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arXiv:1707.09462 · Quantum Information Processing

Demonstration of the no-hiding theorem on the 5-Qubit IBM quantum computer in a category-theoretic framework

Amolak Ratan Kalra, Navya Gupta, Bikash K. Behera, Shiroman Prakash, Prasanta Kumar Panigrahi

Published Apr 22, 2019• 22 citations
arXivHTMLPDF
DOI
10.1007/s11128-019-2288-4

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Within the constraint network phase transition framework, this paper reconstructs the threat of quantum computing to cryptography as a spectrum of threetypes of information barriers: spectrum‐hiding, geometric‐torsion, and theorem‐rigidity.Spectrum‐hiding hardness (RSA, ECC) has been penetrated by the quantum Fouriertransform; geometric‐torsion hardness (lattice cryptography) is quantum‐resistantbut relies on continuously tunable parameters and unproven computational assumptions, suffering from parameter illusion. Theorem‐rigidity hardness is rootedin discrete uniqueness locked by mathematical classification theorems; its securitybasis is jointly constituted by classification theorems, the structural‐reconstructionhardness assumption, and combinatorial expansion. Classification theorems exclude continuous deformation attack paths; the structural‐reconstruction hardnessassumption maintains one‐wayness under partial invariant disclosure; combinatorial expansion exponentially amplifies the discrete base structure space to resistGrover search. A categorical inadmissibility proof further shows that, under therestriction of no irreducible multiplicity, the category of rigid structures cannot befaithfully embedded into the quantum‐solvable category, thereby blocking spectralmanifestation of the quantum Fourier transform at the structural level. This papercompletes a paradigm shift from parametric belief to theorem‐guaranteed security,providing a theoretical coordinate for post‐quantum cryptography.
Established threat-modeling frameworks contain no dedicated axis for quantum-compute threats. The individual threats are well studied, harvest-now-decrypt-later, Grover/Shor capability escalation, quantum side-channels, and circuit fingerprinting each have an active literature, but they are scattered across separate research communities and are not consolidated into a taxonomy usable within a standard data-flow threat-modeling process alongside STRIDE and LINDDUN. This work introduces QUANTA, a quantum-compute threat axis of seven categories (Q1 harvest-now-decrypt-later, Q2 superposition manipulation, Q3 cross-framework convergence attack, Q5 capability escalation, Q6 collapse side-channel, Q7 algorithm identification; Q4 is reassigned to the companion morphic axis). The contribution is stated narrowly and honestly: the novelty is the axis. The consolidation and framing, not the individual threats, most of which are prior art. The work further distinguishes, explicitly, between categories that can be demonstrated as executable attacks in a simulator environment and those that cannot. Two categories: superposition manipulation (Q2) and a cross-framework convergence attack (Q3) are demonstrated as real, reproducible exploits against a live PennyLane/Qiskit cross-framework verification engine, with a benign control that correctly reads as defended. The remaining categories require a cryptographically-relevant quantum computer or physical quantum hardware and are explicitly out of scope for empirical demonstration; they are not claimed. Of the two demonstrated, the convergence attack (Q3) is the one genuinely quantum-specific and apparently-novel threat: it exists only because two quantum frameworks with opposite qubit-ordering conventions are cross-checked, allowing a real divergence to hide behind a benign convention gap. Keywords and subjects:threat modeling; moving-target defense; polymorphism; cyber deception; morphic security; adversarial robustness; STRIDE; LINDDUN; reproducible security research; post-quantum signatures; MASQUE; MASQUARAIDE QUANTA is one of two original axes in the MASQUE threat model within the MASQUARAIDE project, alongside the morphic-polymorphic axis CHIRAGE. This deposit includes the paper, the attack-demonstration harness, the cross-framework engine, and machine-readable results, released with an SHA3-256 file manifest and an ML-DSA-65 (FIPS 204) signature over the manifest anchor, so that every verdict can be reproduced or refuted.