A Hard Limit on How Much Secret Data Power Traces Can Leak

In the paper's words

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.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Using the entropic uncertainty relation with quantum memory [2] and the mutual‑information formulation of information exclusion [3], we derive an explicit bound $$ I\bigl(\text{additive trace};v(n)\bigr)\leq 0.6\ \text{bits}, $$ where 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].

   from Abstract

2. Numerical evaluation of the bound yielding $I\leq0.6$ bits, based on the complementarity constant $c=\tfrac12$ from an entanglement‑assisted experiment [4] and a 40 % GUP correction reported for high‑energy scattering [1] (Section 4).

   from 1. Introduction

3. Converting to bits using $\log_{2}e$ gives $$ S_{\max}^{\text{bits}} = \frac{2\pi}{\ln 2}\approx \frac{6.2832}{0.6931}=9.06\ \text{bits}. \tag{10} $$ Because the GUP analysis of [1] reports a 40 % reduction in observable deviations at $200$ GeV, we apply the same factor to the holographic bound: $$ S_{\text{eff}}^{\text{bits}} = \eta\,S_{\max}^{\text{bits}} = 0.60\times9.06 = 5.44\ \text{bits}. \tag{11} $$ This coarse holographic ceiling is far above the entropic‑uncertainty ceiling (0.60 bits) and therefore does not tighten the result; however, it demonstrates that the GUP‑induced correction is consistent across disparate information‑theoretic contexts.

   from 3. Incorporating holographic‑type entropy limits (GUP‑induced)

4. Data acquisition: Sampling rate must resolve the additive trace at the clock frequency (e.g., $\ge$ 100 MS/s).

   from 8. Practical Implications and Engineering Pathways

5. Phenomenological analysis of Compton scattering shows deviations from the Standard Model up to $40\%$ at energies around $200\,$GeV for the positive $2\sigma$ bound [1, § 4].

   from 2. Background and Related Work

6. We use this $40\%$ figure as a multiplicative reduction factor on information‑theoretic bounds.

   from 2. Background and Related Work

How it is done

1. Using the entropic uncertainty relation with quantum memory [2] and the mutual‑information formulation of information exclusion [3], we derive an explicit bound $$ I\bigl(\text{additive trace};v(n)\bigr)\leq 0.6\ \text{bits}, $$ where 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].

   from Abstract

2. If a theoretical bound existed, designers could certify that any additive observation leaks at most a fixed number of bits, regardless of implementation details.

   from 1. Introduction

3. Phenomenological analysis of Compton scattering shows deviations from the Standard Model up to $40\%$ at energies around $200\,$GeV for the positive $2\sigma$ bound [1, § 4].

   from 2. Background and Related Work

4. We model the side‑channel trace as a binary measurement $R$ performed on a classical register $A$ that stores the additive result $m=a+b$.

   from 3. Methods

What would falsify it

1. The complementarity constant $c=\tfrac12$ is taken from a specific Pauli‑observable experiment [4]; other measurement pairs may yield larger $c$, weakening the bound.

   from Limitations

2. The information‑exclusion inequality is applied with $I(S\!:\!B)=0$, an optimistic assumption that the complementary observable leaks nothing.

   from Limitations

3. If an experiment measuring the mutual information between an additive side‑channel trace and the valuation vector of a secret integer yields a value greater than $0.60$ bits , the present theoretical framework is falsified.

   from Falsification Criterion

Where the claim stops

1. Conditional min‑entropy $H_{\min}(AB)=0$ assumes maximal correlation between the additive result and the secret; real systems may have higher entropy, which would tighten the bound further.

   from Limitations

2. The information‑exclusion inequality is applied with $I(S\!:\!B)=0$, an optimistic assumption that the complementary observable leaks nothing.

   from Limitations

3. By interpreting the abc conjecture through the lens of entropic uncertainty relations, we have derived a concrete, provable upper bound of $0.60$ bits on the mutual information between additive side‑channel traces and the prime‑factor valuation vector of a secret integer.

   from 9. Conclusion

Where to read

1. Abstract161 words · 1 min
2. 1. Introduction247 words · 1 min
3. 2. Background and Related Work331 words · 1 min
4. 3. Methods190 words · 1 min
5. 4. Analysis170 words · 1 min
6. 5. Results85 words · 1 min
7. 6. Extended Derivations and Worked Examples1,574 words · 7 min
8. 7. Discussion212 words · 1 min
9. 8. Practical Implications and Engineering Pathways329 words · 1 min
10. 9. Conclusion89 words · 1 min
11. Provenance and AI Involvement225 words · 1 min