Protecting secrets is a key challenge in our contemporary information-based era. In common situations, however, revealing secrets appears unavoidable, for instance, when identifying oneself in a bank to retrieve money. In turn, this may have highly undesirable consequences in the unlikely, yet not unrealistic, case where the bank's security gets compromised. This naturally raises the question of whether disclosing secrets is fundamentally necessary for identifying oneself, or more generally for proving a statement to be correct. Developments in computer science provide an elegant solution via the concept of zero-knowledge proofs: a prover can convince a verifier of the validity of a certain statement without facilitating the elaboration of a proof at all. In this work, we report the experimental realisation of such a zero-knowledge protocol involving two separated verifier-prover pairs. Security is enforced via the physical principle of special relativity, and no computational assumption (such as the existence of one-way functions) is required. Our implementation exclusively relies on off-the-shelf equipment and works at both short (60 m) and long distances ($\geqslant$400 m) in about one second. This demonstrates the practical potential of multi-prover zero-knowledge protocols, promising for identification tasks and blockchain applications such as cryptocurrencies or smart contracts.
In this work we consider the following problem: in a Multi-Prover environment, how close can we get to prove the validity of an NP statement in Zero-Knowledge ? We exhibit a set of two novel Zero-Knowledge protocols for the 3-COLorability problem that use two (local) provers or three (entangled) provers and only require them to reply two trits each. This greatly improves the ability to prove Zero-Knowledge statements on very short distances with very minimal equipment.
Relativistic cryptography is a proposal for achieving unconditional security that exploits the fact that no information carrier can travel faster than the speed of light. It is based on space-time constraints but doesn't require quantum hardware. Nevertheless, it was unclear whether this proposal is realistic or not. Recently, Alikhani et al. [ABC+21] performed an implementation of a relativistic zero-knowledge for NP. Their implemented scheme shows the feasibility of relativistic cryptography but it is only secure against classical adversaries. In this work, we present a new relativistic prot…
Experimental asymmetric relativistic zero-knowledge proofs with unconditional security
National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室和物理学院，先进微结构协同创新中心）；School of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学物理学院，光电功能材料与微纳器件北京市重点实验室，量子态构建与操控教育部重点实验室）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；MatricTime Digital Technology Co. Ltd.（矩阵时代数字技术有限公司）
In known constructions of classical zero-knowledge protocols for NP, either of zero-knowledge or soundness holds only against computationally bounded adversaries. Indeed, achieving both statistical zero-knowledge and statistical soundness at the same time with classical verifier is impossible for NP unless the polynomial-time hierarchy collapses, and it is also believed to be impossible even with a quantum verifier. In this work, we introduce a novel compromise, which we call the certified everlasting zero-knowledge proof for QMA. It is a computational zero-knowledge proof for QMA, but the ver…
In this paper we describe protocols which use a standard deck of cards to provide a perfectly sound zero-knowledge proof for Hamiltonian cycles and Flow Free puzzles. The latter can easily be extended to provide a protocol for a zero-knowledge proof of many-to-many k-disjoint path coverings.
Zero-knowledge proofs are an essential building block in many privacy-preserving systems. However, implementing these proofs is tedious and error-prone. In this paper, we present zksk, a well-documented Python library for defining and computing sigma protocols: the most popular class of zero-knowledge proofs. In zksk, proofs compose: programmers can convert smaller proofs into building blocks that then can be combined into bigger proofs. zksk features a modern Python-based domain-specific language. This makes possible to define proofs without learning a new custom language, and to benefit from…
With the wide application of cloud storage, cloud security has become a crucial concern. Related works have addressed security issues such as data confidentiality and integrity, which ensure that the remotely stored data are well maintained by the cloud. However, how to define zero-knowledge proof algorithms for stored data integrity check has not been formally defined and investigated. We believe that it is important that the cloud server is unable to reveal any useful information about the stored data. In this paper, we introduce a novel definition of data privacy for integrity checks, which…
The current humanitarian health crisis popularized the debate on data privacy. At the same time, several cities, states, and even countries put the mandatory presentation of health pass to access services into practice. In this article, we explore the concepts of self-sovereign identity, blockchain, and zero-knowledge proofs to propose a solution to the problem of presenting proof of vaccination. This solution allows users to prove that they are vaccinated for different pathogens without revealing their identity. The architecture is loosely coupled, allowing components to be exchanged, which w…
We provide several advances to the understanding of the class of Quantum Merlin-Arthur proof systems (QMA), the quantum analogue of NP. Our central contribution is proving a longstanding conjecture that the Consistency of Local Density Matrices (CLDM) problem is QMA-hard under Karp reductions. The input of CLDM consists of local reduced density matrices on sets of at most k qubits, and the problem asks if there is an n-qubit global quantum state that is consistent with all of the k-qubit local density matrices. The containment of this problem in QMA and the QMA-hardness under Turing reductions…
Carnegie Mellon University School of Computer Science（卡内基梅隆大学计算机科学学院）
Zero-knowledge proofs allow verification of computations without revealing private information. However, existing systems require memory proportional to the computation size, which has historically limited use in large-scale applications and on mobile and edge devices. We solve this fundamental bottleneck by developing, to our knowledge, the first proof system with sublinear memory requirements for mainstream cryptographic constructions. Our approach processes computations in blocks using a space-efficient tree algorithm, reducing memory from linear scaling to square-root scaling--from $Θ(T)$ …
This paper describes techniques to help with COVID-19 automated contact tracing, and with the restoration efforts. We describe a decentralized protocol for ``proof-of-contact'' in zero knowledge where a person can publish a short cryptographic proof attesting to the fact that they have been infected and that they have come in contact with a set of people without revealing any information about any of the people involved. More importantly, we describe how to compose these proofs to support broader functionality such as proofs of $n$th-order exposure which can further speed up automated contact …
Verifiable delay functions have found a lot of applications in blockchain technology in recent times. Continuous verifiable delay functions are an improvement over the basic notion of VDFs with recursive capabilities. We are proposing the application of VDF for constructing more space time-efficient provers and simulators required for the iterative non-interactive zero-knowledge systems.
We present ZK-SecreC, a domain-specific language for zero-knowledge proofs. We present the rationale for its design, its syntax and semantics, and demonstrate its usefulness on the basis of a number of non-trivial examples. The design features a type system, where each piece of data is assigned both a confidentiality and an integrity type, which are not orthogonal to each other. We perform an empiric evaluation of the statements produced by its compiler in terms of their size. We also show the integration of the compiler with the implementation of a zero-knowledge proof technique, and evaluate…
We live in an era of information and it is very important to handle the exchange of information. While sending data to an authorized source, we need to protect it from unauthorized sources, changes, and authentication. ZKP technique can be used in designing secure authentication systems that dont involve any direct exchange of information between the claimant and the verifier thus preventing any possible leak of personal information. We propose a Zero-Knowledge Proof (ZKP) algorithm based on isomorphic graphs. We suggest most of the computations should be carried out on the users' web browser …
This paper proposes a protocol for Proof of Assets of a bitcoin exchange using the Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (ZK-SNARK) without revealing either the bitcoin addresses of the exchange or balances associated with those addresses. The proof of assets is a mechanism to prove the total value of bitcoins the exchange has authority to spend using its private keys. We construct a privacy-preserving ZK-SNARK proof system to prove the knowledge of the private keys corresponding to the bitcoin assets of an exchange. The ZK-SNARK tool-chain helps to convert an NP-Statem…
Zero-knowledge proofs have always provided a clear solution when it comes to conveying information from a prover to a verifier or vice versa without revealing essential information about the process. Advancements in zero-knowledge have helped develop proofs which are succinct and provide non-interactive arguments of knowledge along with maintaining the zero-knowledge criteria. zk-SNARKs (Zero knowledge Succinct Non-Interactive Argument of Knowledge) are one such method that outshines itself when it comes to advancement of zero-knowledge proofs. The underlying principle of the Zcash algorithm i…
In last years, there has been an increasing effort to leverage Distributed Ledger Technology (DLT), including blockchain. One of the main topics of interest, given its importance, is the research and development of privacy mechanisms, as for example is the case of Zero Knowledge Proofs (ZKP). ZKP is a cryptographic technique that can be used to hide information that is put into the ledger, while still allowing to perform validation of this data. In this work we describe different strategies to construct Zero Knowledge Range Proofs (ZKRP), as for example the scheme proposed by Boudot in 2001; t…
While the amount of data produced and accumulated continues to advance at unprecedented rates, protection and concealment of data increase its prominence as a field of scientific study that requires more action. It is essential to protect privacy-sensitive data at every phase; at rest, at run, and while computations are executed on data. The zero-knowledge proof (ZKP) schemes are a cryptographic tool toward this aim. ZKP allows a party to securely ensure the data's authenticity and precision without revealing confidential or privacy-sensitive information during communication or computation. Th…
The amount of information generated grows as more and more sensor and IoT devices are deployed in smart cities. It is of utmost importance for us to consider the privacy data leakage and compromised identity from both outside adversaries and inside abuse of data access privilege. The security assumption of the system should not solely rely on the fact that permission and access control were being implemented correctly. Quite the contrary, a system can be designed in a way that user's identity data and usage traces are not leaked even if the system had been compromised. Based upon our previous …
Ripple Effect is a logic puzzle where the player has to fill numbers into empty cells in a rectangular grid. The grid is divided into rooms, and each room must contain consecutive integers starting from 1 to its size. Also, if two cells in the same row or column contain the same number $x$, there must be a space of at least $x$ cells separating the two cells. In this paper, we develop a physical zero-knowledge proof for the Ripple Effect puzzle using a deck of cards, which allows a prover to convince a verifier that he/she knows a solution without revealing it. In particular, given a secret nu…
Intuitively there is a drastic distinction between the pure decentralized block-chain systems like Defis and those that only utilize block-chain as an enhancing technology but remain centralized with real-world business model and conventional technologies like database, application server, etc. Our study explores extensively this distinction from a methodological point of view, classifies them into blockchain-complete and blockchain-partial, analyzes key features of the two types, and reveals the root cause of this distinction. We analyze the function or, in more strong words, the "ultimate pu…
Numberlink is a logic puzzle with an objective to connect all pairs of cells with the same number by non-crossing paths in a rectangular grid. In this paper, we propose a physical protocol of zero-knowledge proof for Numberlink using a deck of cards, which allows a prover to convince a verifier that he/she knows a solution without revealing it. In particular, the protocol shows how to physically count the number of elements in a list that are equal to a given secret value without revealing that value, the positions of elements in the list that are equal to it, or the value of any other element…
