We propose the first generalization of the famous Non-Interactive Zero-Knowledge (NIZK) proofs to quantum languages (NIZKoQS) and we provide a protocol to prove advanced properties on a received quantum state non-destructively and non-interactively (a single message being sent from the prover to the verifier). In our second orthogonal contribution, we improve the costly Remote State Preparation protocols [Cojocaru et al. 2019 ; Gheorghiu and Vidick 2019 ] that can classically fake a quantum channel (this is at the heart of our NIZKoQS protocol) by showing how to create a multi-qubit state from a single superposition. Finally, we generalize these results to a multi-party setting and prove that multiple parties can anonymously distribute a GHZ state in such a way that only participants knowing a secret credential can share this state, which could have applications to quantum anonymous transmission, quantum secret sharing, quantum onion routing and more.
We propose the first generalization of the famous Non-Interactive\nZero-Knowledge (NIZK) proofs to quantum languages (NIZKoQS) and we provide a\nprotocol to prove advanced properties on a received quantum state\nnon-destructively and non-interactively (a single message being sent from the\nprover to the verifier).\n In our second orthogonal contribution, we improve the costly Remote State\nPreparation protocols [CCKW18,CCKW19,GV19] that can classically fake a quantum\nchannel (this is at the heart of our NIZKoQS protocol) by showing how to create\na multi-qubits state from a single superposition.\n Finally, we generalize these results to a multi-party setting and prove that\nmultiple parties can anonymously distribute a GHZ state in such a way that only\nparticipants knowing a secret credential can share this state, which could have\napplications to quantum anonymous transmission, quantum secret sharing, quantum\nonion routing and more.\n
Due to the need to maintain confidentiality, redundancy, and openness, the usage of Blockchain and other DLTs has dramatically advanced in recent years, and is being recommended for various applications. In blockchain, these capabilities are supplied by means of hash functions and public-key encryption. However, the rapid development of quantum computation in the near future has opened the door to the Grover and Shor algorithms. These algorithms challenge both public and hash encryption, causing blockchains to redesign and use quantum attack-tolerant cryptosystems; this produces cryptosystems which are considered post-quantum cryptosystems, which are quantum-resistant. This paper reviews current scientists on quantum blockchain for such purposes. In addition, the major challenges are studied with the most important post-quantum blockchain systems. In addition, the most promising post quantum signature encryption and digital blockchain signature schemes are detailed in terms of the functionality and durability of the most promising public signatures. In this article, researchers and developers in blockchain have an extensive perspective and practical advice on post-quantum blockchain protection.
Hyoungsung Kim, Jaehyuk Jang, Sangjun Park, Heung-No Lee
The error-correction code based proof-of-work (ECCPoW) algorithm is based on a low-density parity-check (LDPC) code. The ECCPoW is possible to impair ASIC with its time-varying capability of the parameters of LDPC code. Previous researches on the ECCPoW algorithm have presented its theory and implementation on Bitcoin. But they do not discuss how stable the block generation time is. A finite mean block generation time (BGT) and none heavy-tail BGT distribution are the ones of the focus in this study. In the ECCPoW algorithm, BGT may show a long-tailed distribution due to time-varying cryptographic puzzles. Thus, it is of interest to see if the BGT distribution is not heavy-tailed and if it shows a finite mean. If the distribution is heavy-tailed, then confirmation of a transaction cannot be guaranteed. We present implementation, simulation, and validation of ECCPoW Ethereum. In implementation, we explain how the ECCPoW algorithm is integrated into Ethereum 1.0 as a new consensus algorithm. In the simulation, we perform a multinode simulation to show that the ECCPoW Ethereum works well with automatic difficulty change. In the validation, we present the statistical results of the two-sample Anderson-Darling test to show that the distribution of BGT satisfies the necessary condition of the exponential distribution. Our implementation is downloadable at https://github.com/cryptoecc/ETH-ECC.
In this paper, we introduce a new approach to fix the validation of a block and the assignment of a new block in a blockchain infrastructure by using a novel negotiation procedure. The block validation and assignment are reached thanks to negotiation procedures based on an extended probability environment. Also, by using a multiscale approach (typical of Complexity Theory) and Quantum and Relativistic Mechanics, the result appears to solve some of the most relevant questions in the Blockchain context, which are the democracy and the randomness of the validator of a block and the assignment of the new one. The selection of actors to mine is invariant concerning the number of addresses, i.e., the coins of owners, which have more chance to be selected generally. This work is the companion of CQKD (Computational Quantum Key Distribution), as we will see in the introduction, where we considered the infrastructural question of the key distribution; also, it is a very effective application of the decision and reasoning in incompleteness or uncertainty conditions as described in the previous and prodromic paper as described in the introduction too.
This White Paper introduces and contributes the first implementation of the Decentralized Voting Algorithm. First, Part I provides an overview for the software structures relevant to this work. Second, Part II introduces a decentralized voting algorithm for transferring value on blockchain networks. Third, Part III explains the voting algorithm’s implementation in reach, including the backend architecture, web deployment, and quantum integration. Perhaps most significantly, this paper solves the Decentralized Voting Problem with a new quantum consensus system.
Rahul Saha, Gulshan Kumar, Tannishtha Devgun, William J. Buchanan · 8 authors
The decentralization and transparency have provided wide acceptance of blockchain technology in various sectors through numerous applications. The claimed security services by blockchain have been proved using various cryptographic techniques, mainly public key infrastructure and digital signatures. However, the use of generic cryptographic primitives using large prime numbers or elliptic curves with logarithms is going to be an issue with quantum computers as those techniques are vulnerable in post-quantum era. Therefore, the paradigm shift from pre-quantum to the post-quantum era has necessitated new cryptographic developments which are robust against quantum attacks and applicable in blockchain for post-quantum decentralization. Therefore, we have presented a solution for post-quantum decentralization in the blockchain. It uses lattices with polynomials for identity-based encryption (IBE) and aggregate signatures for the consensus to ensure efficiency and suitability in post-quantum blockchain applications. We experiment the proposed approach based on delay, throughput, energy consumption and complexity. The comparative results prove that the presented work is efficient.
Novak Kaluđerović, Thorsten Kleinjung, Dušan Kostić
Linear Legendre pseudorandom functions were introduced in 1988 by Damgrd, and higher degree generalisations were introduced by Russell and Shparlinski in 2004. We present new key recovery methods that improve the state of the art for both cases. For degree r 3 we give an attack that runs in time O( p r -3 ) after O( p 3 ) precomputation for the most relevant high degree case; it is based on the action of the group of Mbius transformations on degree r polynomials. For r < 3 we give an O( p r/2 ) attack with O( p r/4 ) oracle queries. In the linear case we recovered the keys for the 64, 74 and 84-bit prime Ethereum challenges, being the first to solve the 84-bit case.
Prabhanjan Ananth, Kai-Min Chung, Rolando L. La Placa
We study the notion of zero-knowledge secure against quantum polynomial-time verifiers (referred to as quantum zero-knowledge) in the concurrent composition setting. Despite being extensively studied in the classical setting, concurrent composition in the quantum setting has hardly been studied. We initiate a formal study of concurrent quantum zero-knowledge. Our results are as follows: -Bounded Concurrent QZK for NP and QMA: Assuming post-quantum one-way functions, there exists a quantum zero-knowledge proof system for NP in the bounded concurrent setting. In this setting, we fix a priori the number of verifiers that can simultaneously interact with the prover. Under the same assumption, we also show that there exists a quantum zero-knowledge proof system for QMA in the bounded concurrency setting. -Quantum Proofs of Knowledge: Assuming quantum hardness of learning with errors (QLWE), there exists a bounded concurrent zero-knowledge proof system for NP satisfying quantum proof of knowledge property. Our extraction mechanism simultaneously allows for extraction probability to be negligibly close to acceptance probability (extractability) and also ensures that the prover's state after extraction is statistically close to the prover's state after interacting with the verifier (simulatability). The seminal work of [Unruh EUROCRYPT'12], and all its followups, satisfied a weaker version of extractability property and moreover, did not achieve simulatability. Our result yields a proof of quantum knowledge system for QMA with better parameters than prior works.
This paper proposes a protocol for lottery and a protocol for auction on quantum Blockchain. Our protocol of lottery satisfies randomness, unpredictability, unforgeability, verifiability, decentralization and unconditional security. Our protocol of auction satisfies bid privacy, posterior privacy, bids' binding, decentralization and unconditional security. Except quantum Blockchain, the main technique involved in both protocols is quantum bit commitment.
Md. Atik Shahriar, Faisal Haque Bappy, A. K. M. Fakhrul Hossain, Dayamoy Datta Saikat · 7 authors
Blockchain technology has evolved through many changes and modifications, such as smart-contracts since its inception in 2008. The popularity of a blockchain system is due to the fact that it offers a significant security advantage over other traditional systems. However, there have been many attacks in various blockchain systems, exploiting different vulnerabilities and bugs, which caused a significant financial loss. Therefore, it is essential to understand how these attacks in blockchain occur, which vulnerabilities they exploit, and what threats they expose. Another concerning issue in this domain is the recent advancement in the quantum computing field, which imposes a significant threat to the security aspects of many existing secure systems, including blockchain, as they would invalidate many widely-used cryptographic algorithms. Thus, it is important to examine how quantum computing will affect these or other new attacks in the future. In this paper, we explore different vulnerabilities in current blockchain systems and analyse the threats that various theoretical and practical attacks in the blockchain expose. We then model those attacks using Petri nets concerning current systems and future quantum computers.
It has been predicted that more devices will be connected to the internet network along with the development of IoT, and that will increase the complexity in the security system. The most important thing in security systems is the process of encryption and authentication. Various encryption techniques are developed to overcome security problems of the data. One of the methods used for authentication of data is Zero Knowledge Proof. This method works to identify the authenticity of someones statement to proof without showing any knowledge of the statement mentioned. This research will mainly discuss about the security of data transmission system by combining data encryption and data authentication. The proposed data encryption is using Advanced Encryption System and method for authentication of data using the Zero Knowledge Proof. This research will conduct the development methods of authentication Zero Knowledge Proof from previous research and the result was compared with the proposed method based on the simulation results transmission system client and server. Experiments will be conducted using thirty-text data, each of data will be measured on the performance of both encryption and authentication process between the previous method and proposed method. Experimental results show the performance of the proposed method has better speed to process application for security of data transmission systems, with performance to authenticate approximately 5 ms from the client side and server side.
Michele Ciampi, Alexandru Cojocaru, Elham Kashefi, Atul Mantri
Secure two-party computation considers the problem of two parties computing a\njoint function of their private inputs without revealing anything beyond the\noutput. In this work, we consider the setting where the two parties (a\nclassical Alice and a quantum Bob) can communicate only via a classical\nchannel. Our first result shows that it is in general impossible to realize a\ntwo-party quantum functionality with black-box simulation in the case of\nmalicious quantum adversaries. In particular, we show that the existence of a\nsecure quantum computing protocol that relies only on classical channels would\ncontradict the quantum no-cloning argument.\n We circumvent this impossibility following three different approaches. The\nfirst is by considering a weaker security notion called one-sided simulation\nsecurity. This notion protects the input of one party (the quantum Bob) in the\nstandard simulation-based sense and protects the privacy of the other party's\ninput (the classical Alice). We show how to realize a protocol that satisfies\nthis notion relying on the learning with errors assumption. The second way to\ncircumvent the impossibility result, while at the same time providing standard\nsimulation-based security also against a malicious Bob, is by assuming that the\nquantum input has an efficient classical representation.\n Finally, we focus our attention on the class of zero-knowledge\nfunctionalities and provide a compiler that takes as input a classical proof of\nquantum knowledge (PoQK) protocol for a QMA relation R and outputs a\nzero-knowledge PoQK for R that can be verified by classical parties. The direct\nimplication of our result is that Mahadev's protocol for classical verification\nof quantum computations (FOCS'18) can be turned into a zero-knowledge proof of\nquantum knowledge with classical verifiers. To the best of our knowledge, we\nare the first to instantiate such a primitive.\n
Amelia Holcomb, Geovandro C. C. F. Pereira, Bhargav Das, Michele Mosca
Hyperledger Fabric is a prominent and flexible solution for building permissioned distributed ledger platforms. Access control and identity management relies on a Membership Service Provider (MSP) whose cryptographic interface only handles standard PKI methods for authentication: RSA and ECDSA classical signatures. Also, MSP-issued credentials may use only one signature scheme, tying the credential-related functions to classical single-signature primitives. RSA and ECDSA are vulnerable to quantum attacks, with an ongoing post-quantum standardization process to identify quantum-safe drop-in replacements. In this paper, we propose a redesign of Fabric's credential-management procedures and related specifications in order to incorporate hybrid digital signatures, protecting against both classical and quantum attacks using one classical and one quantum-safe signature. We create PQFabric, an implementation of Fabric with hybrid signatures that integrates with the Open Quantum Safe (OQS) library. Our implementation offers complete crypto-agility, with the ability to perform live migration to a hybrid quantum-safe blockchain and select any existing OQS signature algorithm for each node. We perform comparative benchmarks of PQFabric with each of the NIST candidates and alternates, revealing that long public keys and signatures lead to an increase in hashing time that is sometimes comparable to the time spent signing or verifying messages itself. This is a new and potentially significant issue in the migration of blockchains to post-quantum signatures.
Over the past few years, massive cyberattacks have dominated the public imagination. Most \nAmericans have been directly affected by data breaches and an overwhelming majority believe \nthat they are no longer in control of their data. At the same time, there are important applications in \nwhich the aggregation of private data is unavoidable. Not surprisingly, there has been considerable \ninterest in developing protocols for secure multi-party computation (MPC), i.e., N parties providing \nprivate inputs to jointly compute some function f. Recent developments in MPC have led to leaps \nin efficiency and MPC is quickly becoming a practical approach for privacy-centric distributed \napplications. As MPC applications become deployed, guaranteeing the security of these protocols, \neven when interacting with other applications, is essential. The standard approach to showing \nsecurity of MPC protocols under arbitrary composition is through the universal composability (UC) \nframework. There has been much prior work on this topic; however, most previous work either \nmakes synchronicity assumptions or does not guarantee output delivery in the presence of even \none fault. For practical MPC applications, though, dealing with asynchronicity and robustness is \nessential. In this thesis, we describe two new keywords, eventually and leak, that aid in defining \nprotocols in the asynchronous world and define wrappers that implement these within the UC \nframework. We then use this novel wrapper to give a UC-realization of a reliable broadcast primitive, by means of Bracha’s classic protocol. Finally, we define and prove a realization of what we call the \nsmart contract model of MPC, which serves as a UC-idealization of asynchronous, robust MPC.
Open access
Advancements in Semiconductor Devices and Circuit Design
The posthoc verification protocol [J. F. Fitzsimons, M. Hajdu{\v s}ek, and T. Morimae, Physical Review Letters {\bf120}, 040501 (2018)] enables an information-theoretically-sound non-interactive verification of quantum computing, but the message from the prover to the verifier is quantum and the verifier has to do single-qubit measurements. The Mahadev protocol removes these quantum parts, but the soundness becomes the computational one. In this paper, we construct an information-theoretically-sound non-interactive classical verification protocol for quantum computing with a trusted center. The trusted center sends random BB84 states to the prover, and the classical descriptions of these BB84 states to the verifier. The messages from the center to the prover and the verifier are independent of the instance. By slightly modifying our protocol, we also construct a non-interactive statistical zero-knowledge proof system for QMA with the trusted center.
Shreya Banerjee, Arghya Mukherjee, Prasanta K. Panigrahi
This paper proposes a protocol to prepare a blockchain using quantum tools which maintains the distributive nature of the blockchain and provides security against a quantum attacker. The authors provide an example of a two blockchain prepared in IBM 5 qubit quantum computer, as a proof of concept with fidelity close to 0.9548.
We put forward the idea that classical blockchains and smart contracts are potentially useful primitives not only for classical cryptography, but for quantum cryptography as well. Abstractly, a smart contract is a functionality that allows parties to deposit funds, and release them upon fulfillment of algorithmically checkable conditions, and can thus be employed as a formal tool to enforce monetary incentives. In this work, we give the first example of the use of smart contracts in a quantum setting. We describe a simple hybrid classical-quantum payment system whose main ingredients are a classical blockchain capable of handling stateful smart contracts, and quantum lightning, a strengthening of public-key quantum money introduced by Zhandry (Eurocrypt'19). Our hybrid payment system employs quantum states as banknotes and a classical blockchain to settle disputes and to keep track of the valid serial numbers. It has several desirable properties: it is decentralized, requiring no trust in any single entity; payments are as quick as quantum communication, regardless of the total number of users; when a quantum banknote is damaged or lost, the rightful owner can recover the lost value.
The field of post-quantum cryptography studies cryptographic systems that are secure against an adversary in possession of a quantum computer. In 2017, the National Institute of Standards and Technology (NIST) initiated a process to standardize quantum-resistant public-key cryptographic algorithms (NIST PQC Project). In this thesis we analyze the performance and security of the Bit-Flipping Key Encapsulation Mechanism (BIKE) -- one of the candidates in the NIST PQC project which advanced to the second round of the standardization process. BIKE is a code-based cryptographic system featuring three different variants of the protocol. In the first round of the NIST PQC project BIKE offered security only against chosen-plaintext attacks (CPA). In the second round, BIKE introduced three new variants that are claimed to be secure also against chosen-ciphertext attacks (CCA). Firstly, we build a secure implementation of the CCA protocol and show that its performance characteristics are only negligibly worse than the CPA variant. In the key decapsulation phase of the protocol BIKE uses a decoding algorithm which fails with some probability, called the Decoding Failure Rate (DFR). We analyze the DFR of two decoders used in BIKE, Back-Flip and Black-Gray, and propose a new decoder, called Black-Gray-Flip, that achieves the same DFR as the two previously used decoders while being almost twice as fast. Finally, we propose an algorithm for inversion of binary polynomials in a polynomial ring used in BIKE-2, the second variant of BIKE. Our implementation of the inversion significantly outperforms previously used algorithms. With this and the fact that the bandwidth requirement for BIKE-2 is the smallest among the three variants, BIKE-2 is positioned as the preferable variant of BIKE. The second part of this thesis studies the Legendre pseudorandom function (PRF) which is proposed to be used in the context of blockchains. We present a new algorithm for cryptanalysis of the Legendre PRF. The complexity of our algorithm is lower than the previous best known algorithm. Moreover, we show the results of breaking three Legendre PRF challenges posed by the Ethereum foundation. The most difficult challenge that we solved set the new record which is not broken so far.
James Bartusek, Andrea Coladangelo, Dakshita Khurana, Fermi Ma
We investigate the round complexity of maliciously-secure two-party quantum computation (2PQC) with setup, and obtain the following results:
- A three-message protocol (two-message if only one party receives output) in the common random string (CRS) model assuming classical two-message oblivious transfer (OT) with post-quantum malicious security. This round complexity is optimal for the sequential communication setting. Under the additional assumption of reusable malicious designated-verifier non-interactive zero-knowledge (MDV-NIZK) arguments for NP, our techniques give an MDV-NIZK for QMA. Each of the assumptions mentioned above is known from the quantum hardness of learning with errors (QLWE).
- A protocol with two simultaneous rounds of communication, in a quantum preprocessing model, assuming sub-exponential QLWE. In fact, we construct a three-round protocol in the CRS model with only two rounds of online communication, which implies the above result. Along the way, we develop a new delayed technique that we call simulation via teleportation, which may be useful in other settings.
In addition, we perform a preliminary investigation into barriers and possible approaches for two-round 2PQC in the CRS model, including an impossibility result for a natural class of simulators, and a proof-of-concept construction from a strong form of quantum virtual black-box (VBB) obfuscation.
Prior to our work, maliciously-secure 2PQC required round complexity linear in the size of the quantum circuit.
Cryptocurrencies are more than a decade old and several issues have been discovered since their then. One of these issues is a partial negation of the intent to “democratize” money by decentralizing control of the infrastructure that creates, transmits, and stores monetary data. The Programmatic Proof of Work (ProgPoW) algorithm is intended as a possible solution to this problem for the Ethereum cryptocurrency. This paper examines ProgPow’s claim to be Application Specific Integrated Circuit (ASIC) resistant. This is achieved by isolating the proof-of-work code from the Ethereum blockchain, inserting the ProgPoW algorithm, and measuring the performance of the new implementation as a multithread CPU program, as well as a GPU implementation. The most remarkable difference between the ProgPoW algorithm and the currently implemented Ethereum Proof-of Work is the addition of a random sequence of math operations in the main loop that require increased memory bandwidth. Analyzing and comparing the performance of the CPU and GPU implementations should provide an insight into how the ProgPoW algorithm might perform on an ASIC.