Factoring integers using SIMD sieves 1st Edition by Brandon Dixon, Arjen K Lenstra ISBN

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Author: Brandon Dixon, Arjen K Lenstra

“Factoring Integers Using SIMD Sieves” by Brandon Dixon and Arjen K. Lenstra is a research paper/book that explores advanced methods of factoring large integers, specifically focusing on the use of SIMD (Single Instruction, Multiple Data) parallelism in sieving algorithms. The goal of this work is to improve the efficiency and performance of integer factorization, which is a crucial area in cryptography, especially in the context of RSA encryption.

Factoring integers using SIMD sieves 1st Table of contents:

• Related Work

  • Review of Previous Factorization Algorithms (e.g., Quadratic Sieve, General Number Field Sieve)
  • SIMD in Computational Number Theory
  • Previous Attempts to Apply SIMD to Sieving Algorithms

• Theoretical Foundation of SIMD Sieves

  • Overview of Sieving Algorithms
  • SIMD Architecture and How It Enhances Sieving
  • Mathematical Models for SIMD Sieving
  • Performance Analysis of SIMD in Integer Factorization

• Design of the SIMD Sieving Algorithm

  • Algorithmic Approach for SIMD-Optimized Sieving
  • Pseudocode for SIMD Sieving Algorithm
  • Key Optimizations in SIMD Implementation
  • Complexity Analysis of the Proposed Approach

• Implementation

  • Hardware and Software Setup for SIMD Sieving
  • SIMD Libraries and Tools Used
  • Code Design and Parallelism Strategies
  • Practical Considerations for Scaling the Algorithm

• Experimental Results

  • Experimental Setup for Testing the SIMD Sieving Algorithm
  • Benchmarking and Performance Metrics
  • Comparison with Traditional Sieving Methods
  • Speedup and Efficiency Improvements
  • Scalability with Increasing Integer Size

• Applications in Cryptography

  • Potential Impact of SIMD-Accelerated Factorization on RSA Security
  • How Faster Factorization Affects Cryptographic Protocols
  • Countermeasures and Mitigations for SIMD-Enhanced Factorization

• Challenges and Future Work

  • Technical and Computational Challenges in SIMD Sieving
  • Potential Improvements for Even Larger Integer Factorizations
  • Integrating SIMD Sieves with Other Factorization Techniques
  • Future Research Directions

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