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REVIEW 4 major objections 6 minor 300 references

Verifiable random sampling produces fresh, publicly checkable samples from any target distribution using quantum circuit sampling and a timed public ledger.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-30 22:37 UTC pith:2DKPJJCJ

load-bearing objection Solid packaging of RCS certified randomness into a publicly verifiable, composable sampling primitive; the security claim is real but narrower than the abstract suggests. the 4 major comments →

arxiv 2607.26734 v1 pith:2DKPJJCJ submitted 2026-07-29 cs.CR

Verifiable Random Sampling

Yeoh Wei Zhu , Soorya Rethinasamy , Anthony Alexiades Armenakas , Yash Satsangi , Shaltiel Eloul , Ruslan Shaydulin This is my paper
classification cs.CR
keywords verifiable random samplingrandom circuit samplingcertified randomnessconstructive cryptographyquantum-proof extractorblockchain randomnesscross-entropy benchmarkingrejection sampling
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.

Standard verifiable random functions fix a deterministic map once the public key is published, so colluding parties or grinders can precompute favorable input-output pairs. This paper defines verifiable random sampling (VRS): a multiparty protocol whose output is a fresh sample statistically close to a chosen target distribution, together with a transcript any third party can check. The concrete construction derives challenge circuits from a blockchain block hash, has a quantum provider run random circuit sampling under a block-interval deadline, and lets an honest verifier extract a near-uniform sample (then lift it to any distribution by rejection sampling with error). Security is proved in the constructive cryptography model so the protocol composes with other cryptography. The point is publicly verifiable freshness without relying on a secret key or trusting a beacon committee.

Core claim

The authors introduce VRS as a primitive and construct VRS from random quantum circuit sampling, a timed batched bulletin board with entropy, and a quantum-proof two-source extractor. With an honest verifier and a corrupted client and provider, the real protocol is indistinguishable from an ideal VRS resource that outputs a sample statistically close to the target distribution only when the transcript is timely, correctly derived, and passes the cross-entropy test. The same uniform sampler lifts to arbitrary distributions via a proved rejection-sampling-with-error lemma.

What carries the argument

The ideal resource VRS together with the real converters that attach client, provider, and verifier to a timed bulletin board, authenticated channels, and a private extractor seed. The load-bearing step is that a timely, XEB-passing response carries enough smooth min-entropy for a quantum-proof extractor to produce a near-uniform sample that third parties can re-verify from the public transcript.

Load-bearing premise

Classical machines cannot usefully predict which random-circuit outputs are heavy versus light fast enough to spoof a high cross-entropy score inside the blockchain block deadline, so a passing response must still carry genuine quantum entropy.

What would settle it

Exhibit a classical algorithm that, within one block interval after the challenge circuits are fixed by the block hash, returns strings that pass the protocol’s XEB threshold while the smooth min-entropy of the response falls below the extractor’s requirement; the ideal-resource indistinguishability would then fail.

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

If this is right

  • Smart contracts can derive near-uniform samples from on-chain transcripts without trusting a VRF key holder or a beacon committee.
  • e-lottery and leader-election protocols can enforce public fairness while keeping sample freshness against grinding and collusion.
  • Any distribution, not only uniform bits, becomes available by rejection sampling once a near-uniform VRS sample exists.
  • The same interface can later swap the RCS entropy source for a fault-tolerant NP-search certified-randomness protocol without redesigning the multiparty wrapping.
  • Composability in constructive cryptography lets VRS be plugged into larger multiparty protocols as a modular randomness resource.

Where Pith is reading between the lines

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

  • If block-interval timing is the only freshness clock, chain reorganizations or miner timestamp games become first-class attacks on the entropy bound and deserve explicit economic modeling.
  • Domain separation via context strings turns one public entropy drip into many independent per-application samples, which is a practical alternative to running many separate beacons.
  • Verification cost in GPU-hours remains the deployment bottleneck; parallelizing XEB checks or moving to preimage-sampling certified randomness would decide whether VRS is usable at high frequency.
  • The construction separates ‘prove quantum entropy existed’ from ‘expand to a named distribution,’ a split that could apply to other physical entropy sources once they have a public timing and scoring interface.

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

4 major / 6 minor

Summary. The paper introduces verifiable random sampling (VRS), a primitive that outputs a fresh sample statistically close to a target distribution D together with a publicly verifiable transcript, addressing collusion and grinding limitations of VRFs. It gives a concrete construction VRS^{B3^{T,E}}_U based on random circuit sampling (RCS) certified randomness, a timed batched bulletin board B3^{T,E} (instantiated by blockchain), domain separation, and a quantum-proof two-source extractor; a lift to arbitrary D uses a new rejection-sampling-with-error lemma. Security is argued in the constructive cryptography framework: correctness (Theorem 8) and the main claim that an honest verifier with corrupted client and provider obtains an ideal-resource sample (Theorem 9), with hybrids sketched in Appendix E reducing to an imported smooth min-entropy bound (Theorem 4) under Assumption 1 and block timing T ≤ τ_res.

Significance. If the security claim holds at the advertised strength, VRS would be a useful composable primitive for blockchain randomness, e-lotteries, and smart-contract sampling: it targets information-theoretic freshness and public verifiability where VRFs are deterministic and beacons lack strong consumer-side proofs. Strengths include a clean ideal-resource formulation in CC, an explicit multiparty protocol with on-chain timing and anti-post-selection checks, a nontrivial error-tolerant rejection-sampling lemma (Lemma 10), and grounding in experimentally demonstrated RCS certified-randomness work. The contribution is primarily definitional and architectural rather than a new hardness result; its lasting value depends on whether the security reduction can be completed for a realistic adversary class and whether the RCS/XEB assumptions and verification cost are acceptable in the intended deployments.

major comments (4)
  1. [Theorem 9, Appendix E, Section 3.1] Theorem 9 / Appendix E: The central indistinguishability π_V(B3||AUT||Seed_V) ≈ VRS_U σ_{{P,E,T}} is only sketched. Hybrids H2–H3 import the smooth min-entropy bound of Theorem 4 for a classical PPT distinguisher limited to at most Q_C honest quantum-oracle queries (the one-shot model of [36]). The manuscript itself states (Section 3.1, Conclusion) that this is narrower than the general adversary of [37] and leaves the extension open. Without an explicit reduction from distinguishing advantage to a violation of Assumption 1 or of the B3 timing/entropy bounds—and without treating classical post-processing, cross-session quantum side information, or multi-client/multi-block interaction—the public-verifiability claim under fully corrupted T and P is not discharged at the strength advertised. Complete the proof or sharply restate the adversary class in the theorem statement and abstract.
  2. [Section 3.1, Assumption 1, Theorem 4] Section 3.1, Assumption 1 and Theorem 4: The extractor step (Hybrid H3) and ideal-resource sample quality rest entirely on unstructuredness of RCS / hardness of spoofing XEB so that frugal rejection sampling is optimal, plus T ≤ τ_res. This is a strong, non-standard cryptographic assumption (related to but not identical to LLHA). The paper should state quantitative parameter regimes (n, M, χ, α, Q_min, E, BIDτ) under which κ_2 is large enough for a concrete extractor error, and clarify what breaks if the adversary has more classical simulation power than the frugal strategy or if block intervals are adversarially jittered within the consensus rules.
  3. [Section 5.4, Section A.2, Section 2.2] Section 5.4 Figure 4 and Section A.2: Public verifiability for third-party observers and alternate corruption patterns (malicious V; all of T,P,V malicious) is handled by informal seed instantiations (future block hash, NIZK, attached seed). These are not modeled inside the ideal resource or the proven converter π_V; Theorem 9 only covers honest V with private Seed_V. Either extend the CC statement to these setups or clearly separate “core theorem” from “deployment sketches,” and specify how earliest-transcript / BIDmin / CTX checks compose when the observer is not V.
  4. [Section 5.3, Section A.7] Section 5.3 / A.7: Security uses H^comp_min(Hash(B,aux)) ≥ E and honest mining for timestamps. Brief remarks on few-bit biasability are insufficient for a composable ideal resource: biased or withheld block entropy can correlate challenge circuits with a grinding client, and miner timestamp flexibility can stretch the effective response window beyond τ_res. The ideal B3^{T,E} should state precise failure conditions, and Theorem 9 should quantify degradation when E is reduced or T is only an honest-majority statistical bound.
minor comments (6)
  1. [Table 1] Table 1 marks RB as not publicly verifiable and CR-RCS as not publicly verifiable; a short footnote defining the exact comparison criteria (who verifies, against what trust) would avoid ambiguity with existing beacon literature.
  2. [Figure 1, Figure 4, Figure 6] Figure 1 and the Step 0–3 summary are helpful but the mapping from T/P/V interfaces in Figure 6 to the ideal resource commands in Figure 4 could be tabulated once for readability.
  3. [Definition 6, Section 3] Notation: both Seed_chl / Seed_ext (Definition 6) and the ideal Seed^ℓ_I resource appear; unify naming. Also clarify whether Measure(⃗C|0^{n·M}⟩) is sequential single-circuit measurement or a joint measurement.
  4. [Lemma 10, Section 6.1] Lemma 10: state whether M in the rejection bound is the usual envelope constant and give a short concrete example (e.g., sampling a biased bit or a small discrete D) so implementers can see 2Mε_u/(1−2Mε_u).
  5. [Section 1.1] Related work: briefly position against other blockchain randomness designs (e.g., RANDAO + VDF, drand, threshold BLS beacons) beyond the high-level Table 1 categories.
  6. [Section 5.5, Theorem 8] Typos / polish: “Prover P” vs “Provider P” in Section 5.5; “relabeling and inspection” in Theorem 8 proof is too thin even for correctness—cite extractor parameters explicitly; arXiv ID formatting and repeated author-affiliation blocks are fine for preprint but should be cleaned for journal submission.

Circularity Check

0 steps flagged

No significant circularity: VRS security is a standard ideal/real composition around an externally cited entropy engine, not a result forced by its own inputs.

full rationale

The paper’s load-bearing chain is: (i) RCS + XEB under Assumption 1 / the min-entropy bound of Theorem 4 imported from Liu et al. [36] and complexity background from Aaronson–Hung [3]; (ii) a quantum-proof two-source extractor (Definition 5); (iii) a timed bulletin board B3^{T,E} and domain-separation/earliest-transcript rules; (iv) CC converters that construct an independently specified ideal resource VRS^{B3}_D (Figure 4), with Theorem 9 argued via hybrids that replace the extractor output by uniform and relabel interfaces. The ideal resource is not defined to equal the real protocol: honest P samples from the circuit distribution and honest V outputs u∼D only after TestXEB, timing, and uniqueness checks; corrupted interfaces allow arbitrary C′/R′/u. Lemma 10 (rejection sampling with error) is proved from first principles in Appendix D and is not a fit renamed as a prediction. Overlap of one coauthor with the cited RCS experiments [36, 37] is ordinary engineering reuse of an externally published, experimentally falsifiable entropy source; the hardness premise remains the external unstructuredness/LLHA-style assumptions, not a self-referential uniqueness theorem or a parameter fitted to the claimed output. No step reduces a claimed prediction to its defining input by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 7 axioms · 2 invented entities

The central security claim rests on imported hardness/entropy results for RCS, standard extractor and CC composition theorems, and several blockchain and timing modeling assumptions. No numerical parameters are fitted to new data in this text; free parameters are protocol thresholds inherited from the entropy theorem and blockchain model.

free parameters (4)
  • XEB threshold χ and test-set size α
    Protocol accept/reject thresholds that determine Q_min and the entropy lower bound; chosen to match the imported certified-randomness analysis rather than derived here.
  • Block time bound T and BIDτ (with T ≤ τ_res)
    Timing parameters that enforce the response deadline ruling out classical simulation; set relative to the hardware/adversary model of the cited RCS protocols.
  • Blockchain hash computational min-entropy lower bound E
    Assumed entropy in block headers used to freshen challenge circuits; taken from prior Bitcoin-style analyses, not re-estimated.
  • Extractor error parameters (ε_s, ε_ext, ε_2) and output length ℓ
    Statistical distance and seed-length knobs that make the extracted sample close to uniform; standard cryptographic parameters, not fitted to new experiments in this paper.
axioms (7)
  • domain assumption Assumption 1: RCS output distributions are unstructured; best classical XEB optimization is frugal rejection sampling.
    Stated in Section 3.1; load-bearing for the min-entropy bound used in Hybrids H2–H3 and Theorem 9.
  • domain assumption Entropy guarantee of Theorem 4 (from Liu et al. / related RCS certified-randomness work) under Q-query oracle access and non-abort.
    Imported as the quantitative entropy engine; without it the extractor precondition fails.
  • standard math Existence of a quantum-proof strong two-source extractor (Definition 5 / Lemma 74 of cited work).
    Standard cryptographic primitive used to turn smooth min-entropy into near-uniform bits.
  • domain assumption Ideal batched bulletin board B3^{T,E} with honest miner, chronological timestamps, inter-block time < T, and H_comp_min(block hash) ≥ E.
    Section 5.3 modeling assumption that supplies both freshness for circuits and the public deadline.
  • standard math Constructive cryptography composition and distinguishing advantage definitions (Maurer–Renner).
    Framework in which real≈ideal is proved; not re-derived.
  • domain assumption LLHA / hardness of spoofing related to LLQSV in the background complexity justification (Section C).
    Used to motivate Assumption 1 and the entropy theorems; experimental path relies more on Assumption 1 than on a fully instantiated LLHA protocol.
  • domain assumption Seed (extractor second source) remains independent of the provider’s response until response publication.
    Required by the extractor theorem; enforced by modeling Seed_V as private or as a future block hash depending on corruption pattern.
invented entities (2)
  • Verifiable Random Sampling (VRS) primitive and ideal resource VRS^{B3}_{T,E}_D no independent evidence
    purpose: Name and ideal functionality for publicly verifiable sampling from a target distribution with freshness, as a replacement for deterministic VRFs in multiparty settings.
    New interface (Gen/Chal/Res/Eval) and CC resource capturing honest-V / corrupt-T+P behavior; the main conceptual contribution.
  • Timed batched bulletin board resource B3^{T,E} no independent evidence
    purpose: Abstract the blockchain (or similar) features needed: timed batches, public posts, and entropy-bearing auxiliary headers.
    Ideal resource invented for the model; intended to be instantiated by Bitcoin/Ethereum-style ledgers under extra assumptions.

pith-pipeline@v1.2.0-daily-grok45 · 32937 in / 3879 out tokens · 64423 ms · 2026-07-30T22:37:07.555754+00:00 · methodology

0 comments
read the original abstract

Verifiable random functions (VRF) underpin a wide range of applications that require publicly verifiable evaluations of a pseudorandom function on a given input. However, once the public key is published, the induced function is fixed and is a deterministic function of the input. This determinism can enable collusion and grinding-style attacks in which adversaries precompute and selectively exploit favorable input-output pairs. To address these limitations, we introduce the formal notion of verifiable random sampling (VRS). We propose a concrete VRS construction based on random quantum circuit sampling (RCS) executable on today's quantum computing devices. VRS supports multiparty protocols in which the verifier's final output is a sample that is statistically close to a specified target distribution, while remaining publicly verifiable. We model the construction and prove its security within the constructive cryptography (CC) framework, thereby ensuring composability with other cryptographic protocols. Overall, our results provide a mechanism for verifiable random sampling that simultaneously guarantees sample freshness and public verifiability, enabling applications that require unpredictable, fresh randomness while preserving fairness through public verifiability.

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