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  "id": "oai:papers.qnfo.org:abc-uncertainty-principle-bounds-on-additive-leakage-of-prime-factors",
  "slug": "abc-uncertainty-principle-bounds-on-additive-leakage-of-prime-factors",
  "title": "abc‑Uncertainty Principle Bounds on Additive Leakage of Prime Factors",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Side‑channel attacks on cryptographic hardware often exploit additive traces such as power consumption or timing, which correlate with the prime‑factor structure of secret operands. Existing leakage models lack provable information‑theoretic ceilings linking an additive observation to the valuation vector v(n)=(v₂,v₃,v₅,dots) of a secret integer n. We bridge this gap by recasting the abc conjecture as an uncertainty‑principle‑type inequality. Using the entropic uncertainty relation with quantum memory [2] and the mutual‑information formulation of information exclusion [3], we derive an explicit bound Ibigl(additive trace;v(n)bigr)≤ 0.6 bits, where the numerical value follows from the complementarity constant c=1/2 (yielding log₂(1/c)=1 bit) and a 40 % GUP‑induced reduction reported for high‑energy processes [1]. The bound is tight under the worst‑case assumption of vanishing conditional min‑entropy. We discuss how this ceiling improves side‑channel‑resilience guarantees for RSA‑like primitives and outline a minimal experimental protocol that would falsify the result. The work thus provides a concrete, provable leakage limit grounded in number‑theoretic conjectures and quantum‑information uncertainty relations.",
  "abstract_markdown": "Side‑channel attacks on cryptographic hardware often exploit additive traces such as power consumption or timing, which correlate with the prime‑factor structure of secret operands. Existing leakage models lack provable information‑theoretic ceilings linking an additive observation to the valuation vector $v(n)=(v_2,v_3,v_5,\\dots)$ of a secret integer $n$. We bridge this gap by recasting the abc conjecture as an uncertainty‑principle‑type inequality. Using the entropic uncertainty relation with quantum memory [2] and the mutual‑information formulation of information exclusion [3], we derive an explicit bound  \n\\[\nI\\bigl(\\text{additive trace};v(n)\\bigr)\\leq 0.6\\ \\text{bits},\n\\]  \nwhere the numerical value follows from the complementarity constant $c=\\tfrac12$ (yielding $\\log_2(1/c)=1$ bit) and a 40 % GUP‑induced reduction reported for high‑energy processes [1]. The bound is tight under the worst‑case assumption of vanishing conditional min‑entropy. We discuss how this ceiling improves side‑channel‑resilience guarantees for RSA‑like primitives and outline a minimal experimental protocol that would falsify the result. The work thus provides a concrete, provable leakage limit grounded in number‑theoretic conjectures and quantum‑information uncertainty relations.",
  "date": "2026-10-20",
  "first_published": "2026-10-20",
  "last_revised": "2026-10-20T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/abc-uncertainty-principle-bounds-on-additive-leakage-of-prime-factors",
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  "version_url": "https://papers.qnfo.org/papers/abc-uncertainty-principle-bounds-on-additive-leakage-of-prime-factors/v/1.0.0",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "abc‑Uncertainty Principle Bounds on Additive Leakage of Prime Factors"
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    "publicationYear": "2026",
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        "description": "Side‑channel attacks on cryptographic hardware often exploit additive traces such as power consumption or timing, which correlate with the prime‑factor structure of secret operands. Existing leakage models lack provable information‑theoretic ceilings linking an additive observation to the valuation vector v(n)=(v₂,v₃,v₅,dots) of a secret integer n. We bridge this gap by recasting the abc conjecture as an uncertainty‑principle‑type inequality. Using the entropic uncertainty relation with quantum memory [2] and the mutual‑information formulation of information exclusion [3], we derive an explicit bound Ibigl(additive trace;v(n)bigr)≤ 0.6 bits, where the numerical value follows from the complementarity constant c=1/2 (yielding log₂(1/c)=1 bit) and a 40 % GUP‑induced reduction reported for high‑energy processes [1]. The bound is tight under the worst‑case assumption of vanishing conditional min‑entropy. We discuss how this ceiling improves side‑channel‑resilience guarantees for RSA‑like primitives and outline a minimal experimental protocol that would falsify the result. The work thus provides a concrete, provable leakage limit grounded in number‑theoretic conjectures and quantum‑information uncertainty relations.",
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