Post-Quantum Alignment: Hash-Based Security Without Vulnerable Hardness Assumptions

Mechanism

The mechanism that delivers post-quantum alignment is the dynamic hash chain that binds successive identity states. Each participant in the system maintains a chain in which the value at step n is computed as H(s_n, c_n, r_n), where H is a cryptographic hash function, s_n is the prior chain state, c_n is the freshly captured biological-identity signal, and r_n is a domain-separated context tag describing the operation, time window, and scope. The output becomes s_{n+1}, and the cycle repeats. There is no long-lived private key, no certificate, no public-key signature, and no key-agreement protocol whose security would collapse under a sufficiently capable quantum computer.

Verification of any single transition requires only the prior state, the asserted next state, and the context binding. A verifier reproduces H over the asserted inputs and confirms the equality. Forging a transition requires either inverting the hash to discover an admissible preimage, locating a second preimage that hashes to the same successor, or guessing the per-step capture in advance of its acquisition. The first two attacks are reduced by Grover's algorithm to roughly the square root of the classical search cost, which is addressed by selecting hash output sizes of 384 bits or larger so that the post-Grover security margin remains at or above 192 bits. The third attack is bounded by the entropy of the live capture, which the trust-slope validator measures and rejects when below threshold.

The trust-slope validator is the second structural component. It evaluates the rate at which successive states accumulate evidence of continuity. A genuine participant produces a slope inside a narrow corridor defined by capture freshness, response timing, and scope coherence. A replay attempt produces a flat slope because the captures repeat. A synthetic substitution produces a slope outside the corridor because the inferred entropy distribution diverges from the participant's historical distribution. None of these tests depends on a hardness assumption that quantum search undermines; they depend on statistical properties of fresh signal that no offline computation can manufacture.

The biological-identity thread is the third component. It supplies the per-step entropy that prevents precomputation. Because the thread is sampled at the moment of operation rather than retrieved from storage, an adversary holding a quantum computer cannot mount a harvest-now-decrypt-later attack: there is no stored ciphertext whose key the adversary plans to recover. The signal that protects the operation exists only at the instant the operation is authorized.

Together these three components produce a continuity guarantee whose strength is bounded only by the symmetric primitives that underpin it. Symmetric primitives are not the targets of any presently known polynomial-time quantum algorithm. The system therefore inherits the post-quantum posture of its hash function rather than depending on a separate post-quantum module added on top.

Operating Parameters

The operating parameters determine the post-quantum margin in concrete deployments. The hash function is configurable; SHA-384, SHA3-384, SHA-512, and SHA3-512 are appropriate selections. SHAKE256 with a 512-bit output provides extendable-output flexibility for combining the chain output with auxiliary commitments. Output sizes below 384 bits are excluded because Grover's quadratic speedup would reduce them to below 128 bits of effective security, which is insufficient for long-lived archival evidence.

The chain step interval is bounded between sub-second values for high-frequency operations and several minutes for low-frequency continuity checks. The interval is selected per scope: a financial-authorization scope may step on every transaction, while a presence scope may step at fixed cadence. The validator carries the interval as a scope parameter and rejects steps whose timestamps fall outside the permitted window.

The biological-identity capture must satisfy a minimum entropy floor measured in bits. The floor varies by modality and by deployment policy; representative ranges are 60 to 80 bits per capture for behavioral signals and 80 to 120 bits for physiological signals after fuzzy extraction. The trust-slope validator computes the running entropy estimate and refuses to advance the chain when the estimate falls below the floor.

The context tag carries domain separation, scope identifier, time window, and a counter. Domain separation prevents cross-protocol confusion in which a chain output from one scope is replayed into another. The counter prevents within-window reordering. The time window is bounded by the chain step interval and by an explicit drift tolerance that accommodates clock skew across federated participants without admitting replay attacks beyond the tolerance.

The verifier's work factor is constant per step and independent of chain length. Verification of a sequence of N steps requires N hash evaluations and N slope checks, both of which parallelize trivially. There is no quadratic or exponential growth in verification cost as the chain extends. Long-running participants therefore do not accumulate a verification burden that would force pruning or checkpointing for performance reasons; pruning is available as a policy choice rather than a structural necessity.

Alternative Embodiments

A first embodiment uses SHA3-512 throughout and accepts the entire output as the next chain state. This embodiment maximizes post-Grover margin at the cost of a 512-bit state per participant per step. It is appropriate for long-archival deployments where evidence must remain verifiable across decades.

A second embodiment uses SHAKE256 with a 384-bit output and concatenates the output with a separate Merkle-tree commitment to a batch of contemporaneous events. This embodiment supports auditable batch processing while preserving per-step continuity. The Merkle tree itself is hash-based and inherits the same post-quantum posture as the chain.

A third embodiment composes the dynamic hash chain with a stateless hash-based signature scheme such as SPHINCS+ for occasional out-of-band attestations. The signatures are not required for continuity but are useful when a participant must produce a non-interactive proof of state for an external auditor. Because SPHINCS+ is itself hash-based, the composite remains free of any non-hash hardness assumption.

A fourth embodiment performs the chain over a hardware-rooted entropy source whose readings are mixed into the per-step capture. The mixing is performed with a keyed hash construction whose key is itself derived from the chain state, eliminating the need for a separate long-lived key.

A fifth embodiment operates the chain across a federation of verifiers, each holding only the prefix of the chain relevant to its scope. Cross-scope attestations are produced by hashing a scope-bound chain output together with a federation context tag. No verifier is required to hold the full participant history, and no central authority issues credentials.

A sixth embodiment substitutes a sponge construction with adjustable rate and capacity for the fixed-output hash, allowing capacity to be tuned to the desired post-quantum margin while keeping rate matched to the throughput of the underlying capture pipeline.

Composition

Post-quantum alignment composes with the other primitives of the keyless identity system without modification. The trust-slope validator consumes the chain output as one of its inputs and produces an admit-or-reject decision that downstream policies treat as the authoritative continuity signal. Because the chain output is a hash, the validator's interface is agnostic to the specific hash function selected, and a deployment can rotate hash functions over time without changing the validator implementation.

The biological-identity thread composes with the chain through the per-step capture. The thread's privacy-preserving fuzzy extractor produces a stable seed from a noisy biometric reading; the extractor's output is mixed into the chain rather than stored. Storage of raw biometric data is therefore not required, and the post-quantum posture of the chain extends to cover the biometric pathway by virtue of the mixing.

The append-only lineage record composes with the chain by recording, for each step, the asserted successor state, the context tag, the slope evaluation result, and any auxiliary commitments. The lineage is itself a hash-linked structure, so it inherits the post-quantum posture of its constituent steps. Auditors verify the lineage by replaying the hash chain, which requires no quantum-vulnerable primitive at any point.

The system composes with classical TLS, mTLS, and similar transport-layer protections without depending on them for continuity. If the transport layer is compromised by a future quantum attack on its key exchange, the continuity guarantee at the identity layer remains intact because no chain secret was ever transmitted in transport-protected form. The transport layer carries chain outputs, which are public values once committed.

Prior-Art Distinction

Hash chains have appeared in prior systems including Lamport one-time passwords, S/KEY, Merkle hash trees, and various blockchain commitment schemes. These prior systems use hash chains for authentication of discrete events or for tamper-evident logging. They do not bind the chain to a continuously refreshed biological-identity thread, do not evaluate a trust slope across successive steps, and do not carry the chain as the participant's identity. The combination disclosed here is structurally distinct.

Post-quantum signature schemes including SPHINCS+, XMSS, and LMS provide hash-based signatures for individual messages. They do not provide continuity of identity; each signature is a discrete proof of knowledge of a one-time or few-time key. The keyless identity system uses such signatures only as optional adjuncts and does not depend on them for the core continuity property.

Lattice-based schemes including Kyber and Dilithium are post-quantum but introduce new hardness assumptions whose long-term security is the subject of ongoing cryptanalysis. The disclosed system avoids these assumptions entirely, relying instead on the better-understood security of cryptographic hash functions. This is a deliberate architectural choice rather than an incidental property.

Biometric authentication systems in the prior art store templates or template-derived data and compare incoming captures against the store. Such systems are vulnerable to harvest-now-decrypt-later attacks against any encrypted template store and to template-theft attacks against any plaintext store. The disclosed system stores no template; the per-step capture is consumed into the chain and discarded. There is therefore no template store that a quantum-equipped adversary can target.

Disclosure Scope

This disclosure covers the use of a hash-based dynamic chain bound to a biological-identity thread and validated by a trust-slope evaluator as the structural means of providing post-quantum continuity for keyless identity. The scope includes any cryptographic hash function whose security is believed to reduce to preimage and collision resistance under a quantum adversary, any biological-identity capture modality that meets the stated entropy floor, and any deployment topology that admits per-step verification of the chain.

The scope further includes the composition of the foregoing with hash-based signature schemes, hash-linked lineage records, sponge constructions, and federated scope-bound verification. The scope excludes systems whose continuity guarantee depends on integer factorization, discrete logarithms over finite fields or elliptic curves, or any other algebraic problem known to be susceptible to polynomial-time quantum attack.

The disclosure is structural rather than algorithmic: the protected matter is the architectural choice to make post-quantum security a property of identity continuity itself, achieved by selecting only primitives that retain meaningful security under quantum adversaries and by binding those primitives to live capture rather than to stored secrets. Implementations that adopt the architecture inherit the property; implementations that retain key-based or algebra-based continuity do not, regardless of whether they layer post-quantum modules on top.