Factoring Estimates for a 1024-Bit RSA Modulus 1st edition by Arjen Lenstra, Eran Tromer, Adi Shamir, Wil Kortsmit, Bruce Dodson, James Hughes, Paul Leyland ISBN 3540205920 9783540205920

Factoring Estimates for a 1024-Bit RSA Modulus 1st edition by Arjen Lenstra, Eran Tromer, Adi Shamir, Wil Kortsmit, Bruce Dodson, James Hughes, Paul Leyland – Ebook PDF Instant Download/Delivery. 3540205920, 978-3540205920
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Product details:

ISBN 10:       3540205920
ISBN 13: 978-3540205920
Author:         Arjen Lenstra, Eran Tromer, Adi Shamir, Wil Kortsmit, Bruce Dodson, James Hughes, Paul Leyland
 

Factoring Estimates for a 1024-Bit RSA Modulus 1st Table of contents:

• Introduction

  • 1.1 Background on RSA Cryptography
  • 1.2 The Importance of Factoring in Cryptography
  • 1.3 Scope of the Paper
  • 1.4 Organization of the Paper

• Preliminaries

  • 2.1 RSA Cryptosystem Overview
  • 2.2 Definition and Characteristics of a 1024-Bit RSA Modulus
  • 2.3 Common Algorithms for Integer Factorization
    • 2.3.1 Trial Division
    • 2.3.2 Pollard’s Rho Algorithm
    • 2.3.3 Quadratic Sieve
    • 2.3.4 General Number Field Sieve (GNFS)

• Factoring 1024-Bit Moduli

  • 3.1 General Challenges in Factoring Large Numbers
  • 3.2 Progress in Factoring 1024-Bit RSA Moduli
    • 3.2.1 Historical Attempts and Their Results
    • 3.2.2 Milestones in Factoring 1024-Bit Numbers
  • 3.3 Computational Complexity of Factoring Large Numbers
    • 3.3.1 Complexity of GNFS for 1024-Bit Moduli
    • 3.3.2 Time Estimates Based on Current Algorithms

• Advances in Factoring Techniques

  • 4.1 General Number Field Sieve (GNFS)
    • 4.1.1 Overview and Steps of GNFS
    • 4.1.2 Efficiency Improvements for 1024-Bit Moduli
  • 4.2 Quantum Computing and its Impact on Factoring
    • 4.2.1 Shor’s Algorithm and Quantum Computers
    • 4.2.2 Potential Quantum Threat to RSA
  • 4.3 New Algorithms and Approaches in Integer Factorization
    • 4.3.1 Elliptic Curve Factorization
    • 4.3.2 Special-Purpose Algorithms for RSA Moduli

• Empirical Estimates and Computational Results

  • 5.1 Estimating Time Complexity for Factoring a 1024-Bit Modulus
  • 5.2 Results from Recent Factoring Efforts
    • 5.2.1 Successful Factoring Attempts
    • 5.2.2 Computational Resources and Time Analysis
  • 5.3 Future Projections for Factoring 1024-Bit Moduli
    • 5.3.1 Expected Timeline for Factoring Based on Current Progress
    • 5.3.2 Impact of Technological Advances on Factoring Estimates

• Security Implications of Factoring 1024-Bit Moduli

  • 6.1 Impact on RSA-Based Cryptosystems
  • 6.2 Evaluating the Security of 1024-Bit RSA in the Context of Modern Cryptanalysis
  • 6.3 Transitioning to Larger Key Sizes: 2048-Bit RSA and Beyond
  • 6.4 Security Recommendations for RSA in the Post-Quantum Era

• Future Research Directions

  • 7.1 Improvements in Classical Factorization Algorithms
  • 7.2 The Role of Quantum Computing in Cryptanalysis
  • 7.3 Exploring Alternative Cryptographic Systems Resistant to Factoring
  • 7.4 Theoretical Bounds on the Difficulty of Factoring Large Moduli

• Conclusion

  • 8.1 Summary of Key Findings
  • 8.2 Long-Term Security of RSA
  • 8.3 Final Thoughts on the Feasibility of Factoring 1024-Bit Moduli

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