Post-quantum signatureless authorization with recursive verification

Post‑Quantum Signatureless Authorization with Recursive Verification

Digital signatures are the backbone of blockchain authority, but they rely on factoring or discrete‑log assumptions that break under Shor’s algorithm. A newer paradigm—signatureless authorization—replaces signatures with fresh zero‑knowledge proofs of knowledge of a reusable secret. The recent research paper and accompanying implementation demonstrate how this approach can be made post‑quantum secure and efficiently verifiable in a recursive proof system.

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1. How Signatureless Authorization Works

• Authority secret and commitment: An authority generates a secret `s` and publishes a public commitment `a = Addr(s)`. The commitment is address‑compatible, meaning it can be used directly as an account identifier.
• Intent binding: For each request the authority wants to approve, the requester defines a canonical intent `I`. The intent is hashed to `m = ID(I)`, and the pair `x = (m, a)` is fed into the proof transcript before any challenge is issued. This binds the proof to both the specific action and the authority.
• Zero‑knowledge proof: The prover (the authority) produces a fresh, randomized ZK proof that it knows a secret `s` satisfying `Addr(s)=a`. Because the randomness is freshly sampled for each request, the same secret can be safely reused.
• Safety against replay: The protocol includes a nonce, counter, or resource reference that must be consumed, ensuring that collected proofs cannot be replayed or adapted to new intents.

The core security challenge is safe reuse: an adversary may gather many valid proofs and try to combine them to forge a new authorization. The construction in the paper addresses this by a careful binding of the intent and by proving security in a quantum‑chosen‑request model.

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2. Binary‑Field Construction and Recursive Verification

The scheme is built over the binary field `𝔽{2^{128}}` embedded in `𝔽{2^{256}}`. Key components include:

• Poseidon2b authority circuit: A width‑four Poseidon permutation computes the secret‑to‑commitment relation.
• Masked degree‑10 reduction: Transforms the authority trace into eleven linear claims over a 2,048‑cell source bank, with explicit masking to hide intermediate values.
• Affine Reed–Solomon code argument: Authenticates the evaluations using 65 code queries, providing a succinct proof of correct computation.
• Recursive verifier: Checks all relations using compatible binary‑field arithmetic, allowing the authority proof to be nested inside larger execution proofs (e.g., rollup or account proofs).

The paper proves that the masking ranks, adaptive simulation, and extraction steps all hold with negligible error (bounded by `5^{-65} + 701202001642/2^{255}`). This guarantees that even a quantum adversary with coherent access cannot forge a fresh capsule without solving the underlying authority relation.

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3. Quantum Security Guarantees

In the quantum chosen‑request security game, the adversary may request authorizations for adaptively chosen intents. A forgery is an accepted capsule for a new intent under the same authority. The security reduction shows:

``` Pr[ForgeQ] ≤ Advpre^Q + εsim^Q + εext^Q + ε_id^Q ```

where the terms correspond to authority‑preimage recovery, simulation error, extraction error, and intent‑binding failure. Under the paper’s concrete parameters (e.g., call budget `T ≤ 2^{24}` yielding a forgery probability below `2^{-67}`), the overall quantum forgery probability is astronomically low.

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4. Performance and Practical Measurements

The implementation, written in Rust and benchmarked on an Intel Core i7‑1365U, reports the following median times (five fresh proofs, three verifications each):

| Scenario | Proving | Verification | Capsule size | |----------|---------|--------------|--------------| | Payment (1 in, 1 out) | 893.8 ms | 25.59 ms | 88,760–90,168 bytes | | Consolidation (8 in, 2 out) | 814.1 ms | 25.60 ms | 88,888–90,104 bytes |

The maximum capsule size is about 92 KB. Verification is lightweight because it runs inside a recursive proof system that already handles other execution constraints.

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5. Applications and Integration Points

Because the authority proof is separate from the execution logic, the same statement structure can be reused for:

• Service‑request authorizations (APIs, cloud functions)
• Device command approvals (IoT, hardware wallets)
• Artifact approvals in supply‑chain contexts

For Ethereum, natural integration spots include:

• Rollups: Authority proofs can be posted as part of rollup data, allowing the rollup operator to verify user intent without signatures.
• Proof‑verified accounts: Accounts that already carry recursive proofs of state transitions could embed the authority proof directly, simplifying the verification pipeline.
• Layer‑2 smart contracts: Contracts could accept a capsule as proof of permission, delegating signature verification to the ZK proof.

Future work could compare the cost of these authority proofs against traditional post‑quantum signatures (e.g., lattice‑based schemes) when both are verified inside the same proof system.

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6. Closing Thoughts

Signatureless authorization offers a compelling route to post‑quantum security for blockchain and other decentralized systems. By binding each request to a fresh zero‑knowledge proof of knowledge, the protocol eliminates the need for large, quantum‑vulnerable signatures while preserving the ability to reuse a single secret safely. The recursive verification framework ensures that these proofs can be composed with existing execution proofs, keeping verification costs modest. As quantum‑resistant cryptography matures, approaches like this will be essential for maintaining trust in permissioned actions across the decentralized web.