Stream Ciphers

In cryptography, ciphers is the technical term for encryption and decryption algorithms. They are an important sub-family that features high speed and easy implementation and are an essential part of wireless internet and mobile phones.

 

Unlike block ciphers, stream ciphers work on single bits or single words and need to maintain an internal state to change the cipher at each step. Typically stream ciphers can reach higher speeds than block ciphers but they can be more vulnerable to attack. Here, mathematics comes into play. Number theory, algebra and statistics are the key to a better understanding of stream ciphers and essential for an informed decision on their safety.

 

Since the theory is less developed, stream ciphers are often skipped in books on cryptography. This book fills this gap. It covers the mathematics of stream ciphers and its history, and also discusses many modern examples and their robustness against attacks.

 

Part I covers linear feedback shift registers, non-linear combinations of LFSRs, algebraic attacks and irregular clocked shift registers. Part II studies some special ciphers including the security of mobile phones, RC4 and related ciphers, the eStream project and the blum-blum-shub generator and related ciphers.

 

Stream Ciphers requires basic knowledge of algebra and linear algebra, combinatorics and probability theory and programming. Appendices in Part III help the reader with the more complicated subjects and provides the mathematical background needed. It covers, for example, complexity, number theory, finite fields, statistics, combinatorics. Stream Ciphers concludes with exercises and solutions and is directedtowards advanced undergraduate and graduate students in mathematics and computer science.

From the book reviews:

“This book focuses on the theory of stream ciphers and their applications. … Seldom does one find a summary of the theory of stream ciphers as systematic as that in the book under review. … the book covers completely the topic of attacks on stream ciphers … . This is a remarkable book and it should be of interest to scholars and students in discrete mathematics, cryptography, coding theory, computer security and related fields.” (Zhixiong Chen, Mathematical Reviews, March, 2014)

“Starting with a historical overview, this book gives a very good and comprehensive introduction to the mathematics of stream ciphers. … the book can serve as a valuable contribution to advanced undergraduate and graduate cryptography lectures in mathematics and computer science.” (Wilfried Meidl, zbMATH, Vol. 1288, 2014)

“Provide a coherent discussion of stream ciphers, how they are implemented, and how they can be attacked. … The material is presented in a logical fashion. The writing is clear and the mathematics well presented … . The book is intended for advanced undergraduate and graduate students of mathematics or computer science. … it presents the reader with applications in a number of important theoretical areas of mathematics and computer science, including graph theory, complexity and performance analysis of algorithms, P versus NP, and more.” (G. R. Mayforth, Computing Reviews, September, 2013)

The author's research includes: Discrete Mathematics/Combinatorics and its application. Finite Geometry (partial ovoids, spreads, etc.) Cryptography (e.g. Visual Cryptography) Complexity Theory (parallel automata) Coding Theory (geometric constructions, convolutional codes, etc.) Miscellaneous