Number Field Sieve Cryptanalysis Algorithms for Most Efficient Prime Factorization on Composites

Future-Proof Your Career: Let's Help You Evolve Beyond AI! Google AI Podcasts on We Build Quantum Minds for Quantum Uncertainty Beyond AI-GenAI: Podcast 1. https://youtu.be/96qsSnn4aFk Podcast 2. https://youtu.be/QH4OJukSW9k Podcast 3. https://youtu.be/CyYt1PbFAsA

"Data is Profoundly Dumb." -- Judea Pearl

“Consciousness is not a Computation” – Roger Penrose

ChatGPT: Quantum Generative AI Pioneer: https://tinyurl.com/QuantumGenAI .

2024: New York State Capitol Conference Presentation: "Beyond GenAI: HAI: How to Ensure You Are Not Replaced by GenAI-LLMs" : Save 99% Of Your Search-Learning Time-Costs With Our "Generative AI Meta Search Engine"™, World's First Augmented-AI Generative Browser and MetaGenAI-MetaSearchEngine: We Create the Digital Future™. You Can Too! Let's Show You How!: New York State Government: "Join Dr. Yogi Malhotra to get up to speed on Cloud Technology." YM-ABC™: 30-Years Ahead on Digital Artificial Intelligence-Human Intelligence: - Dr. Yogesh Malhotra "Yogi" :

📚 AWS-Quantum Valley Building Future of AI-Quantum Networks

📚 AWS-Quantum Valley Building Event Driven Architectures for Quantum Uncertainty-Complexity

• MIT Computer Science & AI Lab Faculty-SME Expert: Human Centered Artificial Intelligence Pioneer: Inspired by John Holland 1995: R&D Ranked for Impact Among AI Nobel Laureates such as Herbert Simon

• Princeton-Goldman Sachs-JP Morgan Quantitative Finance & Trading Faculty-SME & Industry Expert: R&D Impact Among Finance Nobel Laureates such as Black-Scholes, Harry Markowitz, William Sharpe

• AWS Partner-New York State-Pentagon Cloud Computing Self-Adaptive Systems Expert: 30-Yr AI-Agility & Cyber-Resilience Engineering Self-Adaptive Complex Systems Practices, Technologies & Networks Pioneer

Research & Publications Archive - Download Full-Text Articles.

Download Full-Text: SSRN: https://ssrn.com/abstract=2553544

Abstract

The two fundamental axioms, Shannon’s Maxim and Kerckhoffs’s Principle, underlying the formulation of cryptography and encryption standards are analyzed to examine how they can be advanced in order to develop more robust encryption and cryptography mechanisms that can withstand the onslaught of attacks using increasingly sophisticated and efficient cryptanalysis algorithms such as NFS (Number Field Sieve).

Notes: Within four weeks of the original publication of this research report, Google announced its intent to switch from RSA-1024 to RSA-2048. The original report was published about two weeks before the revelation of the Snowden affair in the public media.

Keywords: Cryptography, Encryption, Shannon’s Maxim, Kerckhoffs's Principle, Cryptanalysis Algorithms, Special Purpose Factoring Algorithms (SPFA), General Purpose Factoring Algorithms (GPFA), Algebraic Number Field Sieves, Number Field Sieve Algorithms, Primes Factorization, RSA-1024, RSA-2048

JEL Classification: C00, C6, C60, C63, C69, C8, D8, D80, D81, D82, D83, D84, L63, L86, F1, G1, O3

Suggested Citation:

Malhotra, Yogesh, Number Field Sieve Cryptanalysis Algorithms for Most Efficient Prime Factorization on Composites (May 3, 2013). Available at SSRN: https://ssrn.com/abstract=2553544.