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Rivest, Shamir, and Adleman (RSA) algorithm remains foundational to securing digital communications, making it a significant cryptanalysis focus. This paper provides a comprehensive analysis of the current state of quantum cryptanalysis concerning RSA, focusing on \(n-\) bit factoring attacks and emerging quantum techniques. We highlight recent advancements in notable previous studies, especially regarding the practical conditions necessary for large-scale quantum attacks on RSA, including resource requirements. The paper summarizes recent advancements in classical and quantum methodologies, particularly regarding abstract qubit requirements, measurement depth, and Toffoli gate optimizations, while also presenting a proposed design for an improved Schonhage-Strassen algorithm in quantum environments. Furthermore, we assess advancements in multiplication optimization, state distillation, and qubit optimization. We present a comprehensive curve analysis that details the estimated space and time requirements for RSA factoring, offering significant insights into the viability and obstacles of prospective quantum cryptanalysis.

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RSA Quantum Cryptanalysis: A Thorough Exploration of n–Bit Attacks and Emerging Factoring Techniques

  • 会议论文

  • 发表日期：

    2025年

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  • Rini Wisnu Wardhani,
  • Dedy Septono Catur Putranto,
  • Howon Kim

摘要

Rivest, Shamir, and Adleman (RSA) algorithm remains foundational to securing digital communications, making it a significant cryptanalysis focus. This paper provides a comprehensive analysis of the current state of quantum cryptanalysis concerning RSA, focusing on \(n-\) bit factoring attacks and emerging quantum techniques. We highlight recent advancements in notable previous studies, especially regarding the practical conditions necessary for large-scale quantum attacks on RSA, including resource requirements. The paper summarizes recent advancements in classical and quantum methodologies, particularly regarding abstract qubit requirements, measurement depth, and Toffoli gate optimizations, while also presenting a proposed design for an improved Schonhage-Strassen algorithm in quantum environments. Furthermore, we assess advancements in multiplication optimization, state distillation, and qubit optimization. We present a comprehensive curve analysis that details the estimated space and time requirements for RSA factoring, offering significant insights into the viability and obstacles of prospective quantum cryptanalysis.