Analysis and Design of Stream Ciphers

1. Introduction.- 2. Stream Ciphers.- 2.1. Theoretical versus Practical Security.- 2.2. The Key Stream Generator.- 2.3. The Synchronization (Problem) of Stream Ciphers.- 3. Algebraic Tools.- 3.1. Finite Fields and Polynomials.- 3.2. Linear Feedback Shift Registers (LFSRs) and Sequences.- 3.3. Minimal Polynomial and Traces.- 4. Random Sequences and Linear Complexity.- 5. Nonlinear Theory of Periodic Sequences.- 5.1. Nonlinear Operations on Phases of a Sequence with Irreducible Minimal Polynomial.- 5.2. Nonlinear Operations on Sequences with Distinct Minimal Polynomials.- 5.3. Correlation-Immunity of Memoryless Combining Functions.- 5.4. Summary and Conclusions.- 6. Multiple Speed: An Additional Parameter in Secure Sequence Generation.- 6.1. The Simulated Linear Feedback Shift Register.- 6.2. A Random Number Generator Suggested by a Linear Cipher Problem.- 6.2.1. The Random Sequence Generator.- 6.2.2. Analysis of the Random Sequence Generator.- 6.2.3. Extensions and Comments.- 7. The Knapsack as a Nonlinear Function.- 7.1. The Significance of the Knapsack for Secrecy Systems.- 7.2. Addition is a Cryptographically Useful Function.- 7.3. The Knapsack in GF(2)-Arithmetic.- 8. The Hard Knapsack Stream Cipher.- 8.1. System Description.- 8.2. Analysis of the Knapsack Stream Cipher.- 8.3. Conclusions and Design Considerations.- 8.4. Simulation Results of Small Scale Knapsack Stream Ciphers.- 9. Nonlinear Combining Functions with Memory.- 9.1. Correlation Immunity.- 9.2. The Summation Principle.- 9.3. Summary and Conclusions.- Literature References.