Quantum Attacks on Bitcoin, and How to Protect Against Them

Aggarwal, Divesh; Brennen, Gavin K.; Lee, Troy; Sántha, Miklós; Tomamichel, Marco

doi:10.5195/ledger.2018.127

Cited by 107 publications

(92 citation statements)

References 42 publications

(25 reference statements)

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“…In the case of error rates, although error rates of 10 −3 combined with <100ns gate times have not yet been demonstrated, an ultimate error rate of 10 −5 may even be pessimistic, if more exotic technologies such as topological quantum computers come to fruition; an effective error rate of 10 −9 has been assumed elsewhere in the literature for such devices [84]. See [3] for a more detailed performance extrapolation.…”

Section: Parametermentioning

confidence: 99%

“…Here we outline our resource methdology, which follows a model developed by several previous works in this area [3,8,10,53,78]. The model assumes that the quantum computation is encoded using the surface code [53], a quantum error-correcting code with properties that make it an excellent candidate for implementation on near-term hardware platforms (e.g.…”

Section: Timing and Cost Modelmentioning

confidence: 99%

“…Toffoli and T gates can be implemented faulttolerantly using a state injection technique where a special state is prepared offline (a Toffoli state [48,61] or T state [27]), and then used to implement the corresponding gate. We include in Appendix A an algorithm for computing the costs associated with this, based on the protocol of [48,61] and using the analysis of [78] (see also [3,53]). Some illustrative spacetime costs are shown in Table 3 for Toffoli gates, which dominate the complexity of the circuits we consider; the values for T gates are similar.…”

Section: Timing and Cost Modelmentioning

confidence: 99%

See 2 more Smart Citations

Applying quantum algorithms to constraint satisfaction problems

Montanaro

Campbell

Khurana

2019

Quantum

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Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best classical algorithms and taking into account realistic hardware parameters and overheads for fault-tolerance.All known examples of such speedups correspond to problems related to simulation of quantum systems and cryptography. Here we apply general-purpose quantum algorithms for solving constraint satisfaction problems to two families of prototypical NP-complete problems: boolean satisfiability and graph colouring. We consider two quantum approaches: Grover's algorithm and a quantum algorithm for accelerating backtracking algorithms. We compare the performance of optimised versions of these algorithms, when applied to random problem instances, against leading classical algorithms. Even when considering only problem instances that can be solved within one day, we find that there are potentially large quantum speedups available. In the most optimistic parameter regime we consider, this could be a factor of over 10 5 relative to a classical desktop computer; in the least optimistic regime, the speedup is reduced to a factor of over 10 3 . However, the number of physical qubits used is extremely large, and improved fault-tolerance methods will likely be needed to make these results practical. In particular, the quantum advantage disappears if one includes the cost of the classical processing power required to perform decoding of the surface code using current techniques. Many quantum algorithms are known, for tasks as diverse as integer factorisation [92] and computing Jones polynomials [4]. Indeed, at the time of writing, the Quantum Algorithm Zoo website [62] cites 392 papers on quantum algorithms. However, there Ashley

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Section: Parametermentioning

confidence: 99%

Section: Timing and Cost Modelmentioning

confidence: 99%

Section: Timing and Cost Modelmentioning

confidence: 99%

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Applying quantum algorithms to constraint satisfaction problems

Montanaro

Campbell

Khurana

2019

Quantum

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“…Furthermore, there is always the case that personal data to become unreadable or available to everyone when the key is either lost or becomes accidentally known [78], [64], [79]. Taken into account that data shall remain encrypted across their life cycle, a further limitation derives from the rapid advancements in quantum computing which, according to experts, is going to break most encryption schemes used nowadays [80], [81], [82], [83]. To avoid information be susceptible to decryption once quantum computers become available, sensitive data need to be protected in the long term by using symmetric algorithms with long key lengths.…”

Section: A Bypassing Blockchain's Immutabilitymentioning

confidence: 99%

Blockchain Mutability: Challenges and Proposed Solutions

Πολίτου

Casino

Alepis

et al. 2021

IEEE Trans. Emerg. Topics Comput.

151

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Blockchain's evolution during the past decade is astonishing: from bitcoin to over 2.000 altcoins, and from decentralised electronic payments to transactions programmable by smart contracts and complex tokens governed by decentralised organisations. While the new generation of blockchain applications is still evolving, blockchain's technical characteristics are also advancing. Yet, immutability, a hitherto indisputable property according to which blockchain data cannot be edited nor deleted, remains the cornerstone of blockchain's security. Nevertheless, blockchain's immutability is being called into question lately in the light of the new erasing requirements imposed by the GDPR's "Right to be Forgotten (RtbF)" provision. As the RtbF obliges blockchain data to be editable in order restricted content redactions, modifications or deletions to be applied when requested, blockchains compliance with the regulation is indeed challenging, if not impracticable. Towards resolving this contradiction, various methods and techniques for mutable blockchains have been proposed in an effort to satisfy regulatory erasing requirements while preserving blockchains' security. To this end, this work aims to provide a comprehensive review on the state-of-the-art research approaches, technical workarounds and advanced cryptographic techniques that have been put forward to resolve this conflict and to discuss their potentials, constraints and limitations when applied in the wild to either permissioned or permissionless blockchains.Index Terms-Blockchain, immutability, Right to be forgotten, GDPR

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“…We note that the security of Bitcoin from the viewpoint of attacks from quantum computers has been considered in Ref. [6]. Large-scale quantum computers that enable to realize such an algorithm, however, are not yet available.…”

Section: Introductionmentioning

confidence: 99%

Detecting Brute-Force Attacks on Cryptocurrency Wallets

Kiktenko

Kudinov

Fedorov

2019

Business Information Systems Workshops

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Blockchain is a distributed ledger, which is protected against malicious modifications by means of cryptographic tools, e.g. digital signatures and hash functions. One of the most prominent applications of blockchains is cryptocurrencies, such as Bitcoin. In this work, we consider a particular attack on wallets for collecting assets in a cryptocurrency network based on brute-force search attacks. Using Bitcoin as an example, we demonstrate that if the attack is implemented successfully, a legitimate user is able to prove that fact of this attack with a high probability. We also consider two options for modification of existing cryptocurrency protocols for dealing with this type of attacks. First, we discuss a modification that requires introducing changes in the Bitcoin protocol and allows diminishing the motivation to attack wallets. Second, an alternative option is the construction of special smart-contracts, which reward the users for providing evidence of the brute-force attack. The execution of this smart-contract can work as an automatic alarm that the employed cryptographic mechanisms, and (particularly) hash functions, have an evident vulnerability.

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Quantum Attacks on Bitcoin, and How to Protect Against Them

Cited by 107 publications

References 42 publications

Applying quantum algorithms to constraint satisfaction problems

Applying quantum algorithms to constraint satisfaction problems

Blockchain Mutability: Challenges and Proposed Solutions

Detecting Brute-Force Attacks on Cryptocurrency Wallets

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