Binding/Format: Hardback
ISBN: 978-1-4398313-5-9
Publish Date: 31st January 2011
Pages: 300 pages
Series: Discrete Mathematics and Its Applications
This book is the first comprehensive volume on RC4, the most popular and widely deployed state-of-the-art software stream cipher algorithm. After the basic fundamentals of cryptography, the text provides substantial coverage of stream ciphers in general. Other topics covered include key scheduling, key recovery, WEP attacks, and keystream generation. The book also explores both LFSR and non-LFSR-based hardware stream ciphers as well as software stream ciphers. The techniques and analysis presented can be applied to many RC4-like stream ciphers that are based on arrays and modular addition. The authors provide end-of-chapter exercises along with a number of illustrative tables and figures.
Introduction to Cryptography
Stream Ciphers and RC4
Analysis of Key Scheduling
Key Recovery from State Information
WEP Attacks
Analysis of Keystream Generation
State Recovery from Keystream
Other Keystream-Based Attacks
Variants of RC4
Conclusion
Appendices
Bibliography
Index
This textbook presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory.
These topics are covered in 12 chapters and more than 200 solved exercises.
Clear, concise, and self-contained, this textbook may be used by undergraduate and graduate students, as well as highschool mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, this fascinating branch of mathematics.
Irrationality and Diophantine Approximation
Representations of Real Numbers by Infinite Series and Products
Continued Fractions
Regular Continued Fractions
Quadratic Fields and Diophantine Equations
Squares and Sums of Squares
Arithmetical Functions
Pade Approximants
Algebraic Numbers and Irrationality Measures
Number Fields
Ideals
Introduction to Transcendence Methods
Readership: Undergraduate and graduate students in mathematics, and high school mathematics teachers.
350pp (approx.) Pub. date: Scheduled Winter 2010
ISBN: 978-981-4307-45-1
ISBN: 978-981-4307-46-8(pbk)
This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The mathematical problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. While the depth of knowledge involved is not beyond the contents of the textbooks for graduate students, discovering the solution of the problems requires a deep understanding of the mathematical principles plus skilled techniques. For students, this book is a valuable complement to textbooks. Whereas for lecturers teaching graduate school mathematics, it is a helpful reference.
Algebra:
Linear Algebra
Group Theory
Ring Theory
Field and Galois Theory
Topology:
Point Set Topology
Homotopy Theory
Homology Theory
Differential Geometry:
Differential Geometry of Curves
Differential Geometry of Surfaces
Differential Geometry of Manifold
Real Analysis:
Measurability and Measure
Integral
Space of Integrable Functions
Differential
Miscellaneous Problems
Complex Analysis:
Analytic and Harmonic Functions
Geometry of Analytic Functions
Complex Integration
The Maximum Modulus and Argument Principles
Series and Normal Families
Partial Differential Equations:
General Theory
Elliptic Equations
Parabolic Equations
Hyperbolic Equations
Readership: PhD mathematics students and lecturers.
650pp (approx.) Pub. date: Scheduled Spring 2011
ISBN: 978-981-4304-95-5
ISBN: 978-981-4304-96-2(pbk)