Bitcoin and its underlying blockchain protocol have recently received significant attention in the context of building distributed systems and foundations of the consensus problem. At the same time, the rapid development in quantum computing makes the threats to cryptography more and more concerning. In this work, we revisit the formal security of the core of the Bitcoin consensus protocol, called the Bitcoin backbone (Eurocrypt 2015), in the presence of quantum adversaries -- i.e. adversaries equipped with quantum computers.
We show that the security of the Bitcoin backbone holds under a quantum analogue of the ``honest majority'' assumption that we develop. The critical ingredient of proving security of the blockchain is to analyzing the quantum query complexity of a Chain-of-Proofs-of-Work search problem. This problem in turn reduces to a problem we call multi-solution Bernoulli search, for which we establish its quantum query complexity. This can be viewed as an extension of a threshold direct product theorem to an average-case unstructured search problem. Our proof, adding to active recent efforts, simplifies and generalizes the powerful recording technique due to Zhandry (Crypto 2019).
Our analysis indicates that the security of the Bitcoin backbone protocol is guaranteed provided that the number of adversarial quantum queries is bounded so that each quantum query is worth $O(p^{-1/2})$ classical ones, where $p$ is the probability of success of a single classical query to the protocol's underlying hash function. Perhaps surprisingly, the wait time for safe settlement of transactions in the case of quantum adversaries matches (up to a constant) the safe settlement time in the classical case and thus does not result in any further overhead.
Bitcoin and its underlying blockchain protocol have recently received significant attention in the context of building distributed systems and foundations of the consensus problem. At the same time, the rapid development in quantum computing makes the threats to cryptography more and more concerning. In this work, we revisit the formal security of the core of the Bitcoin consensus protocol, called the Bitcoin backbone (Eurocrypt 2015), in the presence of quantum adversaries -- i.e. adversaries equipped with quantum computers.
We show that the security of the Bitcoin backbone holds under a quantum analogue of the ``honest majority'' assumption that we develop. The critical ingredient of proving security of the blockchain is to analyzing the quantum query complexity of a Chain-of-Proofs-of-Work search problem. This problem in turn reduces to a problem we call multi-solution Bernoulli search, for which we establish its quantum query complexity. This can be viewed as an extension of a threshold direct product theorem to an average-case unstructured search problem. Our proof, adding to active recent efforts, simplifies and generalizes the powerful recording technique due to Zhandry (Crypto 2019).
Our analysis indicates that the security of the Bitcoin backbone protocol is guaranteed provided that the number of adversarial quantum queries is bounded so that each quantum query is worth O(p−1/2) classical ones, where p is the probability of success of a single classical query to the protocol's underlying hash function. Perhaps surprisingly, the wait time for safe settlement of transactions in the case of quantum adversaries matches (up to a constant) the safe settlement time in the classical case and thus does not result in any further overhead.
A proof of work (PoW) is an important cryptographic construct enabling a party to convince others that they invested some effort in solving a computational task. Arguably, its main impact has been in the setting of cryptocurrencies such as Bitcoin and its underlying blockchain protocol, which received significant attention in recent years due to its potential for various applications as well as for solving fundamental distributed computing questions in novel threat models. PoWs enable the linking of blocks in the blockchain data structure and thus the problem of interest is the feasibility of obtaining a sequence (chain) of such proofs. In this work, we examine the hardness of finding such chain of PoWs against quantum strategies. We prove that the chain of PoWs problem reduces to a problem we call multi-solution Bernoulli search, for which we establish its quantum query complexity. Effectively, this is an extension of a threshold direct product theorem to an average-case unstructured search problem. Our proof, adding to active recent efforts, simplifies and generalizes the recording technique of Zhandry (Crypto'19). As an application, we revisit the formal treatment of security of the core of the Bitcoin consensus protocol, the Bitcoin backbone (Eurocrypt'15), against quantum adversaries, while honest parties are classical and show that protocol's security holds under a quantum analogue of the classical “honest majority'' assumption. Our analysis indicates that the security of Bitcoin backbone is guaranteed provided the number of adversarial quantum queries is bounded so that each quantum query is worth O(p−1/2) classical ones, where p is the success probability of a single classical query to the protocol's underlying hash function. Somewhat surprisingly, the wait time for safe settlement in the case of quantum adversaries matches the safe settlement time in the classical case.
A proof of work (PoW) is an important cryptographic construct enabling a party to convince others that they invested some effort in solving a computational task. Arguably, its main impact has been in the setting of cryptocurrencies such as Bitcoin and its underlying blockchain protocol, which received significant attention in recent years due to its potential for various applications as well as for solving fundamental distributed computing questions in novel threat models. PoWs enable the linking of blocks in the blockchain data structure and thus the problem of interest is the feasibility of obtaining a sequence (chain) of such proofs. In this work, we examine the hardness of finding such chain of PoWs against quantum strategies. We prove that the chain of PoWs problem reduces to a problem we call multi-solution Bernoulli search, for which we establish its quantum query complexity. Effectively, this is an extension of a threshold direct product theorem to an average-case unstructured search problem. Our proof, adding to active recent efforts, simplifies and generalizes the recording technique due to Zhandry (Crypto 2019). In addition, we revisit the formal treatment of security of the core of the Bitcoin consensus protocol, called the Bitcoin backbone (Eurocrypt 2015), against quantum adversaries and show that its security holds under a quantum analogue of the ``honest majority'' assumption that we formulate. Our analysis indicates that security of the Bitcoin backbone protocol is guaranteed provided that the number of adversarial quantum queries is bounded so that each quantum query is worth O(p−1/2) classical ones, where p is the probability of success of a single classical query to the protocol's underlying hash function. Somewhat surprisingly, the wait time for safe settlement in the case of quantum adversaries matches the safe settlement time in the classical case.
In this work we first examine the hardness of solving various search problems by hybrid quantum-classical strategies, namely, by algorithms that have both quantum and classical capabilities. We then construct a hybrid quantum-classical search algorithm and analyze its success probability. Regarding the former, for search problems that are allowed to have multiple solutions and in which the input is sampled according to arbitrary distributions we establish their hybrid quantum-classical query complexities -- i.e., given a fixed number of classical and quantum queries, determine what is the probability of solving the search task. At a technical level, our results generalize the framework for hybrid quantum-classical search algorithms proposed by Rosmanis. Namely, for an arbitrary distribution D on Boolean functions, the probability an algorithm equipped with τc classical and τq quantum queries succeeds in finding a preimage of 1 for a function sampled from D is at most νD⋅(2τc+2τq+1)2, where νD captures the average (over D) fraction of preimages of 1. As applications of our hardness results, we first revisit and generalize the security of the Bitcoin protocol called the Bitcoin backbone, to a setting where the adversary has both quantum and classical capabilities, presenting a new hybrid honest majority condition necessary for the protocol to properly operate. Secondly, we examine the generic security of hash functions against hybrid adversaries. Regarding our second contribution, we design a hybrid algorithm which first spends all of its classical queries and in the second stage runs a ``modified Grover'' where the initial state depends on the distribution D. We show how to analyze its success probability for arbitrary target distributions and, importantly, its optimality for the uniform and the Bernoulli distribution cases.
It is widely recognized that quantum computers pose a fundamental threat to blockchain security. Post-quantum cryptography (PQC) migration is therefore an urgent challenge, yet the following question has remained unanswered: by when must the migration be completed to maintain the security of crypto assets? To address this question, we first formalize the migration process and the quantum adversary based on the Bitcoin backbone protocol framework. We then establish a threshold on the tolerable quantum adversary's capability. Specifically, we prove that a security property migration liveness holds with overwhelming probability if and only if Δeff ≥ Δ∗= ⌈4/(1 − )⌉, where Δeff is the number of rounds from the broadcast of a migration transaction until the quantum adversary can produce a forged transaction, is the honest mining success probability, and is the concentration quality of the underlying random variables. We further extend the analysis to encompass broader classes of blockchains and migration paths by parameterizing the number of honest blocks required during the migration window, with practical implications for real-world deployment.
Quantum computers pose a significant threat to blockchain technology’s security, which heavily relies on public-key cryptography and hash functions. The cryptographic algorithms used in blockchains, based on large odd prime numbers and discrete logarithms, can be easily compromised by quantum computing algorithms like Shor’s algorithm and its future qubit variations. This survey paper comprehensively examines the impact of quantum computers on blockchain security and explores potential mitigation strategies. The survey focuses on the quantum security of blockchain’s fundamental building blocks, including digital signatures, hash functions, consensus algorithms, and smart contracts. We analyze the vulnerabilities introduced by quantum computers and discuss potential countermeasures and enhancements to ensure the integrity and confidentiality of blockchain systems. Furthermore, we investigate the quantum attack surface of blockchains, identifying potential avenues for exploiting quantum computing to strengthen existing attacks. We emphasize the need for developing quantum-resistant defenses and explore solutions for mitigating the threat of quantum computers to blockchains, including the adoption of quantum and post-quantum blockchain architectures. The paper also discusses the limitations of current efforts, such as the computational overhead of post-quantum algorithms and the practical challenges in real-world deployment, illustrated through case studies of Bitcoin and Ethereum. Future research directions include developing scalable quantum-resistant blockchain protocols, optimizing cryptographic implementations for embedded devices, and establishing standardized security frameworks to mitigate emerging quantum attacks.
The rapid advancement of quantum computing presents a fundamental challenge to modern cryptographic security, particularly in the domain of hash functions that ensure data integrity, authentication, and blockchain security. Traditional crypto graphic hash functions such as SHA-256, SHA-3, and BLAKE2 rely on computational hardness assumptions that become obsolete in the presence of large-scale quantum computers. Shor’s algorithm can efficiently break RSA and ECC-based cryptosys tems, while Grover’s algorithm reduces the security of traditional hash functions by square root complexity, significantly weakening their preimage and collision resistance. This quantum threat necessitates the development of post-quantum secure hashing techniques that remain resilient against both classical and quantum adversaries. This paper proposes Quantum Hashing, a novel cryptographic framework that integrates quantum entanglement, lattice-based cryptography, and hybrid quantum classical hashing to construct post-quantum secure hash functions. We introduce a formal model for Quantum Collision Resistance (QCR) and provide entropy-based ran domness enhancement to ensure unpredictable hash outputs. Unlike classical hashing approaches, our framework leverages the hardness of lattice problems (e.g., Shortest Vector Problem, Learning with Errors) to withstand quantum attacks while incorpo rating Quantum Key Distribution (QKD) mechanisms to enhance entropy and key management. Furthermore, we evaluate the security of Quantum Hashing under various attack models, comparing its resistance against Grover’s search and collision attacks. We benchmark its performance against NIST Post-Quantum Cryptography (PQC) final ists, including CRYSTALS-DILITHIUM, SPHINCS+, and Falcon, demonstrating that our approach offers superior resilience while maintaining computational feasibility. Additionally, we present an implementation of Quantum Hashing using Qiskit, show casing its practical applicability in quantum circuits and quantum-secure blockchain architectures. Our findings highlight that Quantum Hashing provides a scalable, entropy-efficient, and post-quantum resilient cryptographic primitive suitable for next-generation cryptographic applications. This work paves the way for secure post-quantum digital signatures, blockchain consensus mechanisms, and zero-knowledge proof systems that require tamper-resistant hashing in a quantum computing era.