Massively parallel computation of discrete logarithms 1st edition by Daniel Gordont, Kevin McCurley ISBN 3540573401 9783540573401

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ISBN 10:      3540573401
ISBN 13: 978-3540573401 
Author:         Daniel M. Gordont, Kevin S. McCurley

Massively parallel computation of discrete logarithms 1st Table of contents:

1. Introduction

   • Overview of discrete logarithms and their importance in cryptography.
   • The role of massively parallel computation in solving discrete logarithms.
   • Applications and challenges in cryptographic systems.

2. Fundamentals of Discrete Logarithms

   • Definition and properties of discrete logarithms.
   • Group theory and its relevance to discrete logarithms.
   • Key concepts: cyclic groups, field sizes, and modular arithmetic.

3. Cryptographic Applications of Discrete Logarithms

   • RSA and Diffie-Hellman key exchange.
   • ElGamal encryption and digital signatures.
   • Security implications of the discrete logarithm problem.

4. Parallel Computation Models

   • Introduction to parallel computing and its types (shared memory, distributed memory, hybrid).
   • Parallel algorithms for computational number theory.
   • Hardware considerations: GPUs, FPGAs, and multi-core processors.

5. Algorithms for Computing Discrete Logarithms

   • Classical algorithms: Baby-step Giant-step, Pollard’s rho, and others.
   • Optimized algorithms for parallel execution.
   • Trade-offs between memory usage and computational efficiency.

6. Massively Parallel Approaches to Discrete Logarithms

   • Divide-and-conquer techniques in parallel computation.
   • Parallelization of number-theoretic algorithms.
   • Parallel Pollard’s rho algorithm and its variations.
   • SIMD (Single Instruction Multiple Data) and MIMD (Multiple Instruction Multiple Data) approaches.

7. GPU and FPGA-based Parallelization

   • Utilization of GPU architecture for discrete logarithms.
   • FPGA-based parallel algorithms: design and implementation.
   • Comparison of GPU and FPGA in parallel discrete logarithm computation.

8. Optimization Techniques

   • Memory management and data locality in parallel algorithms.
   • Load balancing and task scheduling for parallel computations.
   • Optimizing communication in distributed parallel systems.

9. Performance Analysis

   • Benchmarking parallel discrete logarithm algorithms.
   • Performance evaluation on different hardware platforms.
   • Real-world case studies and performance metrics.

10. Applications in Cryptanalysis

• Solving discrete logarithms in real-world cryptographic systems.
• Attacks on elliptic curve cryptography (ECC) and RSA.
• Practical challenges in breaking cryptographic protocols using parallel computation.

11. Challenges and Future Directions

• Scalability issues in parallel discrete logarithm computation.
• Future hardware developments (quantum computing, neuromorphic computing).
• Potential improvements in algorithm design for large-scale computations.

12. Conclusion

• Summary of key findings in massively parallel computation of discrete logarithms.
• Importance of parallelization in advancing cryptographic research.

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