Massively parallel elliptic curve factoring 1st edition by Dixon, Lenstra ISBN 3540564133 9783540564133

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Product details:

ISBN 10:     3540564133
ISBN 13: 978-3540564133
Author:         B. Dixon, A. K. Lenstra 

Massively parallel elliptic curve factoring 1st  Table of contents:

• Introduction

  • Overview of elliptic curve factoring.
  • Significance of elliptic curve methods in number theory and cryptography.
  • The role of massively parallel computation in optimizing elliptic curve factoring.

• Elliptic Curve Factoring Basics

  • Introduction to elliptic curves over finite fields.
  • The elliptic curve factorization method: Theorems and key concepts.
  • Group structure of elliptic curves and their relevance to factoring.

• Mathematical Foundations of Elliptic Curve Factorization

  • Finite field arithmetic and elliptic curve operations.
  • Modular arithmetic in elliptic curve factorization.
  • Mathematical challenges and constraints in the elliptic curve factoring method.

• Elliptic Curve Factorization Algorithms

  • Basic elliptic curve factorization algorithm.
  • Pollard’s rho method for elliptic curve factoring.
  • Generalizations and optimizations of elliptic curve methods.
  • Comparison with traditional integer factorization algorithms.

• Parallel Algorithms for Elliptic Curve Factoring

  • Introduction to parallel computing in number-theoretic algorithms.
  • Parallelization strategies for elliptic curve factorization.
  • Divide-and-conquer techniques and their application to elliptic curves.
  • Parallel Pollard’s rho method and its extensions.

• Massively Parallel Architectures for Factoring

  • Utilizing multi-core CPUs for elliptic curve factoring.
  • Graphics Processing Units (GPUs) for parallel factorization.
  • FPGA-based architectures for accelerating elliptic curve factoring.
  • Distributed computing for large-scale elliptic curve factorization.

• Optimization Techniques for Parallel Elliptic Curve Factorization

  • Efficient memory management and data locality for parallel implementations.
  • Load balancing and task scheduling in massively parallel systems.
  • Communication strategies for distributed elliptic curve factoring.

• Implementation on Supercomputers and Cloud Systems

  • Large-scale implementations of elliptic curve factoring on supercomputers.
  • Cloud-based parallel computation for factorization tasks.
  • Case studies and performance benchmarks.

• Applications in Cryptanalysis

  • Breaking RSA and elliptic curve cryptography (ECC) with elliptic curve factorization.
  • Potential impacts on modern cryptographic systems.
  • Real-world cryptographic vulnerabilities exposed by elliptic curve factoring.

• Challenges in Massively Parallel Elliptic Curve Factoring

  • Scalability challenges for large elliptic curve factorizations.
  • Computational complexity and parallel overhead.
  • Issues in maintaining synchronization across distributed systems.

• Future Directions and Emerging Technologies

  • Quantum computing’s potential impact on elliptic curve factorization.
  • Neuromorphic computing and its potential for number-theoretic algorithms.
  • Advancements in algorithmic design for better parallelization.

• Conclusion

  • Recap of the importance of massively parallel elliptic curve factoring.
  • Key findings and advancements in parallelization for factorization methods.
  • Future prospects in both cryptographic applications and computational number theory.

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