Quantum computers threaten computational hardness assumptions used by public-key transport and classical archives. They do not magically extract secrets that never appear in an authorization transcript under empty effective mutual information. Separate post-quantum transport migration (hybrid KEMs, algorithm agility) from Channel Zero authorization emptiness so buyers do not treat “quantum breaks everything” as one control family.
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 computational hardness assumptions (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 rests on a hardness clock- a computational hardness assumption whose deadline algorithms and machines can move. 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 computational hardness assumptions 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 computational hardness assumption.
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 those bounds 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.
