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Cybersecurity

Efficient post-quantum secure deterministic wallet scheme

Mingxing Hu, Zhen Liu, Yunhong Zhou

Published Aug 3, 2024• 8 citations
Publisher

Abstract

Abstract Since the advent of Bitcoin, cryptocurrencies have gained substantial popularity, and crypto wallets have evolved into the predominant tool for safeguarding and managing cryptographic keys to access cryptocurrency funds. Deterministic wallets are proposed as an advanced wallet mechanism to provide benefits such as low-maintenance, easy backup and recovery, and support for functionalities required by cryptocurrencies. Alkeilani Alkadri et al. (ACM CCS’20) presented the first post-quantum secure deterministic wallet scheme, but it exhibits a gap to bridge before achieving practical applicability, as reflected in both their concrete parameters size and computational efficiency. In this paper, we propose an efficient post-quantum secure deterministic wallet scheme. In particular, we present a new construction method for deterministic wallets, prove the security in the quantum random oracle model, and provide an efficient instantiation. The comparison result, with the work of Alkeilani Alkadri et al. (ACM CCS’20), shows our work has a comprehensive improvement on efficiency, e.g., the pk size is $$\approx 40.7$$ ≈ 40.7 times shorter, sk is $$\approx 9.2$$ ≈ 9.2 times shorter, and the signing time is $$\approx 3.1$$ ≈ 3.1 times faster.

DOI
10.1186/s42400-024-00216-w

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Abstract Since the advent of Bitcoin, cryptocurrencies have gained substantial popularity, and crypto wallets have evolved into the predominant tool for safeguarding and managing cryptographic keys to access cryptocurrency funds. Deterministic wallets are proposed as an advanced wallet mechanism to provide benefits such as low-maintenance, easy backup and recovery, and support for functionalities required by cryptocurrencies. Alkeilani Alkadri et al. (ACM CCS’20) presented the first post-quantum secure deterministic wallet scheme, but it exhibits a gap to bridge before achieving practical applicability, as reflected in both their concrete parameters size and computational efficiency. In this paper, we propose an efficient post-quantum secure deterministic wallet scheme. In particular, we present a new construction method for deterministic wallets, prove the security in the quantum random oracle model, and provide an efficient instantiation. The comparison result, with the work of Alkeilani Alkadri et al. (ACM CCS’20), shows our work has a comprehensive improvement on efficiency, e.g., the pk size is ≈40.7\approx 40.7≈40.7 ≈ 40.7 times shorter, sk is ≈9.2\approx 9.2≈9.2 ≈ 9.2 times shorter, and the signing time is ≈3.1\approx 3.1≈3.1 ≈ 3.1 times faster.
Most blockchain solutions are susceptible to quantum attackers as they rely on cryptography that is known to be insecure in the presence of quantum adversaries. In this work we advance the study of quantum-resistant blockchain solutions by giving a quantum-resistant construction of a deterministic wallet scheme. Deterministic wallets are frequently used in practice in order to secure funds by storing the sensitive secret key on a so-called cold wallet that is not connected to the Internet. Recently, Das et al. (CCS'19) developed a formal model for the security analysis of deterministic wallets and proposed a generic construction from certain types of signature schemes that exhibit key rerandomization properties. We revisit the proposed classical construction in the presence of quantum adversaries and obtain the following results.
Cryptocurrency networks crucially rely on digital signature schemes, which are used as an authentication mechanism for transactions. Unfortunately, most major cryptocurrencies today, including Bit-coin and Ethereum, employ signature schemes that are susceptible to quantum adversaries, i.e., an adversary with access to a quantum computer can forge signatures and thereby spend coins of honest users. In cryptocurrency networks, signature schemes are typically not executed in isolation, but within a so-called cryptographic wallet. In order to achieve security against quantum adversaries, the signature scheme and the cryptographic wallet must withstand quantum attacks.
Blockchain technology has gained significant prominence in recent years due to its public, distributed, and decentration characteristics, which was widely applied in all walks of life requiring distributed trustless consensus. However, the most cryptographic protocols used in the current blockchain networks are susceptible to the quantum attack with rapid development of a sufficiently large quantum computer. In this paper, we first give an overview of the vulnerabilities of the modern blockchain networks to a quantum adversary and some potential post-quantum mitigation methods. Then, a new lattice-based signature scheme has been proposed, which can be used to secure the blockchain network over existing classical channels. Meanwhile, the public and private keys are generated by the Bonsai Trees technology withRandBasisalgorithm from the root keys, which not only ensure the randomness, but also construct the lightweight nondeterministic wallets. Then, the proposed scheme can be proved secure in random oracle model, and it is also more efficient than similar literatures. In addition, we also give the detailed description of the post-quantum blockchain transaction. Furthermore, this work can help to enrich the research on the future post-quantum blockchain (PQB).
Current solutions to quantum vulnerabilities of widely used cryptographic schemes involve migrating users to post-quantum schemes before quantum attacks become feasible. This work deals with protecting quantum procrastinators: users that failed to migrate to post-quantum cryptography in time. To address this problem in the context of digital signatures, we introduce a technique called signature lifting, that allows us to lift a deployed pre-quantum signature scheme satisfying a certain property to a post-quantum signature scheme that uses the same keys. Informally, the said property is that a post-quantum one-way function is used "somewhere along the way" to derive the public-key from the secret-key. Our constructions of signature lifting relies heavily on the post-quantum digital signature scheme Picnic (Chase et al., CCS'17). Our main case-study is cryptocurrencies, where this property holds in two scenarios: when the public-key is generated via a key-derivation function or when the public-key hash is posted instead of the public-key itself. We propose a modification, based on signature lifting, that can be applied in many cryptocurrencies for securely spending pre-quantum coins in presence of quantum adversaries. Our construction improves upon existing constructions in two major ways: it is not limited to pre-quantum coins whose ECDSA public-key has been kept secret (and in particular, it handles all coins that are stored in addresses generated by HD wallets), and it does not require access to post-quantum coins or using side payments to pay for posting the transaction.
Nowadays, blockchain has become one of the most cutting-edge technologies, which has been widely concerned and researched. However, the quantum computing attack seriously threatens the security of blockchain, and related research is still less. Targeting at this issue, in this paper, we present the definition of post-quantum blockchain (PQB) and propose a secure cryptocurrency scheme based on PQB, which can resist quantum computing attacks. First, we propose a signature scheme based on lattice problem. We use lattice basis delegation algorithm to generate secret keys with selecting a random value, and sign message by preimage sampling algorithm. In addition, we design the first-signature and last-signature in our scheme, which are defined as double-signature. It is used to reduce the correlation between the message and the signature. Second, by combining the proposed signature scheme with blockchain, we construct the PQB and propose this cryptocurrency scheme. Its security can be reduced to the lattice short integer solution (SIS) problem. At last, through our analysis, the proposed cryptocurrency scheme is able to resist the quantum computing attack and its signature satisfies correctness and one-more unforgeability under the lattice SIS assumption. Furthermore, compared with previous signature schemes, the sizes of signature and secret keys are relatively shorter than that of others, which can decrease the computational complexity. These make our cryptocurrency scheme more secure and efficient.
Smart contracts are cryptographic protocols that are enforced without a judiciary. Smart contracts are used occasionally in Bitcoin and are prevalent in Ethereum. Public quantum money improves upon cash we use today, yet the current constructions do not enable smart contracts. In this work, we define and introduce quantum payment schemes, and show how to implement prudent contracts -- a non-trivial subset of the functionality that a network such as Ethereum provides. Examples discussed include: multi-signature wallets in which funds can be spent by any 2-out-of-3 owners; restricted accounts that can send funds only to designated destinations; and "colored coins" that can represent stocks that can be freely traded, and their owner would receive dividends. Our approach is not as universal as the one used in Ethereum since we do not reach a consensus regarding the state of a ledger. We call our proposal prudent contracts to reflect this. The main building block is either quantum tokens for digital signatures (Ben-David and Sattath QCrypt'17, Coladangelo et al. Crypto'21), semi-quantum tokens for digital signatures (Shmueli'22) or one-shot signatures (Amos et al. STOC'20). The solution has all the benefits of public quantum money: no mining is necessary, and the security model is standard (e.g., it is not susceptible to 51\% attacks, as in Bitcoin). Our one-shot signature construction can be used to upgrade the Bitcoin network to a quantum payment scheme. Notable advantages of this approach are: transactions are locally verifiable and without latency, the throughput is unbounded, and most importantly, it would remove the need for Bitcoin mining. Our approach requires a universal large-scale quantum computer and long-term quantum memory; hence we do not expect it to be implementable in the next few years.