MOSES DOGONYARO NOEL, Onomza Victor Waziri, Shafi’i Muhammad Abdulhamid, Adebayo Joseph Ojeniyi
Modern computing devices use classical algorithms such as Rivest Shamir Adleman (RSA) and Elliptic Curve Digital Signature Algorithm (ECDSA) for their security. The securities of these algorithms relied on the problem and difficulty of integer factorization and also calculating the Discrete Logarithm Problems. With the introduction of quantum computers, recent research is focusing on developing alternative algorithms which are supposed to withstand attacks from quantum computers. One of such alternatives is the Hash-based Digital Signature Schemes. Chosen hash-based signature schemes over classical algorithms is because their security is on the hash function used and that they are metaheuristic in nature. This research work presents basic analysis and the background understanding of Stateful Hash-based Signature Schemes, particularly the Lamport One-Time Signature Scheme, Winternitz One-Time Signature Scheme, and the Merkle Signature Scheme. The three schemes selected are stateful, hence has common features and are few-time hash-based signature schemes. The selected Stateful Hash-based Digital Signature Schemes were analyzed based on their respective key generation, signature generation, signature verification, and their security levels. Practical working examples were given for better understanding. With the analyses, Merkle Signature Scheme proves to be the best candidate to be used in the Bitcoin Proof of Work protocol because of its security and its advantage of signing many messages.
Amr M. Khalifa, Ayman M. Bahaa-Eldin, Mohamed Sobh
Advances in both quantum computation and blockchain systems necessitate a rigid analysis for the security of blockchains in the advent of powerful quantum computers. Computational problems that are proved or believed to be intractable by classical computers are known to be attacked by well-studied quantum algorithms. Such problems are used as basis to secure blockchains and hence the security of such systems must be defended. As proof-of-work is used in early blockchains to maintain consensus, proof-of-stake was proposed to lower its high energy consumption and provide a higher network throughput. Proof-of-Stake has hence got an increasing interest, variations, implementations and enhancements whilst its quantum security defenses remained almost the same. By comparing proof-of-work to proof-of-stake, we find that the latter is more vulnerable to certain attack vectors. We suggest general defenses for quantum-resilient blockchains and thoroughly analyze post-quantum signature schemes to select an appropriate alternative to the most serious threat on conventional digital signatures.
We provide several advances to the understanding of the class of Quantum Merlin-Arthur proof systems (QMA), the quantum analogue of NP. First, we answer a longstanding open question by showing that the Consistency of Local Density Matrices problem is QMA-complete under Karp reductions. We also show for the first time a commit-and-open computational zero-knowledge proof system for all of QMA as a quantum analogue of a sigma protocol. We then define a Proof of Quantum Knowledge, which guarantees that a prover is effectively in possession of a quantum witness in an interactive proof, and show that our zero-knowledge proof system satisfies this definition. Finally, we show that our proof system can be used to establish that QMA has a quantum non-interactive zero-knowledge proof system in the secret parameters setting.
Our main technique consists in developing locally simulatable proofs for all of QMA: this is an encoding of a QMA witness such that it can be efficiently verified by probing only five qubits and, furthermore, the reduced density matrix of any five-qubit subsystem can be computed in polynomial time and is independent of the witness. This construction follows the techniques of Grilo, Slofstra, and Yuen [FOCS 2019].
Muhammad Taimour Azhar, Muhammad Burhan Khan, Asim ur Rehman Khan
A block chain is referred to as a growing list of records which are linked using cryptography. It is simple and open ledger that records all the transactions in block structures. These block structures are bound with each other by using Quantum Cryptographic protocols. The block chain is democratic system in which concerned parties get access by using a key to perform transaction. The well-known type of Quantum Cryptography protocol is Quantum Key Distribution (QKD). With the help of QKD our Crypto-currency system is secured when passage in between transmitting end and receiving end shouldn't be intrude by third party. Secrecy of the system depends upon different factors like efficient and optimized key rate, secure carrier of modulating signal. In this work the transparency and immunity of block chain based crypto-currency system is analyzed with simulation of six state QKD Protocol. The generation of key rate is observed to ensure the path for production of better crypto-currency system. A Mathematical model is used to obtain the desire constraints so that linear relationship can be achieved. At application level this study contributes to the implementation of crypto-currency system through six state QKD protocol.
We model the hardware and software architecture for generalized Internet of Things (IoT) by quantum cloud-computing and blockchain. To reduce the measurement error and increase the efficiency of quantum entanglement (i.e. the capability of fault tolerance) in the current quantum computers and communications, we design a quantum-computing chip by modelling it as a multi-input multi-output (MIMO) quantum channel and obtain its channel capacity via our recently derived mutual information formula. To capture the internal qubit data flow dynamics of the channel, we model it via a deep convolutional neural network (DCNN) with generalized stochastic pooling in terms of resource-competition among different quantum eigenmodes or users. The pooling is corresponding to a resource allocation policy with two levels of competitions as in cognitive radio: the first one is on users’ selection in a ‘win–lose’ manner; the second one is on resourcesharing among selected users in a ‘win–win’ manner. To wit, our scheduling policy is the one by mixing a saddle point to a zero-sum game problem and a Pareto optimal Nash equilibrium point to a nonzero- sum game problem. The effectiveness of our policy is proved by diffusion modelling with theory and numerical examples.
Blockchains interoperability is one of the hardest problems to be solved in the nowadays blockchain ecosystem that contains thousands of different blockchains. This paper focuses on swapping assets from a blockchain to another without a trusted third party. One recent scheme for atomically swapping assets, Atomic Cross Chain Swap (ACCS), has been formally analyzed in [2]. This paper proposes an implementation of an ACCS between the two most valued crypto-currencies today: Bitcoin and Ether.
Distributed Ledger Technology (DLT) is a shared, synchronized and replicated data spread spatially and temporally with no centralized administration and/or storage. Each node has a complete and identical set of records. All participants contribute to building and maintaining the distributed ledger. Current DLT technologies fall into two broad categories. Those that use block-chains such as in Bitcoin or Ethereum, and newer approaches which reduce computational loads for verification. All current approaches though difficult to crack can be vulnerable to quantum algorithms using Quantum Information Technologies (QIT). This effort joins the 2 technologies, constructing a Quantum Distributed Ledger (QDL) which provides a higher level of security using QIT and a decentralized data depository using DLT. This enhanced security prevents middleman attacks with quantum computers yet retains the advantages of a decentralized ledger of data.
Xin Sun, Mirek Sopek, Quanlong Wang, Piotr Kulicki
While Blockchain technology is universally considered as a significant technology for the near future, some of its pillars are under a threat of another thriving technology, Quantum Computing. In this paper, we propose important safeguard measures against this threat by developing a framework of a quantum-secured, permissioned blockchain called Logicontract (LC). LC adopts a digital signature scheme based on Quantum Key Distribution (QKD) mechanisms and a vote-based consensus algorithm to achieve consensus on the blockchain. The main contribution of this paper is in the development of: (1) unconditionally secure signature scheme for LC which makes it immune to the attack of quantum computers; (2) scalable consensus protocol used by LC; (3) logic-based scripting language for the creation of smart contracts on LC; (4) quantum-resistant lottery protocol which illustrates the power and usage of LC.
IOTA is a lightweight quantum-resistant distributed ledger protocol designed for Internet of Things devices. The protocol uses a one-time cryptographic signature scheme that is resistant against attacks by quantum computers. This one-time signature scheme results in a portion of an address's private key being revealed in the signature of each outgoing transaction from that address. If an address is used for multiple outgoing transfers, it is feasible for an adversary to forge a signature by using parts of the private key associated with the address that have been revealed. In this paper, we propose the use of the cuckoo filter in the IOTA core lightweight client in order to avoid address reuse. We validate our proposed approach by implementation and evaluation in the real IOTA architecture. The obtained performance results show that the cuckoo filter integration in the IOTA core lightweight client avoids address reuse and makes the process of new address generation much more efficient and secure. Additionally, our approach can be integrated directly into the current IOTA core lightweight client.
We study the relationship between problems solvable by quantum algorithms in polynomial time and those for which zero-knowledge proofs exist. In prior work, Aaronson [arxiv:quant-ph/0111102] showed an oracle separation between BQP and SZK, i.e. an oracle $A$ such that $\mathrm{SZK}^A \not\subseteq \mathrm{BQP}^A$. In this paper we give a simple extension of Aaronson's result to non-interactive zero-knowledge proofs with perfect security. This class, NIPZK, is the most restrictive zero-knowledge class. We show that even for this class we can construct an $A$ with $\mathrm{NIPZK}^A \not\subseteq \mathrm{BQP}^A$.
We study the relationship between problems solvable by quantum algorithms in\npolynomial time and those for which zero-knowledge proofs exist. In prior work,\nAaronson [arxiv:quant-ph/0111102] showed an oracle separation between BQP and\nSZK, i.e. an oracle $A$ such that $\\mathrm{SZK}^A \\not\\subseteq\n\\mathrm{BQP}^A$. In this paper we give a simple extension of Aaronson's result\nto non-interactive zero-knowledge proofs with perfect security. This class,\nNIPZK, is the most restrictive zero-knowledge class. We show that even for this\nclass we can construct an $A$ with $\\mathrm{NIPZK}^A \\not\\subseteq\n\\mathrm{BQP}^A$.\n
Vikram Suresh, Sudhir Satpathy, Raghavan Kumar, Mark Anders · 10 authors
A 0.15mm2Bitcoin mining engine is fabricated in 14nm CMOS with highest-reported energy-efficiency of 0.063J/GHash at 250mV, 25°C. Fully-unrolled SHA256 datapath with Bitcoin-specific lookahead/deferred digest optimizations and 3-cycle distributed scheduler provide 31/56% digest/scheduler delay reductions, resulting in 10% higher energy-efficiency with dual-Vcc operation. 3-phase latch-based clocking with stretchable non-overlapping clocks eliminates all min-delay paths, reducing total sequential power consumption by 50%. Robust mining operation over a wide supply range of 230-900mV is demonstrated, with 10-760MHash/s throughput measured at 100°C.
In this work we consider the interplay between multiprover interactive proofs, quantum entanglement, and zero knowledge proofs - notions that are central pillars of complexity theory, quantum information and cryptography. In particular, we study the relationship between the complexity class MIP*, the set of languages decidable by multiprover interactive proofs with quantumly entangled provers, and the class PZK-MIP*, which is the set of languages decidable by MIP* protocols that furthermore possess the perfect zero knowledge property. Our main result is that the two classes are equal, i.e., MIP* = PZK-MIP*. This result provides a quantum analogue of the celebrated result of Ben-Or, Goldwasser, Kilian, and Wigderson (STOC 1988) who show that MIP = PZK-MIP (in other words, all classical multiprover interactive protocols can be made zero knowledge). We prove our result by showing that every MIP* protocol can be efficiently transformed into an equivalent zero knowledge MIP* protocol in a manner that preserves the completeness-soundness gap. Combining our transformation with previous results, we obtain the corollaries that i) all languages that can be solved in non-deterministic double exponential time have zero knowledge MIP* protocols and ii) all co-recursively enumerable languages (which include undecidable problems as well as all decidable problems) have zero knowledge MIP* protocols with vanishing promise gap.
This paper evaluates the current cybersecurity vulnerability of the prolific use of Elliptical Curve Digital Signature Algorithm (**ECDSA**) cryptography in use by the Bitcoin Core, Ethereum, Bitcoin Cash, and enterprise blockchains such as Multi-Chain and Hyperledger projects Fabric, and Sawtooth Lake. These blockchains are being used in media, health, finance, transportation and government with little understanding, acknowledgment of the risk and no known plans for mitigation and migration to safer public-key cryptography. The second aim is to evaluate ECDSA against the threat of **Quantum Computing** and propose the most practical National Institute of Standards and Technology (NIST) Post-Quantum Cryptography candidate algorithm lattice-based cryptography countermeasure that can be implemented near-term and provide a basis for a coordinated industry-wide lattice-based public-key implementation. Commercial quantum computing research and development is rapid and unpredictable, and it is difficult to predict the arrival of fault-tolerant quantum computing. The current state of covert and classified quantum computing research and advancement is unknown and therefore, it would be a significant risk to blockchain and Internet technologies to delay or wait for the publication of draft standards. Since there are many hurdles Post-Quantum Cryptography (PQC) must overcome for standardisation, coordinated large-scale testing and evaluation should commence promptly.
Lake Bu, Rashmi Agrawal, Hai Cheng, Michel A. Kinsy
The development and implementation of post-quantum cryptosystems have become a pressing issue in the design of secure computing systems, as general quantum computers have become more feasible in the last two years. In this work, we introduce a set of hardware post-quantum cryptographic primitives (PCPs) consisting of four frequently used security components, i.e., public-key cryptosystem (PKC), key exchange (KEX), oblivious transfer (OT), and zero-knowledge proof (ZKP). In addition, we design a high speed polynomial multiplier to accelerate these primitives. These primitives will aid researchers and designers in constructing quantum-proof secure computing systems in the post-quantum era.
Zero-knowledge and multi-prover systems are both central notions in classical and quantum complexity theory. There is, however, little research in quantum multi-prover zero-knowledge systems. This paper studies complexity-theoretical aspects of the quantum multi-prover zero-knowledge systems. This paper has two results: 1.QMIP* systems with honest zero-knowledge can be converted into general zero-knowledge systems without any assumptions. 2.QMIP* has computational quantum zero-knowledge systems if a natural computational conjecture holds. One of the main tools is a test (called the GHZ test) that uses GHZ states shared by the provers, which prevents the verifier's attack in the above two results. Another main tool is what we call the Local Hamiltonian based Interactive protocol (LHI protocol). The LHI protocol makes previous research for Local Hamiltonians applicable to check the history state of interactive proofs, and we then apply Broadbent et al.'s zero-knowledge protocol for QMA \cite{BJSW} to quantum multi-prover systems in order to obtain the second result.
We outline a quantum-enabled blockchain architecture based on a consortium of quantum servers. The network is hybridised, utilising digital systems for sharing and processing classical information combined with a fibre--optic infrastructure and quantum devices for transmitting and processing quantum information. We deliver an energy efficient interactive mining protocol enacted between clients and servers which uses quantum information encoded in light and removes the need for trust in network infrastructure. Instead, clients on the network need only trust the transparent network code, and that their devices adhere to the rules of quantum physics. To demonstrate the energy efficiency of the mining protocol, we elaborate upon the results of two previous experiments (one performed over 1km of optical fibre) as applied to this work. Finally, we address some key vulnerabilities, explore open questions, and observe forward--compatibility with the quantum internet and quantum computing technologies.
We show that every language in QMA admits a classical-verifier, quantum-prover zero-knowledge argument system which is sound against quantum polynomial-time provers and zero-knowledge for classical (and quantum) polynomial-time verifiers. The protocol builds upon two recent results: a computational zero-knowledge proof system for languages in QMA, with a quantum verifier, introduced by Broadbent et al. (FOCS 2016), and an argument system for languages in QMA, with a classical verifier, introduced by Mahadev (FOCS 2018).
This work is an exploration of how graphs and permutations can be applied in the context of quantum information processing. In Chapter 2 we consider problems about the permutations of the subsystems of a quantum system. Explicitly, we attempt to understand the problem of determining if two quantum states of N qubits are isomorphic: if one can be obtained from the other by permuting its subsystems. We show that the well known graph isomorphism problem is a special case of state isomorphism. We also show that the complement of state isomorphism, the problem of determining if two states are not isomorphic, can be verified by a quantum interactive proof system, and that this proof system can be made statistical zero knowledge. We also consider the complexity of isomorphism problems for stabilizer states, and mixed states. In Chapter 3 we work with a special class of quantum states called grid states, in an effort to develop a toy model for mixed state entanglement. The key idea with grid states is that they can be represented by what we call a grid-labelled graph, literally, a graph forced to have vertices on a two dimensional grid. We show that whether or not a grid state is entangled can sometimes be determined solely from the structural properties of its corresponding grid-labelled graph. We use the grid state framework to build families of bound entangled states, suggesting that even in this restricted setting detecting entanglement is non-trivial and will require more than a single entanglement criterion.
Peter B. Rønne, Arash Atashpendar, Kristian Gjøsteen, Peter Y. A. Ryan
We present an approach for performing the tallying work in the coercion-resistant JCJ voting protocol, introduced by Juels, Catalano, and Jakobsson, in linear time using fully homomorphic encryption (FHE). The suggested enhancement also paves the path towards making JCJ quantum-resistant, while leaving the underlying structure of JCJ intact. The exhaustive, comparison-based approach of JCJ using plaintext equivalence tests leads to a quadratic blow-up in the number of votes, which makes the tallying process rather impractical in realistic settings with a large number of voters. We show how the removal of invalid votes can be done in linear time via a solution based on recent advances in various FHE primitives such as hashing, zero-knowledge proofs of correct decryption, verifiable shuffles and threshold FHE. We conclude by touching upon some of the advantages and challenges of such an approach, followed by a discussion of further security and post-quantum considerations.