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REVIEW 4 major objections 4 minor 95 references

This paper claims that a public smart contract can generate hard-to-factor integers with no hidden secrets, making an on-chain solution mathematically compelling evidence of cryptographic quantum supremacy, and can automatically switch sign

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2026-08-04 00:34 UTC pith:N7ANG53V

load-bearing objection A real, well-documented smart-contract system whose advertised proof-of-quantum claim doesn't follow: the on-chain verifier can't distinguish quantum from classical factorization. the 4 major comments →

arxiv 2601.05534 v3 pith:N7ANG53V submitted 2026-01-09 cs.CR

BloQBench: A Blockchain Benchmarking Framework for Quantum Supremacy

Nicholas J.C. Papadopoulos , Ramin Ayanzadeh This is my paper
classification cs.CR
keywords blockchainquantum supremacysmart contractinteger factorizationRSA-UFOpost-quantum signaturesfront-runningEthereum
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 tries to establish that a blockchain can serve as a trustless referee for quantum supremacy: a smart contract generates very large numbers that are hard to factor, without anyone knowing their factors, and publicly verifies any submitted factorization. If a correct factorization of the final remaining number appears on-chain, the authors argue it is virtually indisputable evidence that a quantum computer has broken RSA-level cryptography. They also use that event as an automated trigger for Ethereum accounts to switch to quantum-secure signatures, avoiding the cost of early migration while not delaying protection until the threat is real. The claim matters because it would give the world a public, auditable moment at which post-quantum protection becomes necessary, rather than relying on private or contested lab results.

Core claim

The central object is the RSA-UFO lock: a 4,608-bit integer known to have at least two large prime factors yet generated without anyone knowing those factors. The contract accumulates random 256-bit chunks into 119 locks; based on a per-lock probability of about 0.16 of being hard to factor, 119 locks give roughly a one-in-a-billion chance that all are classically easy. Solvers submit factors; the contract checks that they are prime and multiply to the lock, then marks the lock solved. Because generation never involves a secret, the paper concludes that a correct factorization of the last remaining lock is virtually indisputable evidence that a quantum computer achieved cryptographic quantum

What carries the argument

The trustless generation mechanism: a public contract produces RSA-UFO locks by repeatedly feeding random 256-bit integers into a bytes accumulator until each lock is 4,608 bits; no secret inputs are used, so even the deployer cannot know the factors. On-chain verification uses a probabilistic primality test on submitted factors and checks their product. A commit-reveal scheme with a one-day buffer blocks front-running, and a singleton deployment ensures a single global instance whose solved flag is readable by anyone.

Load-bearing premise

The bytes that build the locks must come from a source no party can predict or control; the paper never says where the 256-bit integers come from, so if a caller or miner can influence them, the 'no pre-computed secrets' claim and the entire probability argument collapse.

What would settle it

Attempt to deploy the contract and feed chosen 256-bit integers into the random bytes accumulator; if this yields a lock whose factorization is known to the caller, then a 'solution' can be submitted without any quantum computer and the blockchain proof is void. Alternatively, a classical factorization of a produced 4,608-bit lock would directly refute the claim that at least one is classically infeasible.

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

If this is right

  • A correct on-chain factorization of the final lock is public, permanent, and independently checkable, so the claimed moment of cryptographic quantum supremacy is auditable by anyone.
  • Blockchain accounts can watch the contract's solved flag and switch to quantum-secure signatures automatically, avoiding both premature cost and delayed vulnerability.
  • The lock parameters (119 locks of 4,608 bits, targeted one-in-a-billion failure) give a concrete, quantitative benchmark definition of cryptographic quantum supremacy.
  • Gas measurements show a factorization puzzle is deployable at roughly 238 million gas and verifiable at about 6.1 million gas per lock, making it feasible to run on Ethereum.
  • The one-day commit-reveal protocol makes front-running impractical even under heavy proposer censorship, keeping the bounty fairly awarded.

Where Pith is reading between the lines

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

  • Editorial extension: The trustlessness depends on the randomness source for the accumulator, which the paper does not specify; if callers or miners can bias the bytes toward numbers with known factors, the whole scheme fails silently.
  • Editorial extension: A quantum computer that can factor these 4,608-bit locks is already strong enough to break 3,072-bit RSA, so the trigger is a lagging indicator; pairing this puzzle with a weaker, earlier-warning verifiable-quantum-advantage puzzle could give more lead time.
  • Editorial extension: The 'no precomputed secrets' design pattern could generalize to any puzzle with an efficient classical verifier and a plausible quantum speedup, if a secret-free generation method exists.
  • Editorial extension: The economic incentive is untested; a bounty near 19 ETH must exceed the real cost of running a quantum attack, and that cost is not estimated in the paper, so the trigger's real-world firing conditions remain open.

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 / 4 minor

Summary. The paper proposes BloQBench, an Ethereum smart-contract framework intended to generate classically intractable integer-factorization puzzles ("locks") using Sander's RSA-UFO technique, reward solvers with bounty funds, and treat a verified on-chain factorization as a public, tamper-proof demonstration of "cryptographic quantum supremacy." The contract is designed to accept submissions of prime factors that multiply to a generated lock, verify them with the Miller-Rabin test, and, upon solution, set a flag that can automatically trigger migration to quantum-secure Lamport signatures. The manuscript reports a Solidity implementation, unit tests, gas measurements for deployment and solution verification, a comparison of prime factorization with order-finding, and a commit-reveal mechanism to mitigate front-running. The central claim is that independent observers can mathematically verify that a submitted solution must have been computed by quantum hardware, and that solving the final lock would be virtually indisputable proof of cryptographic quantum supremacy.

Significance. If the central claim were sound, the framework would provide a transparent, automation-ready benchmark for quantum advantage and a cost-based trigger for post-quantum blockchain migration. The engineering contribution is substantial: the Solidity implementation and tests are publicly archived, gas costs are measured in realistic deployments, and the comparison with order-finding is concrete and useful. However, the paper's core logical claim is not supported by the implemented verifier. The contract checks only the mathematical correctness of a factorization, not the computational mechanism that produced it, so acceptance cannot establish quantum provenance. The randomness-source and probability-parameter issues further undermine the trustless-generation and confidence guarantees. These are load-bearing defects in the manuscript's main contribution, not presentation issues.

major comments (4)
  1. [Abstract and §III] The claim that observers can "mathematically verify that any provided solution ... must have been computationally derived via quantum hardware" is unsupported. The PrimeFactoringBounty contract (refs. [77], [80]) accepts exactly when submitted factors are prime and their product equals the lock. The verifier is method-blind: any correct factorization, whether produced by a classical algorithm, a lucky guess, or by someone who knew the factors during generation, sets the same flag. Acceptance does not encode any information about the computational mechanism. At best, the scheme yields evidence conditional on the classical hardness of the 4608-bit RSA-UFO and on the unstated assumption that any solver must be quantum. Those are cryptographic hardness conjectures, not mathematical proofs. A perfect randomness source would not close this provenance gap.
  2. [§V-A and §IV-A] The random-bytes accumulator "accepts a 256-bit integer and appends it," but the manuscript never states who supplies these integers or what prevents a caller or miner from biasing the locks toward numbers with known factorization. The claimed guarantee of "absolutely no pre-computed secrets" in the abstract and the 119-lock probability argument in §IV-A depend on the locks being uniformly random and unpredictable. As written, if the input is caller-supplied, the generation is not trustless and the probability analysis collapses. The manuscript needs an explicit, game-resistant randomness source or a formal argument that caller influence cannot meaningfully bias the resulting locks.
  3. [§IV-A] The probability calculation is internally inconsistent. The paper quotes Sander's theorem as giving probability ≈0.082 at ξ=1/3 and Anoncoin's result as ≈0.16, then says "we choose the more cost-friendly result of generating 119 locks." But 119 comes from the Anoncoin estimate: ln(10^-9)/ln(1−0.16) ≈ 119. Using the paper's own Sander-based p=0.082 would require ln(10^-9)/ln(1−0.082) ≈ 243 locks to achieve the claimed 10^-9 confidence. The manuscript does not justify preferring the higher Anoncoin estimate, and the stated confidence bound is therefore not met under the Sander-derived probability.
  4. [§III and §VI] The paper states that "both RSA and ECDSA rely on the difficulty of this particular problem," referring to integer factorization. This is inaccurate: ECDSA relies on the elliptic-curve discrete logarithm problem, not integer factorization. While Shor's algorithm solves both, the factorization bounty by itself does not logically imply that ECDSA has been broken. The trigger from a factorization solution to a quantum-secure fallback for ECDSA-based signatures therefore rests on an additional, unstated assumption. This weakens the claimed connection between the implemented puzzle and the practical motivation for switching blockchain signature schemes.
minor comments (4)
  1. [§I] The definition of "cryptographic quantum supremacy" in the introduction is given as the ability to "bypass current cryptographic standards, namely RSA and ECDSA," while the abstract uses "solve practical cryptographic problems." These should be aligned, as the later argument depends on the stricter definition.
  2. [§IV-A] The notation "1/2 ln2(1/2ξ)" is ambiguous; it should be typeset as (1/2)·[ln(1/(2ξ))]^2 to avoid confusion between "ln squared" and "log base 2."
  3. [§III and Fig. 2] The described front-running attack is unclear: an attacker who has not seen the original solution cannot have a valid commit-reveal pair ready to race the original reveal. The "flood for one day" scenario seems to require knowledge of the solution beforehand, which contradicts the stated purpose of the commit-reveal scheme. This section should be rewritten to describe a feasible attack model.
  4. [§III] The phrase "funds sufficient for at least 800,000,000 gas" conflates gas (a unit of computational work) with the currency needed to pay for it. The bounty should be specified in ETH or another currency, with gas as the underlying cost measure.

Circularity Check

0 steps flagged

No circularity found: the core derivation is anchored to external sources and measured gas costs; the quantum-provenance overclaim is an unsupported inference, not a self-referential reduction.

full rationale

BloQBench's derivation chain is not circular. The central parameters come from external sources: RSA-UFO generation from Sander [45], the per-lock secure-generation probability from Anoncoin [54] (cross-checked against Sander's Theorem 1), and classical-hardness expectations from external standards and NISQ analyses. The 119-lock count is computed from an externally supplied probability rather than from the outcome it is meant to predict. The contract verification logic (Miller-Rabin primality checks plus product matching) is publicly inspectable, tested code, and the gas figures are measured from test deployments rather than fitted to the paper's conclusions. The paper does cite co-author prior work ([59], [61]), but only as background on NISQ factorization limits and error-correction challenges; those citations are not load-bearing for the central trustless-generation or bounty-trigger mechanism. The main weakness is interpretive, not circular: the verifier is method-blind, so a successfully submitted factorization establishes only that a factorization was provided, not that it was produced by quantum hardware. The abstract's claim that observers can 'mathematically verify' that a solution 'must have been computationally derived via quantum hardware' therefore imports unproven assumptions of classical infeasibility and provenance attribution. That is an unsupported inference and a correctness/risk issue, not a reduction of the conclusion to the inputs by construction. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' own prior work, and no ansatz is smuggled in via self-citation. Accordingly, the circularity score is 0.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The system's advertised guarantees rest mainly on (1) an externally sourced RSA-UFO probability, (2) an undescribed on-chain randomness source, and (3) the assumption that solving the final lock implies quantum hardware. The gas bounds are measured from tests rather than fitted to data. No new physical or protocol entities are introduced; 'locks' are Sander-style generated integers and 'cryptographic quantum supremacy' is a definition.

free parameters (4)
  • p_rsa_ufo = 0.16
    Probability that a random 4608-bit integer is an RSA-UFO, taken from Anoncoin [54]; Sander's theorem gives about 0.082, and the authors adopt the larger value. Used to derive 119 locks and the 1e-9 confidence claim.
  • num_locks = 119
    Computed as log(1e-9)/log(1-0.16); a design parameter set by the chosen p and target failure probability.
  • lock_bit_size = 4608
    Chosen as 3*1536 bits so a lock can have two prime factors of about 1536 bits under Sander's ξ=1/3 condition; a design choice.
  • min_bounty_gas = 800,000,000
    Set above the measured 741,048,802 gas for verifying solutions to all 119 locks, with a safety margin for gas-price fluctuations.
axioms (5)
  • domain assumption Random 4608-bit integers have at least two prime factors ≥2^1536 with probability about 0.16 (Anoncoin) or 0.082 (Sander), independently across locks.
    Used in §IV-A to derive 119 locks and the one-in-a-billion failure claim; if the true probability is materially lower, the claim collapses.
  • domain assumption The bytes accumulated on-chain are random enough that no party, including the deployer or proposers, can bias locks toward known factorizations.
    Required by the 'no pre-computed secrets' guarantee; §V-A describes an accumulator that accepts 256-bit integers but never specifies the randomness source.
  • domain assumption Classical factoring of a 4608-bit RSA-UFO is intractable, so a successful solution to a classically hard lock implies quantum hardware.
    Needed for the 'proof of quantum supremacy' inference; classical intractability is an unproven computational assumption, and the contract cannot identify which locks are classically hard.
  • domain assumption On-chain Miller-Rabin primality testing with the deployed bases is sound for 4608-bit factors.
    Used for solution verification in the prime-factoring bounty contract; no formal proof of the specific implementation is provided.
  • domain assumption EIP-1559 fee-market dynamics prevent an attacker from censoring a reveal transaction for one day.
    Relied on in §IV-A and Fig. 2 for the commit-reveal front-running defense.

pith-pipeline@v1.3.0-alltime-deepseek · 18904 in / 19277 out tokens · 214106 ms · 2026-08-04T00:34:20.432597+00:00 · methodology

0 comments
read the original abstract

As quantum computing matures, characterizing its practical workloads and verifying quantum supremacy presents a significant challenge. Current benchmarking and claims rely on trust-based verification methods that lack public auditability. We propose a decentralized benchmarking framework implemented via an Ethereum smart contract to provide verifiable assurance in these claims. This framework generates classically intractable puzzles that, crucially, require absolutely no pre-computed secrets. By utilizing the blockchain as an immutable public ledger, independent observers can mathematically verify that any provided solution to the puzzle must have been computationally derived via quantum hardware rather than classically spoofed. Furthermore, we demonstrate how this verifiable benchmarking metric can be utilized as an automation trigger. As a practical example of such a trigger, we focus on the ability for blockchains to automatically switch to quantum-secure signature schemes upon the successful demonstration of cryptographic quantum supremacy. We demonstrate these principles with BloQBench, which implements the concept using integer factorization as the generated puzzle and Lamport signatures as the trigger-based effect. This approach demonstrates a novel use of distributed ledgers for quantum workload characterization, providing a transparent, automated metric for measuring quantum supremacy while managing the performance and complexity trade-offs of post-quantum technology transitions.

Figures

Figures reproduced from arXiv: 2601.05534 by Nicholas J.C. Papadopoulos, Ramin Ayanzadeh.

Figure 1
Figure 1. Figure 1: Flowchart of quantum bounty smart contract. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Timeline of how the commit-reveal scheme prevents front-running. Arrows into the memepool are submitted transactions. Arrows into the bounty [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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