corresponding to integer factorization and discrete logarithm. bankruptcy eleven offers the fundamentals of lattice conception and the lattice foundation relief algorithm―the LLL set of rules and its program 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 safeguard courses. it's also a terrific reference e-book for cryptography execs seeking to grasp public-key cryptography.

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