Blockchain Verifiable Proof of Quantum Supremacy as a Trigger for Quantum-Secure Signatures

Blockchain is a decentralized, distributed ledger technology that ensures transparency, security, and immutability through cryptographic techniques. However, advancements in quantum computing threaten the security of classical cryptographic schemes, jeopardizing blockchain integrity once cryptographic quantum supremacy is achieved. This milestone, defined here as the realization of quantum computers to solve practical cryptographic problems, would render existing security standards vulnerable, exposing blockchain assets (currency, data, etc.) to fraud and theft. To address this risk, we propose and implement a smart contract deployable on the Ethereum blockchain, having the ability to run applications on its blockchain, that generates classically intractable puzzles by probabilistically generating large, hard-to-factor numbers without requiring secret information. This contract then serves two purposes: to establish a mechanism (1) for a trustless, unbiased proof of cryptographic quantum supremacy by verifying solutions to these puzzles, and (2) to protect user funds on Ethereum by triggering quantum-secure fallback protocols upon detecting cryptographic quantum supremacy, since it is desirable to wait as long as possible to fall back to a quantum-secure scheme because of its inherent additional cost and complexity. These mechanisms demonstrate the ability to identify cryptographic vulnerabilities and ensure a smooth transition to quantum-secure standards, safeguarding blockchain assets in a post-quantum era.

💡 Research Summary

The paper addresses a looming security crisis for blockchain systems that rely on classical public‑key cryptography (RSA, ECDSA) once quantum computers become powerful enough to break these schemes—a situation the authors term “cryptographic quantum supremacy.” To provide a practical, trust‑less way of detecting this milestone and to automatically transition blockchain assets to quantum‑secure signatures, the authors design and implement an Ethereum smart contract that generates a set of hard‑to‑factor integers (called “locks”) without any secret information.

The contract uses a probabilistic method derived from Sander’s technique to produce 119 random 4,608‑bit numbers. Statistical analysis shows that, with a confidence level of one in a billion, at least one of these numbers will be infeasible for classical computers to factor, and on average about 19 will be classically intractable. Each lock is associated with a bounty that must cover at least 800 million gas, which the authors estimate to be roughly 19 ETH at a typical gas price. The bounty is dynamically adjusted to keep pace with gas‑price fluctuations, and donations can increase the reward pool.

Any participant may submit a prime‑factorization for any single lock. The contract verifies the solution on‑chain; if correct, the lock is marked solved and cannot be attacked again. When the final lock is solved, the contract flips a public “solved” flag, transfers the entire bounty to the final solver, and disables further interactions. Crucially, the successful resolution of all locks serves as an indisputable, on‑chain proof that a quantum computer has solved a problem (integer factorization) that is classically intractable, thereby confirming cryptographic quantum supremacy.

Upon this confirmation, the contract automatically triggers a fallback to a quantum‑secure signature scheme (e.g., Lamport one‑time signatures). This transition disables the legacy RSA/ECDSA verification logic and activates the new verification code, protecting all subsequent transactions without requiring manual upgrades or hard forks. The authors argue that postponing this switch until it is truly necessary minimizes the additional storage, computation, and economic overhead associated with post‑quantum signatures.

The implementation respects Ethereum’s gas limits by splitting lock generation into many small transactions (the “partial generation” method) and by employing the Singleton pattern to ensure a single contract instance across the network. Security considerations include mitigation of front‑running attacks: solution submissions must meet a minimum gas price and are processed atomically, making it economically unattractive for an attacker to out‑bid a legitimate solver. The contract also prevents re‑submission of solved locks and guards against replay attacks.

Limitations discussed include the reliance on the randomness quality of the probabilistic generator (a weak generator could yield a lock that is easier than expected), the fact that quantum computers capable of running Shor’s algorithm at the required scale may still be years away, and the economic risk that bounty levels might become insufficient if gas prices spike dramatically. The authors suggest possible extensions such as increasing the number of locks, using multi‑chain reward pools, or integrating alternative post‑quantum schemes to improve robustness.

In summary, the paper presents a novel, fully on‑chain mechanism that (1) provides a verifiable, unbiased proof of cryptographic quantum supremacy by leveraging the hardness of integer factorization, and (2) automatically switches a blockchain’s signature verification to a quantum‑secure alternative once that proof is obtained. This dual‑purpose contract offers a concrete pathway for blockchains to safeguard assets against the forthcoming “quantum apocalypse” while avoiding premature adoption of costly post‑quantum cryptography.