Quantum computers threaten computational hardness assumptions. They do not magically extract secrets that never appear in a transcript. Separate post-quantum transport migration from authorization emptiness.
Quantum computers change hardness calendars for some public-key systems. They do not invent a decoder for a ceremony film that never carried the secret. Separate post-quantum transport migration from authorization emptiness.
Formal mathematics
Myth: “Quantum breaks all crypto”
Quantum changes the calendar for some public-key systems. It is not omnipotence. A machine that factors large integers faster does not invent a decoder for a film that never carried the secret.
Technically, two different stories get mashed together. Algebraic structure (RSA and elliptic-curve public keys) faces Shor's algorithm: a quantum algorithm that turns certain hard number-theory problems into something efficiently solvable on a large enough quantum computer. Unstructured search faces Grover's algorithm: a quadratic speedup over classical guessing (powerful, not exponential free lunch).
PQ for transport · emptiness for authorization
Read left as the Shor calendar cracking hardness clocks (RSA/ECC); read right as an empty authorization transcript where Grover still searches emptiness. Crossing out “breaks all crypto” separates myth from model. Takeaway: post-quantum upgrades transport; emptiness claims for authorization are a different job.
Front-load the class split: computational security is a hardness clock: algorithms and machines can move the deadline. Information-theoretic claims care whether secret-relevant information exists in the observation. Quantum attacks computational assumptions; empty-channel authorization asks whether I(X;O∣C)I of X semicolon O given C is zero (notation).
Quantum search bound
Q(M)=Θ(M)
Q of M equals theta of square root M
Read as: For unstructured search over M candidates, the quantum query cost scales on the order of the square root of M.
Arguments
MM
: the size of the unstructured hypothesis or search space
Q(M)Q(M)
: quantum query cost to find a marked item in that space
Operators
Θ\Theta
: asymptotically tight order of growth
M\sqrt{M}
: quadratic speedup over classical linear search
Significance: This is the real Grover-style improvement: powerful, but still a search over candidates rather than a magic transcript decoder.
Computational contrast: Quantum search accelerates computational assumptions; it does not recover a secret when the authorization transcript carries no secret-relevant information.
: no effective leakage from the transcript under the model
Significance: It separates quantum calendar risk from the Channel Zero claim: there must be transcript information before faster search has something to exploit.
Computational contrast: Post-quantum migration updates hardness bets for transport; empty-channel authorization is evaluated by transcript leakage.
Hybrid TLS with post-quantum (PQ) key exchange protects transport: the padlock’s handshake calendar gets a new set of hardness bets. That migration is real and worth shipping. It does not by itself remove ambient credential blast radius: stolen bearer tokens and reusable API keys remain reusable capability after harvest.
PQ for the tunnel; emptiness for authorization. The solutions page explains coexistence without pretending lattices replace Shannon.
Post-quantum hybrid ladder
Read the hybrid ladder as classical plus post-quantum transport (X25519 with Kyber-class KEMs) stacked for channel integrity. It upgrades the hardness calendar for packets in transit, not the empty-channel authorization claim. Takeaway: PQ hybrid is the right tool for transport; Channel Zero emptiness remains a different authorization job.
Harvest-now-decrypt-later (HNDL) targets recorded ciphertext under hardness: archive today, wait for better machines or math, decrypt tomorrow. That threat is real for transport archives whose confidentiality rests on a hardness clock.
If the public observable O carries no secret mutual information given challenge C, “decrypt later” has no secret to decrypt from the ceremony film. The archive is a notebook of surface symbols, not a ciphertext of the witness. That is observer perfect secrecy on the authorization channel, not a stronger AES.
For membership-only empty-channel designs, the relevant attack model is often unstructured search: find a marked hypothesis in a combinatorial space when the transcript exposes only leaf identifiers, not an algebraic witness Shor can invert. Query lower bounds in the Grover / Bennett–Brassard–Bernstein–Vazirani (BBBV) unstructured-search style give a Θ(√M) flavor: quadratic help, still exponential space when M is astronomical.
Public papers on this site map that story without inventing numeric forever-guarantees beyond their abstracts and stated parameters:
Quantum Attack Intractability: quantum algorithms that break hardness assumptions do not automatically recover secrets absent from the transcript; membership-only proofs sit in the Grover/BBBV unstructured-search model.
Quantum Complexity and Physical Bounds: hypothesis-space size, Θ(√M) query lower bounds, and physical-rate caveats under an idealized energy-limited computer. Optimistic ceilings still leave impractical timescales for the long-secret parameterizations examined: parameter dependence is explicit.
Computational & Quantum Intractability for Membership-Only Proofs: rounds-to-uniqueness, classical and quantum time bounds via BBBV/Grover limits, plus resource-model overheads. Conclusion: intractability under the baseline and longer secret lengths examined, not “quantum safe forever” as a slogan.
No fantasy wall-clock numbers appear here beyond what those papers argue under their models. Paradigm comparison across systems: Compare security systems.
Related
Bounds depend on parameters, geometry, and axiom adherence. Under the stated model, quantum is not an automatic break of empty-channel authorization, and PQ transport should coexist with emptiness for authorization. Affirmative claim classes: Claims.
