{"ID":2898362,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.00840","arxiv_id":"2508.00840","title":"Towards Enhanced Quantum Resistance for RSA via Constrained Rényi Entropy Optimization: A Theoretical Framework for Backward-Compatible Cryptography","abstract":"The advent of quantum computing poses a critical threat to RSA cryptography, as Shor's algorithm can factor integers in polynomial time. While post-quantum cryptography standards offer long-term solutions, their deployment faces significant compatibility and infrastructure challenges. This paper proposes the Constrained Rényi Entropy Optimization (CREO) framework, a mathematical approach to potentially enhance the quantum resistance of RSA while maintaining full backward compatibility. By constraining the proximity of RSA primes ($|p-q| \u003c γ\\sqrt{pq}$), CREO reduces the distinguishability of quantum states in Shor's algorithm, as quantified by Rényi entropy. Our analysis demonstrates that for a $k$-bit modulus with $γ= k^{-1/2+ε}$, the number of quantum measurements required for reliable period extraction scales as $Ω(k^{2+ε})$, compared to $\\mathcal{O}(k^3)$ for standard RSA under idealized assumptions. This represents a systematic increase in quantum resource requirements. The framework is supported by constructive existence proofs for such primes using prime gap theorems and establishes conceptual security connections to lattice-based problems. CREO provides a new research direction for exploring backward-compatible cryptographic enhancements during the extended transition to post-quantum standards, offering a mathematically grounded pathway to harden widely deployed RSA infrastructure without requiring immediate protocol or infrastructure replacement.","short_abstract":"The advent of quantum computing poses a critical threat to RSA cryptography, as Shor's algorithm can factor integers in polynomial time. While post-quantum cryptography standards offer long-term solutions, their deployment faces significant compatibility and infrastructure challenges. This paper proposes the Constraine...","url_abs":"https://arxiv.org/abs/2508.00840","url_pdf":"https://arxiv.org/pdf/2508.00840v3","authors":"[\"Ruopengyu Xu\",\"Chenglian Liu\"]","published":"2025-07-04T11:18:34Z","proceeding":"cs.CR","tasks":"[\"cs.CR\",\"math.NT\",\"quant-ph\"]","methods":"[]","has_code":false}