Outlines theory and techniques of calculus, emphasizing strong understanding of concepts, and the basic principles of analysis. Reviews elementary and intermediate calculus and features discussions of elementary-point set theory, and properties of continuous functions.
Appropriate for all graduate-level and advanced undergraduate courses in cryptography and related mathematical fields. Modern Cryptography is an indispensable resource for every advanced student of cryptography who intends to implement strong security in real-world applications. Leading HP security expert Wenbo Mao explains why conventional crypto schemes, protocols, and systems are profoundly vulnerable, introducing both fundamental theory and real-world attacks. Next, he shows how to implement crypto systems that are truly "fit for application," and formally demonstrate their fitness. He begins by reviewing the foundations of cryptography: probability, information theory, computational complexity, number theory, algebraic techniques, and more. He presents the "ideal" principles of authentication, comparing them with real-world implementation. Mao assesses the strength of IPSec, IKE, SSH, SSL, TLS, Kerberos, and other standards, and offers practical guidance on designing stronger crypto schemes and using formal methods to prove their security and efficiency.Finally, he presents an in-depth introduction to zero-knowledge protocols: their characteristics, development, arguments, and proofs. Mao relies on practical examples throughout, and provides all the mathematical background students will need.
Number theory, an ongoing rich area of mathematical exploration, is noted for its theoretical depth, with connections and applications to other fields from representation theory, to physics, cryptography, and more. While the forefront of number theory is replete with sophisticated and famous open problems, at its foundation are basic, elementary ideas that can stimulate and challenge beginning students. This lively introductory text focuses on a problem-solving approach to the subject.
Terminology: Theory, methods and applications addresses language specialists, terminologists, and all those who take an interest in socio-political and technical aspects of Terminology.