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Fig. 3. General categories of quantum cryptography.

Figure 3 General categories of quantum cryptography.

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TABLE I: Available related surveys in the literature.
TABLE I: Available related surveys in the literature.
and consensus is employed to achieve an agreement on the order of events within the chain. Moreover, a set of rules, known as transaction validation mechanism, is employed to ensure the correctness of every block and the transactions contained within it.
and consensus is employed to achieve an agreement on the order of events within the chain. Moreover, a set of rules, known as transaction validation mechanism, is employed to ensure the correctness of every block and the transactions contained within it.
Fig. 2. An overview of the blockchain architecture. By employing the tensor product of vector spaces, we can construct Multiqubit state spaces [112], which are 2”- dimensional complex vector spaces for a system composed of n qubits. We indicate the tensor product of two state- vectors |1) and |2) by |1) @ |2) or |1 2). This idea can naturally be expanded to encompass multiple qubits. Within multiqubit systems, there is a quantum phenomenon referred to as entanglement, wherein the description of the states of the subsystems cannot be provided independently. Mathematically, entangled states are represented as non-simple tensors, indicat- ing that they cannot be factored over the subsystems involved. When certain subsystems can be independently described using a simple tensor, the quantum state is referred to as a product state of those subsystems. Regarding a specific basis, qubits are considered to be in a superposition state when their state-vector is a nontrivial linear combination of basis states. Unlike classical bits, which are limited to being in either the state 0 or 1, a qubit has the potential to exist in any superposition of basis states |0) and |1). The coefficients that define the superposition are referred to as amplitudes, and they are complex numbers. Within quantum mechanics, measurements encompass the
Fig. 2. An overview of the blockchain architecture. By employing the tensor product of vector spaces, we can construct Multiqubit state spaces [112], which are 2”- dimensional complex vector spaces for a system composed of n qubits. We indicate the tensor product of two state- vectors |1) and |2) by |1) @ |2) or |1 2). This idea can naturally be expanded to encompass multiple qubits. Within multiqubit systems, there is a quantum phenomenon referred to as entanglement, wherein the description of the states of the subsystems cannot be provided independently. Mathematically, entangled states are represented as non-simple tensors, indicat- ing that they cannot be factored over the subsystems involved. When certain subsystems can be independently described using a simple tensor, the quantum state is referred to as a product state of those subsystems. Regarding a specific basis, qubits are considered to be in a superposition state when their state-vector is a nontrivial linear combination of basis states. Unlike classical bits, which are limited to being in either the state 0 or 1, a qubit has the potential to exist in any superposition of basis states |0) and |1). The coefficients that define the superposition are referred to as amplitudes, and they are complex numbers. Within quantum mechanics, measurements encompass the
Fig. |. Depiction of a sequence of interconnected blocks.
Fig. |. Depiction of a sequence of interconnected blocks.
CATEGORIZATION OF BLOCKCHAIN-BASED SECURITY WORKS ON VEHICULAR NETWORKS [27]. TABLE VI TABLE VII SUMMARY OF SECURITY REQUIREMENTS IN BLOCKCHAIN-BASED VEHICULAR NETWORKS [27].
CATEGORIZATION OF BLOCKCHAIN-BASED SECURITY WORKS ON VEHICULAR NETWORKS [27]. TABLE VI TABLE VII SUMMARY OF SECURITY REQUIREMENTS IN BLOCKCHAIN-BASED VEHICULAR NETWORKS [27].
KEY PLAYERS IN THE GLOBAL QUANTUM KEY DISTRIBUTION MARKET.
KEY PLAYERS IN THE GLOBAL QUANTUM KEY DISTRIBUTION MARKET.
SOME RESEARCH PAPERS IN QUANTUM CYBERSECURITY [110].
SOME RESEARCH PAPERS IN QUANTUM CYBERSECURITY [110].
documents, will remain valuable even after the advent of quantum computers. If such data, transferred over public networks today, remain relevant for a long time, they may face the threat of being intercepted and decrypted by future quantum computers. For instance, life insurance plans with ex- tended terms or 30-year home mortgage loan agreements could potentially be susceptible to quantum-related risks as they will still be in effect when quantum computers become commer- cially accessible [108]. However, the ease with which PQC algorithms were cracked raises concerns about the outlook for cybersecurity in light of advancements in quantum computing [108]. In summary, due to the limited market share of PQC (currently about 2%), unproven protection from quantum and conventional threats and requiring more computing power and having higher latency, most organizations should wait for PQC technology to mature.
documents, will remain valuable even after the advent of quantum computers. If such data, transferred over public networks today, remain relevant for a long time, they may face the threat of being intercepted and decrypted by future quantum computers. For instance, life insurance plans with ex- tended terms or 30-year home mortgage loan agreements could potentially be susceptible to quantum-related risks as they will still be in effect when quantum computers become commer- cially accessible [108]. However, the ease with which PQC algorithms were cracked raises concerns about the outlook for cybersecurity in light of advancements in quantum computing [108]. In summary, due to the limited market share of PQC (currently about 2%), unproven protection from quantum and conventional threats and requiring more computing power and having higher latency, most organizations should wait for PQC technology to mature.
BLOCKCHAIN PLATFORMS AND WIDELY USED DIGITAL SIGNATURES THAT ARE AFFECTED BY THE QUANTUM THREAT. utilize the ECDSA algorithm with the secp256k1 curve. Ad- ditionally, 10 coins, such as Stellar, Cardano, and Elrond, employ the EdDSA algorithm with curve25519. There are also 8 coins, including Polkadot and Tezos, that make use of multiple signing algorithms and curves, often incorporating both ECDSA/secp256k1 and EdDSA/curve25519 [237]. Fur- ther information on the top cryptocurrencies and their quantum security, particularly regarding the transaction mechanism, is provided in TABLE XII. of consensus efficiency, threshold signatures or aggregated signatures are utilized in blockchain consensus mechanisms to reduce communication complexity and improve scalability. Layer 2 protocols, like payment channels, strive to enhance blockchain throughput by summarizing a significant volume of transactions onto the blockchain. Adaptor signatures have been explored as a means to facilitate layer 2 protocols on blockchains that lack scripting capabilities. Adaptor signatures are a novel type of digital signatures introduced by Poelstra as scriptless scripts [265]. They involve generating a “pre- signature” based on a specific condition and then adapting it to create a complete signature using a witness for that condition. The resulting complete signature appears as a regular signature during verification, making it suitable for blockchain applica- tions. Adaptor signatures offer enhanced functionality and the ability to incorporate conditions surpassing the limitations of the scripting languages of blockchains [165].
BLOCKCHAIN PLATFORMS AND WIDELY USED DIGITAL SIGNATURES THAT ARE AFFECTED BY THE QUANTUM THREAT. utilize the ECDSA algorithm with the secp256k1 curve. Ad- ditionally, 10 coins, such as Stellar, Cardano, and Elrond, employ the EdDSA algorithm with curve25519. There are also 8 coins, including Polkadot and Tezos, that make use of multiple signing algorithms and curves, often incorporating both ECDSA/secp256k1 and EdDSA/curve25519 [237]. Fur- ther information on the top cryptocurrencies and their quantum security, particularly regarding the transaction mechanism, is provided in TABLE XII. of consensus efficiency, threshold signatures or aggregated signatures are utilized in blockchain consensus mechanisms to reduce communication complexity and improve scalability. Layer 2 protocols, like payment channels, strive to enhance blockchain throughput by summarizing a significant volume of transactions onto the blockchain. Adaptor signatures have been explored as a means to facilitate layer 2 protocols on blockchains that lack scripting capabilities. Adaptor signatures are a novel type of digital signatures introduced by Poelstra as scriptless scripts [265]. They involve generating a “pre- signature” based on a specific condition and then adapting it to create a complete signature using a witness for that condition. The resulting complete signature appears as a regular signature during verification, making it suitable for blockchain applica- tions. Adaptor signatures offer enhanced functionality and the ability to incorporate conditions surpassing the limitations of the scripting languages of blockchains [165].
A CONCISE OVERVIEW OF CUTTING-EDGE POST-QUANTUM SIGNATURE SCHEMES [165]. THE SIZE OF AGGREGATE SIGNATURES CORRESPOND TO EACH INDIVIDUAL SIGNER WHEN THERE ARE NV SIGNERS INVOLVED. £ IS THE LENGTH OF THE UNDERLYING LEARNING PARITY WITH NOISE (LPN) PROBLEM. cations and users if such a change were to occur. The authors also identified some approaches for the development of a quantum-resistant digital signature algorithm that can mitigate some of the migration-related challenges. In TABLE XIV, the impacts of replacing ECDSA with a post-quantum signature in different use cases are presented [267]. quired by blockchain systems. Given the diverse range of real-life blockchain applications, only exotic signatures with significant existing blockchain applications are considered and the focus is on practical efficiency rather than theoretical results [165]. Furthermore, since post-quantum ordinary signa- tures have already been extensively surveyed in other studies like [266], they are not discussed in [165]. In TABLE XIII, the overview of cutting-edge post-quantum exotic signature schemes and their applications are provided.
A CONCISE OVERVIEW OF CUTTING-EDGE POST-QUANTUM SIGNATURE SCHEMES [165]. THE SIZE OF AGGREGATE SIGNATURES CORRESPOND TO EACH INDIVIDUAL SIGNER WHEN THERE ARE NV SIGNERS INVOLVED. £ IS THE LENGTH OF THE UNDERLYING LEARNING PARITY WITH NOISE (LPN) PROBLEM. cations and users if such a change were to occur. The authors also identified some approaches for the development of a quantum-resistant digital signature algorithm that can mitigate some of the migration-related challenges. In TABLE XIV, the impacts of replacing ECDSA with a post-quantum signature in different use cases are presented [267]. quired by blockchain systems. Given the diverse range of real-life blockchain applications, only exotic signatures with significant existing blockchain applications are considered and the focus is on practical efficiency rather than theoretical results [165]. Furthermore, since post-quantum ordinary signa- tures have already been extensively surveyed in other studies like [266], they are not discussed in [165]. In TABLE XIII, the overview of cutting-edge post-quantum exotic signature schemes and their applications are provided.
THE EFFECTS OF SUBSTITUTING ECDSA IN VARIOUS USE CASES [267]. BTC AND ETH DENOTE BITCOIN AND ETHEREUM CORRESPONDINGLY. K. AND Kp REPRESENT THE PRIVATE AND PUBLIC-KEYS, RESPECTIVELY.
THE EFFECTS OF SUBSTITUTING ECDSA IN VARIOUS USE CASES [267]. BTC AND ETH DENOTE BITCOIN AND ETHEREUM CORRESPONDINGLY. K. AND Kp REPRESENT THE PRIVATE AND PUBLIC-KEYS, RESPECTIVELY.
SECURITY AND PERFORMANCE REQUIREMENTS FOR BITCOIN [283]. Security and performance requirements for Bitcoin is pro- vided in TABLE XV. Considering this requirements, a separate comparison was conducted to evaluate the application of NIST finalists and alternate candidates of digital signature schemes, such as Dilithium, Falcon, GEMSS128, Picnic2-FS, SPHINCS-s, AQTA, qTESLA-I, XNYSS, NOTS, and Rain- bow, in the Bitcoin network [283]. The timings for signing and verifying are provided and normalized concerning the timings of the classical ECC curve P-256, and alternate candidates are found to be unsuitable for Bitcoin due to issues related to the size of public-key and signature, and also timing performance. While Rainbow shows excellent timing performance, it suffers from a large public-key size and a recent attack. Among the analyzed candidates, Falcon and Dilithium-2 exhibited faster verification times than ECC. Given the significance of verifi- cation in cryptocurrencies, implementing these algorithms for quantum resistant version of Bitcoin should not pose timing performance issues. However, the increased size of public- keys and signatures of Falcon and Dilithium-2 continue to be a matter of concern [283].
SECURITY AND PERFORMANCE REQUIREMENTS FOR BITCOIN [283]. Security and performance requirements for Bitcoin is pro- vided in TABLE XV. Considering this requirements, a separate comparison was conducted to evaluate the application of NIST finalists and alternate candidates of digital signature schemes, such as Dilithium, Falcon, GEMSS128, Picnic2-FS, SPHINCS-s, AQTA, qTESLA-I, XNYSS, NOTS, and Rain- bow, in the Bitcoin network [283]. The timings for signing and verifying are provided and normalized concerning the timings of the classical ECC curve P-256, and alternate candidates are found to be unsuitable for Bitcoin due to issues related to the size of public-key and signature, and also timing performance. While Rainbow shows excellent timing performance, it suffers from a large public-key size and a recent attack. Among the analyzed candidates, Falcon and Dilithium-2 exhibited faster verification times than ECC. Given the significance of verifi- cation in cryptocurrencies, implementing these algorithms for quantum resistant version of Bitcoin should not pose timing performance issues. However, the increased size of public- keys and signatures of Falcon and Dilithium-2 continue to be a matter of concern [283].
PERFORMANCE COMPARISON OF POST-QUANTUM DIGITAL SIGNATURES [148]. a mathematical problem to achieve consensus, utilizing algo- rithms like SHA256, Scrypt, Cryptonight, Equihash and etc. Difficulty adjustment algorithms (DAA) are used to stabilize block generation time, although the original Bitcoin PoW model lacks such an algorithm [147]. The main objective of a blockchain consensus protocol is to establish unanimous agreement among participating nodes regarding the transaction history stored in the blockchain. This is achieved by satisfying several requirements for blockchain consensus. These require- ments include [53], [297]:
PERFORMANCE COMPARISON OF POST-QUANTUM DIGITAL SIGNATURES [148]. a mathematical problem to achieve consensus, utilizing algo- rithms like SHA256, Scrypt, Cryptonight, Equihash and etc. Difficulty adjustment algorithms (DAA) are used to stabilize block generation time, although the original Bitcoin PoW model lacks such an algorithm [147]. The main objective of a blockchain consensus protocol is to establish unanimous agreement among participating nodes regarding the transaction history stored in the blockchain. This is achieved by satisfying several requirements for blockchain consensus. These require- ments include [53], [297]:
COMPARISON OF POST-QUANTUM DIGITAL SIGNATURES (NIST FINALISTS) FOR BLOCKCHAIN APPLICATIONS [148].
COMPARISON OF POST-QUANTUM DIGITAL SIGNATURES (NIST FINALISTS) FOR BLOCKCHAIN APPLICATIONS [148].
BLOCKCHAIN PLATFORMS AND WIDELY USED HASH FUNCTIONS THAT ARE AFFECTED BY THE QUANTUM THREAT.
BLOCKCHAIN PLATFORMS AND WIDELY USED HASH FUNCTIONS THAT ARE AFFECTED BY THE QUANTUM THREAT.
AVAILABLE SURVEYS ON CONSENSUS ALGORITHMS.
AVAILABLE SURVEYS ON CONSENSUS ALGORITHMS.
QUANTUM VULNERABILITIES OF WELL-KNOWN BLOCKCHAINS [185].
QUANTUM VULNERABILITIES OF WELL-KNOWN BLOCKCHAINS [185].
ASSESSMENT OF CONSENSUS ALGORITHMS UTILIZING POST-QUANTUM CRYPTOGRAPHY [158].
ASSESSMENT OF CONSENSUS ALGORITHMS UTILIZING POST-QUANTUM CRYPTOGRAPHY [158].
CONSENSUS ALGORITHMS IN THE LITERATURE WITHOUT A SPECIFIC CLASSIFICATION.
CONSENSUS ALGORITHMS IN THE LITERATURE WITHOUT A SPECIFIC CLASSIFICATION.
Fig. 5. Taxonomy of consensus algorithms.
Fig. 5. Taxonomy of consensus algorithms.
COMPARISON OF SIGNATURE ALGORITHMS FOR SMART CONTRACT SECURITY [348].
COMPARISON OF SIGNATURE ALGORITHMS FOR SMART CONTRACT SECURITY [348].
ATTACKS ON BLOCKCHAINS BY LAYER.
ATTACKS ON BLOCKCHAINS BY LAYER.
OVERVIEW OF ATTACKS ON BLOCKCHAINS AND THEIR IMPLICATIONS IN THE ERA OF QUANTUM COMPUTING (PART 1). breakable security against quantum computers. Quantum key distribution enables secure key sharing, while quantum secure direct communication (QSDC) allows for secure message sharing without a secret key. However, scalability and network size remain challenges for quantum cryptography [234]. able. Increasing the hash length or altering the consensus in blockchain networks can mitigate these risks [234]. Fur- thermore, there are additional solutions that should be taken into account to enhance the security of blockchains against quantum threats.
OVERVIEW OF ATTACKS ON BLOCKCHAINS AND THEIR IMPLICATIONS IN THE ERA OF QUANTUM COMPUTING (PART 1). breakable security against quantum computers. Quantum key distribution enables secure key sharing, while quantum secure direct communication (QSDC) allows for secure message sharing without a secret key. However, scalability and network size remain challenges for quantum cryptography [234]. able. Increasing the hash length or altering the consensus in blockchain networks can mitigate these risks [234]. Fur- thermore, there are additional solutions that should be taken into account to enhance the security of blockchains against quantum threats.
OVERVIEW OF ATTACKS ON BLOCKCHAINS AND THEIR IMPLICATIONS IN THE ERA OF QUANTUM COMPUTING (PART 2). A. Post-quantum Blockchains Another aspect to consider is the security of addresses in blockchain. The use of hash functions ensures that it is mathematically infeasible to drive the public-key from a given P2PKH address. However, when funds are sent from a P2PKH- address, its public-key is exposed during transaction verifica- tion, making it vulnerable to quantum attacks. Approximately 25% of all Bitcoins have addresses that could potentially suffer from such attacks [24].
OVERVIEW OF ATTACKS ON BLOCKCHAINS AND THEIR IMPLICATIONS IN THE ERA OF QUANTUM COMPUTING (PART 2). A. Post-quantum Blockchains Another aspect to consider is the security of addresses in blockchain. The use of hash functions ensures that it is mathematically infeasible to drive the public-key from a given P2PKH address. However, when funds are sent from a P2PKH- address, its public-key is exposed during transaction verifica- tion, making it vulnerable to quantum attacks. Approximately 25% of all Bitcoins have addresses that could potentially suffer from such attacks [24].
SPARE ZN THE COMPARISON AND ANALYSIS OF RELEVANT WORKS IN THE AREA OF QUANTUM BLOCKCHAIN [411]. A: QUANTUM COMPUTING B: BLOCKCHAIN C: QUANTUM BLOCKCHAIN D: HEALTHCARE E: QUANTUM DRONES
SPARE ZN THE COMPARISON AND ANALYSIS OF RELEVANT WORKS IN THE AREA OF QUANTUM BLOCKCHAIN [411]. A: QUANTUM COMPUTING B: BLOCKCHAIN C: QUANTUM BLOCKCHAIN D: HEALTHCARE E: QUANTUM DRONES
and development, incorporating quantum computing and AI deep learning for innovative applications. Overall, blockchain and quantum technologies have the potential to revolutionize various sectors, including medicine, pharmacy, and healthcare systems. TABLE XXX provides the comparison and analysis of previous studies in the quantum blockchain domain [411]. literature on blockchains and quantum computing to establish the current state of research. We then provided an overview of blockchain, highlighting its key components and functionali- ties, while also exploring the preliminaries and key definitions of quantum computing to establish a foundation for under- standing the implications on blockchain security. The applica- tion of blockchains in cybersecurity was thoroughly explored, considering their strengths and vulnerabilities in the context of evolving quantum computing capabilities. Our survey fo- cused specifically on the quantum security of blockchain’s fundamental building blocks, such as digital signatures, hash functions, consensus algorithms, and smart contracts. We analyzed the vulnerabilities introduced by quantum computers, addressing potential countermeasures and enhancements to ensure the integrity and confidentiality of blockchain systems.
and development, incorporating quantum computing and AI deep learning for innovative applications. Overall, blockchain and quantum technologies have the potential to revolutionize various sectors, including medicine, pharmacy, and healthcare systems. TABLE XXX provides the comparison and analysis of previous studies in the quantum blockchain domain [411]. literature on blockchains and quantum computing to establish the current state of research. We then provided an overview of blockchain, highlighting its key components and functionali- ties, while also exploring the preliminaries and key definitions of quantum computing to establish a foundation for under- standing the implications on blockchain security. The applica- tion of blockchains in cybersecurity was thoroughly explored, considering their strengths and vulnerabilities in the context of evolving quantum computing capabilities. Our survey fo- cused specifically on the quantum security of blockchain’s fundamental building blocks, such as digital signatures, hash functions, consensus algorithms, and smart contracts. We analyzed the vulnerabilities introduced by quantum computers, addressing potential countermeasures and enhancements to ensure the integrity and confidentiality of blockchain systems.
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