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REVIEW 2 major objections 14 references

A quantum circuit prepares a superposition over a random affine coset to generate one-shot signatures that classical computers can verify.

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2026-06-26 08:13 UTC pith:S4EBP2KM

load-bearing objection The paper gives an explicit pre-obfuscation circuit for one-shot signatures via puncturable-PRF affine cosets plus a classical membership test, with concrete qubit and gate counts. the 2 major comments →

arxiv 2606.23612 v1 pith:S4EBP2KM submitted 2026-06-22 quant-ph cs.CR

A quantum algorithm for one-shot signatures

Gopikrishnan Muraleedharan , Minh Thuy Truc Pham , Vir Pathak , Thomas Gardner , Chuanqi Zhang , QPerfect , Gavin K. Brennen This is my paper
classification quant-ph cs.CR
keywords one-shot signaturesquantum signaturesaffine coset superpositionpuncturable pseudorandom functioncoset membership testclassical verificationquantum circuit implementationobfuscation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a quantum algorithm for one-shot signatures consisting of a key generation stage that outputs a classical public key and quantum secret key, followed by a signing stage that combines the quantum key with a message to produce a classical signature. The construction prepares a superposition over elements of a random affine coset chosen by a puncturable pseudorandom function and adds a circuit that tests membership in that coset. The signed message can be checked efficiently by a classical verifier with no algorithmic errors in the procedure. Qubit count scales as Θ(κ log(r) + n + l) and gate count as Θ(n³ + nl), where κ is the security parameter, r the public key size, and n + l the signature size with l the message length. Obfuscation is identified as necessary for security against polynomial-time classical and quantum attacks.

Core claim

The paper provides a pre-obfuscation circuit-level implementation of an efficient one-shot signature scheme. The scheme works by preparing a superposition over elements of a random affine coset determined by the output of a puncturable pseudorandom function, together with a circuit that tests coset membership. Key generation produces a classical public key paired with a quantum secret key; signing processes the quantum secret key with a message string to yield a classical signature that a classical verifier can check efficiently.

What carries the argument

Superposition over elements of a random affine coset selected by a puncturable pseudorandom function, together with the coset-membership test circuit.

Load-bearing premise

The construction assumes a secure puncturable pseudorandom function exists to select the random affine coset and that the coset-membership test circuit stays secure after the identified blocks receive appropriate obfuscation.

What would settle it

An efficient classical or quantum algorithm that forges a valid signature on a new message without access to the quantum secret key, or that distinguishes the coset superposition without the obfuscation.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The logical qubit number scales like Θ(κ log(r) + n + l)
  • The gate complexity scales like Θ(n³ + nl)
  • The signed message can be efficiently checked by a classical verifier
  • The scheme applies to delegated signatures, secured token transfer, and publicly verifiable randomness

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The pre-obfuscation circuit could serve as a concrete target for future obfuscation compilers to reach full security.
  • Varying the choice of puncturable pseudorandom function might yield variants with different qubit or gate trade-offs.
  • The classical-verifier property could allow hybrid quantum-classical protocols that avoid quantum communication after key generation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 0 minor

Summary. The paper claims to provide an explicit pre-obfuscation quantum circuit realizing an efficient one-shot signature scheme. Key generation produces a classical public key and quantum secret key; signing processes the quantum key with a message to yield a classical signature verifiable by a classical circuit. The construction prepares a superposition over a random affine coset selected by a puncturable pseudorandom function and includes a coset-membership test. Resource bounds are stated as Θ(κ log(r) + n + l) qubits and Θ(n³ + nl) gates (with κ = Ω(n)), and the manuscript identifies circuit blocks that later require obfuscation for security against classical and quantum polynomial-time adversaries. The scheme is conditional on the existence of a secure puncturable PRF.

Significance. If the circuit construction and coset test are correct, the work would supply a concrete, resource-bounded pre-obfuscation implementation of the one-shot signature primitive with stated applications to delegated signatures, token transfer, and verifiable randomness. Explicit qubit/gate counts and identification of obfuscation targets constitute a useful engineering contribution conditional on standard cryptographic assumptions.

major comments (2)
  1. Abstract and construction description: the assertion that 'there is no algorithmic error in the construction' and that 'the signed message can be efficiently checked by a classical verifier' is stated without derivation steps, gate decomposition, or probability analysis showing that the coset-membership test accepts valid signatures (produced from the affine-coset superposition) with overwhelming probability while rejecting invalid ones. This verification is load-bearing for the central claim of a working signature scheme.
  2. Resource scaling paragraph: the stated bounds Θ(κ log(r) + n + l) qubits and Θ(n³ + nl) gates are given without an accompanying circuit diagram, gate count breakdown, or error analysis that would allow independent confirmation of the scaling or identification of which gates belong to the PRF evaluation versus the membership test.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments. We address the two major comments point-by-point below. Both points identify places where additional explicit derivations would strengthen the manuscript, and we will revise accordingly.

read point-by-point responses

  1. Referee: Abstract and construction description: the assertion that 'there is no algorithmic error in the construction' and that 'the signed message can be efficiently checked by a classical verifier' is stated without derivation steps, gate decomposition, or probability analysis showing that the coset-membership test accepts valid signatures (produced from the affine-coset superposition) with overwhelming probability while rejecting invalid ones. This verification is load-bearing for the central claim of a working signature scheme.

    Authors: The manuscript constructs the coset-membership test explicitly from the affine-coset superposition prepared by the puncturable-PRF circuit; the test is a standard inner-product measurement that accepts with probability 1-negl(κ) on valid signatures by the properties of the coset and rejects invalid inputs with overwhelming probability. We agree that the abstract and high-level description would benefit from an expanded derivation, including the explicit gate decomposition of the test and the probability bound. We will add a dedicated subsection with these steps in the revised version. revision: yes

  2. Referee: Resource scaling paragraph: the stated bounds Θ(κ log(r) + n + l) qubits and Θ(n³ + nl) gates are given without an accompanying circuit diagram, gate count breakdown, or error analysis that would allow independent confirmation of the scaling or identification of which gates belong to the PRF evaluation versus the membership test.

    Authors: The stated bounds follow from adding the known costs of the PRF evaluation circuit (Θ(n³) gates), the superposition preparation over the coset (Θ(κ log r) qubits), and the membership test (Θ(nl) gates). We acknowledge that an explicit breakdown, diagram, and error analysis are not present in the current text. We will insert a table of per-component counts together with a circuit diagram and error analysis in an appendix of the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents an explicit pre-obfuscation circuit construction for a one-shot signature scheme built directly on the standard cryptographic primitive of a puncturable pseudorandom function, together with a coset-membership test. Resource counts are stated as explicit functions of the security parameter and message length with no internal fitting or redefinition of the claimed signature. No load-bearing step reduces by the paper's own equations or self-citation to a quantity defined inside the paper; the construction is conditional on external secure primitives. This is the normal case of a self-contained algorithmic recipe.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The scheme rests on the standard cryptographic assumption that puncturable pseudorandom functions exist and on the modeling choice that obfuscation can be applied to the identified circuit blocks; no new entities are postulated.

free parameters (1)
  • κ = Ω(n)
    Cryptographic security parameter required to be Ω(n) for the stated security level.
axioms (1)
  • domain assumption Existence of secure puncturable pseudorandom functions
    Used to select the random affine coset in the key-generation stage.

pith-pipeline@v0.9.1-grok · 5769 in / 1350 out tokens · 23152 ms · 2026-06-26T08:13:41.532765+00:00 · methodology

0 comments
read the original abstract

We provide a pre-obfuscation circuit-level implementation of an efficient one shot signature scheme, which has known applications to delegated signatures, secured token transfer, and publicly verifiable randomness. The algorithm consists of two stages: a key generation stage where a classical public key/quantum secret key pair is produced, and a signing stage where the quantum secret key is processed with a message string to produce a classical signature. There is no algorithmic error in the construction and the signed message can be efficiently checked by a classical verifier. Our scheme works by preparing a superposition over elements of a random affine coset determined by the output of a puncturable pseudorandom function, together with a circuit that tests coset membership. The logical qubit number scales like $\Theta( \kappa\log(r) + n + l)$ and the gate complexity scales like $\Theta(n^3 + nl)$, where $r$ is the public key size, $n+l$ is the signature size, $l$ is the message size, and $\kappa = \Omega(n)$ is the cryptographic security parameter. We provide explicit qubit and gate counts for varying $n$ and identify the circuit components where obfuscation would be required for security against classical and quantum polynomial time attacks.

Figures

Figures reproduced from arXiv: 2606.23612 by Chuanqi Zhang, Gavin K. Brennen, Gopikrishnan Muraleedharan, Minh Thuy Truc Pham, QPerfect, Thomas Gardner, Vir Pathak.

Figure 1
Figure 1. Figure 1: Signature delegation protocol. To mitigate risks from Bob’s quantum capabilities, Alice uses a post-quantum signature scheme, generating a signing key (PQC.sk) and verification key (PQC.vk). The blue arrows indicate classical communication that are public. parties, even within a local quantum cryptography setting. OSS is used directly in this protocol: Bob, acting as the local quantum entity, generates a q… view at source ↗
Figure 2
Figure 2. Figure 2: Signature delegation chain. The signature can easily be delegated multiple times, with Bob ⇒ Charlie ⇒ · · · ⇒ Dana and the overall signature is the entire signature chain from Alice to the final signer. signer with no classical master key and no trusted setup beyond a common reference string, and crucially, not even the key generator can produce two valid signatures for the same public key. A natural appl… view at source ↗
Figure 3
Figure 3. Figure 3: Workflow diagram of the multi-bit OSS protocol. The dashed boxes represent the part of the circuits that need to be obfuscated and are distributed as classical instructions contained in CRS. Note that in Sign even though the control register |⃗y⟩ representing the public key is classical, it should be treated as a quantum register since those gates it controls are to be obfuscated. The bottom section outlin… view at source ↗
Figure 4
Figure 4. Figure 4: Sample GGM tree with r = 3. The output of the PRG is G(k) = G0∥G1. Evaluating the GGM PPRF on input 011 results in F(k, 011) = G011 = G1(G01) = G1(G1(G0(k))) Given any block cipher that is a secure pseudorandom permutation (PRP), a secure PRG can be constructed using standard PRP-based domain-extension methods. For instance, one may encrypt an incrementing counter and concatenate the resulting blocks (CTR … view at source ↗
Figure 5
Figure 5. Figure 5: Puncturing the GGM tree at 011. The puncturing key is k 011 = {G1, G00, G010}. The punctured path is marked with a red dashed line, and the puncturing key’s nodes are in blue boxes. D. KeyGen As seen in the Workflow diagram 3, the key generation circuit factors as KeyGen = H ⊗n+l ; F; Measure. The factor F is a puncturable PRF that relates public keys to a hidden coset space, encoded as an affine transform… view at source ↗

discussion (0)

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Reference graph

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