Proposal: Fractal‑Logical Spectral Invariants as Post‑Quantum Cryptographic Primitives
Felix Sagaz
Dear PQC Forum members,
I would like to share a new operator‑theoretic approach to post‑quantum cryptography based on resonant spectral invariants of self‑adjoint operators defined on Cantor‑type Hilbert spaces. The construction arises from the Logical‑Fractal Framework, where multi‑scale coherence, spectral gaps, and renormalization fixed points generate reproducible high‑entropy structures.
A preprint describing the mathematical foundations and cryptographic primitives is available here:
“Quantum Cryptography from the Logical‑Fractal Framework” Zenodo preprint (PDF): https://doi.org/10.5281/zenodo.17392811
Core idea. Given a compact self‑similar fractal with a regular resistance form, we construct a quantum‑fractal Hamiltonian
where is a fractional Laplacian and a bounded self‑adjoint operator on a Boolean projector lattice. Under mild assumptions, is self‑adjoint with compact resolvent and discrete spectrum.
From this structure we define three cryptographic primitives:
Spectral gaps as entropy sources.
Renormalization fixed points as scale‑invariant anchors for signatures.
Multi‑scale projectors as encryption operators.
Security assumptions. The hardness relies on:
inverse spectral reconstruction on fractal domains,
identification of resonant subspaces from ciphertext,
stability of renormalization fixed points under perturbations.
These problems appear orthogonal to lattice‑based and code‑based assumptions and may offer diversification for PQC research.
Statistical validation. We benchmark spectral gaps against GOE, Poisson, and 1/f ensembles. The resulting distributions show significant divergence and high entropy, suggesting suitability for key generation.
Purpose of this message. I am sharing this work to receive feedback from the PQC community regarding:
feasibility of developing a full KEM or signature scheme,
interest in collaborating on a reference C implementation,
relevance of operator‑theoretic hardness assumptions for future PQC rounds.
Any comments, critiques, or suggestions are very welcome.
Best regards, Enrique Vidal Silvente