Cryptanalysis of the RC4 Stream Cipher using Evolutionary ...

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Contents 1 Introduction 1 1.1 RC4 State Register . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Thesis Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Background 7 2.1 The Study of Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2 Cryptanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 RC4 Stream Cipher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 Key Scheduling Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Pseudo-Random Generation Algorithm . . . . . . . . . . . . . . . . 11 2.2.3 Data Encryption and Decryption . . . . . . . . . . . . . . . . . . . . 12 iv
2.3 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1 Chromosome Representation . . . . . . . . . . . . . . . . . . . . . . 16 2.3.2 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.3 Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.4 Mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.2 Particle Representation . . . . . . . . . . . . . . . . . . . . . . . . . 21 3 Literature Review 22 3.1 Review of RC4 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1.1 Successful Cryptanalysis of RC4 . . . . . . . . . . . . . . . . . . . . 23 3.1.2 Other Methods for Cryptanalysis of RC4 . . . . . . . . . . . . . . . 25 3.2 Review of Evolutionary Algorithms Literature . . . . . . . . . . . . . . . . . 28 3.2.1 Cryptanalysis Using Genetic Algorithms . . . . . . . . . . . . . . . . 28 3.2.2 Cryptanalysis Using Particle Swarm Optimization . . . . . . . . . . 30 4 Methodology 32 4.1 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 v
Page 1 and 2: Cryptanalysis of the RC4 Stream Cip
Page 3: Acknowledgements First and foremost
Page 7 and 8: 5.2 Particle Swarm Optimization Res
Page 9 and 10: List of Figures 2.1 Single-point cr
Page 11 and 12: Chapter 1 Introduction Over the pas
Page 13 and 14: guage to communicate as well as a s
Page 15 and 16: the ability to encrypt and decrypt
Page 17 and 18: Chapter 2 Background Several topics
Page 19 and 20: 2.1.2 Cryptanalysis The science of
Page 21 and 22: 2.2.1 Key Scheduling Algorithm The
Page 23 and 24: Decryption can therefore be written
Page 25 and 26: 7. Finally, the population is repla
Page 27 and 28: 2.3.3 Crossover Crossover is the re
Page 29 and 30: 2.4 Particle Swarm Optimization Par
Page 31 and 32: Algorithm 4 Particle Swarm Optimiza
Page 33 and 34: 3.1.1 Successful Cryptanalysis of R
Page 35 and 36: est proposed theoretical attack can
Page 37 and 38: try and diagnose the pseudo-random
Page 39 and 40: crypto system with very promising r
Page 41 and 42: amount of generations needed to sol
Page 43 and 44: 4.1 Problem When attacking the RC4
Page 45 and 46: 4.3 Proposed Solution This thesis p
Page 47 and 48: 4.5 Genetic Algorithm Representatio
Page 49 and 50: is to automatically carry over the
Page 51 and 52: The steps in which this algorithm o
Page 53 and 54: Figure 4.4: Example of the steps in
Page 55 and 56:
Algorithm 6 Inversion Mutation (Inv
Page 57 and 58:
4.6.1 Solution Representation To ma
Page 59 and 60:
Chapter 5 Evaluation In the followi
Page 61 and 62:
PMX was able to evolve a solution f
Page 63 and 64:
n non-adaptive mutation adaptive mu
Page 65 and 66:
5.2 Particle Swarm Optimization Res
Page 67 and 68:
of the SA showed that the best solu
Page 69 and 70:
Figure 5.6: Comparison of algorithm
Page 71 and 72:
We also found that for the state re
Page 73 and 74:
Chapter 7 Appendix A n = 6 Generati
Page 75 and 76:
Bibliography [1] Wafaa G Abd-Elmoni
Page 77 and 78:
[13] John J. Grefenstette. Optimiza
Page 79 and 80:
[29] Ilya Mironov. (Not So) Random
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