RC4 Stream Cipher and Its Variants (Hardback) book cover

RC4 Stream Cipher and Its Variants

By Goutam Paul, Subhamoy Maitra

© 2012 – CRC Press

311 pages | 12 B/W Illus.

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pub: 2011-11-16
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RC4 Stream Cipher and Its Variants is the first book to fully cover the popular software stream cipher RC4. With extensive expertise in stream cipher cryptanalysis and RC4 research, the authors focus on the analysis and design issues of RC4. They also explore variants of RC4 and the eSTREAM finalist HC-128.

After an introduction to the vast field of cryptology, the book reviews hardware and software stream ciphers and describes RC4. It presents a theoretical analysis of RC4 KSA, discussing biases of the permutation bytes toward secret key bytes and absolute values. The text explains how to reconstruct the secret key from known state information and analyzes the RC4 PRGA in detail, including a sketch of state recovery attacks. The book then describes three popular attacks on RC4: distinguishing attacks, Wired Equivalent Privacy (WEP) protocol attacks, and fault attacks. The authors also compare the advantages and disadvantages of several variants of RC4 and examine stream cipher HC-128, which is the next level of evolution after RC4 in the software stream cipher paradigm. The final chapter emphasizes the safe use of RC4.

With open research problems in each chapter, this book offers a complete account of the most current research on RC4.


"This remarkable monograph is ‘the first one on RC4.’ The theory surrounding the development of RC4 is very helpful for the study of stream ciphers in general, as the authors say. The book will be of interest to scholars and students whose expertise lies in cryptography, applied mathematics, computer security, and so on."

—Zhixiong Chen, Mathematical Reviews, January 2013

"I am delighted to introduce the first complete book on RC4, the most popular and widely deployed software stream cipher. … This book contains not only the authors’ own research materials, but it has nicely assimilated the results of others to make it a complete treatise on RC4 and its variants. I believe this book will be widely accepted as an important research monograph by both the students and experienced researchers in the field of cryptology."

—From the Foreword by Bimal Roy, founder of the Cryptology Research Society of India and director of the Indian Statistical Institute

Table of Contents

Introduction to Cryptography

Etymology and Some Historical Facts

Primary Goals of Cryptography

Basic Terminology

Cryptographic Attack Models

Cryptographic Security

Private and Public Key Cryptosystems

Stream Ciphers and RC4

Introduction to Stream Ciphers

Attack Models for Stream Cipher Cryptanalysis

Hardware Stream Ciphers

Software Stream Ciphers

On Randomness and Pseudo-Randomness

Analysis of Key Scheduling

Bias of Permutation toward Secret Key

Non-Randomness of Permutation

Movement Frequency of Permutation Values

Key Collisions

Key Recovery from State Information

Reversibility of RC4 PRGA

Recovery through Solving Simultaneous Equations

Improvement by Difference Equations

Group of Key Bytes Approach

Byte by Byte Recovery

Bit by Bit Recovery

Bidirectional Key Search

Analysis of Keystream Generation

Finney Cycles

Glimpse Theorem

Biased Permutation Index Selection for the First Keystream Byte

Characterization of PRGA Evolution

Some Biases in First Keystream Byte toward Secret Key

More Biases in Many Keystream Bytes toward Secret Key

Exhaustive Enumeration of All Biases

State Recovery from Keystream

Distinguishing Attacks

A Theoretical Framework of Distinguishing Attacks

Distinguishers Based on Initial Keystream Bytes

Distinguishers Based on Any Stage of PRGA

WEP and WPA Attacks

RC4 in WEP and the Attack Principle

FMS Attack

Mantin’s Attack

Klein’s Attack

PTW and VX Attacks

RC4 in WPA and Related Attacks

Fault Attacks

Hoch and Shamir’s Attack

Impossible and Differential Fault Attacks

Fault Attack Based on Fork Model

Fault Attack with Pseudo-Random Index Stuck

Variants of RC4

Byte-Oriented Variants

Word-Oriented Variants

RC4-Based Hash


Stream Cipher HC-128

Description of HC-128

Linear Approximation of Feedback Functions

Distinguishing Attacks on HC-128

Collisions in h1, h2 and State Leakage in Keystream

Constructing Full-State Given Only Half-State Information

Design Modification with Respect to Known Observations


Safe Use of RC4

Appendix A: A Sample C Implementation of RC4

Appendix B: Verified Test Vectors of RC4



Research Problems are presented at the end of chapters 3-10.

About the Authors

Goutam Paul is an assistant professor in the Department of Computer Science and Engineering at Jadavpur University. Dr. Paul has published articles in numerous refereed journals, including Discrete Applied Mathematics, Journal of Mathematical Cryptology, and Designs, Codes and Cryptography. His research interests include cryptography, security, steganography, and combinatorial algorithms.

Subhamoy Maitra is a professor at the Indian Statistical Institute. Dr. Maitra has contributed extensively to many peer-reviewed journals, such as IEEE Transactions on Information Theory, Discrete Mathematics, and Designs, Codes and Cryptography. He is also on the editorial board of Cryptography and Communications: Discrete Structures, Boolean Functions and Sequences. His research interests include cryptographically significant Boolean functions, design and cryptanalysis of stream ciphers, analysis of RSA and factorization, and cryptanalysis of digital watermarking schemes.

About the Series

Discrete Mathematics and Its Applications

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Security / Cryptography
MATHEMATICS / Combinatorics