Zero-Knowledge Proofs (ZKPs) are cryptographic primitives allowing a party to prove to another party that the former knows some information while keeping it secret. Such a premise can lead to the development of numerous privacy-preserving protocols in different scenarios, like proving knowledge of some credentials to a server without leaking the identity of the user. Even when the applications of ZKPs were endless, they were not exploited in the wild for a couple of decades due to the fact that computing and verifying proofs was too computationally expensive. However, the advent of efficient schemes (in particular, zk-SNARKs) made this primitive to break into the scene in fields like cryptocurrencies, smart-contracts, and more recently, self-sovereign scenarios: private-by-design identity management and authentication. Nevertheless, its adoption in environments like the Internet of Things (IoT) remains unexplored due to the computational limitations of embedded systems. In this paper, we introduce ZPiE, a C library intended to create ZKP applications to be executed in embedded systems. Its main feature is portability: it can be compiled, executed, and used out-of-the-box in a wide variety of devices. Moreover, our proof-of-concept has been proved to work smoothly in different devices with limited resources, which can execute state-of-the-art ZKP authentication protocols.
Carsten Baum, Alex J. Malozemoff, Marc B. Rosen, Peter Schöll
Zero knowledge proofs are an important building block in many cryptographic applications. Unfortunately, when the proof statements become very large, existing zero-knowledge proof systems easily reach their limits: either the computational overhead, the memory footprint, or the required bandwidth exceed levels that would be tolerable in practice. We present an interactive zero-knowledge proof system for boolean and arithmetic circuits, called $$\mathsf {Mac'n'Cheese}$$ , with a focus on supporting large circuits. Our work follows the commit-and-prove paradigm instantiated using information-theoretic MACs based on vector oblivious linear evaluation to achieve high efficiency. We additionally show how to optimize disjunctions, with a general OR transformation for proving the disjunction of m statements that has communication complexity proportional to the longest statement (plus an additive term logarithmic in m). These disjunctions can further be nested, allowing efficient proofs about complex statements with many levels of disjunctions. We also show how to make $$\mathsf {Mac'n'Cheese}$$ non-interactive (after a preprocessing phase) using the Fiat-Shamir transform, and with only a small degradation in soundness. We have implemented the online phase of $$\mathsf {Mac'n'Cheese}$$ and achieve a runtime of 144 ns per AND gate and 1.5 $$\upmu $$ s per multiplication gate in $$\mathbb {F} _{2^{61} - 1} $$ when run over a network with a 95 ms latency and a bandwidth of 31.5 Mbps. In addition, we show that the disjunction optimization improves communication as expected: when proving a boolean circuit with eight branches and each branch containing roughly 1 billion multiplications, $$\mathsf {Mac'n'Cheese}$$ requires only 75 more bytes to communicate than in the single branch case.
A cryptographic method of digitally securing cryptocurrency wallet seed phrase through Blind Key Encryption is discussed wherein two blind keys random in nature are generated and used to produce two ciphertexts. The mathematical algorithm used in blind key encryption is described in detail and also an explanation is provided as to how the encryption defeats hackers even after they could successfully compromise a ciphertext of the seed phrase along with its decryption key. Different scenarios of storing the ciphertexts are documented.
Pouriya Alikhani, Nicolas Brunner, Claude Crépeau, Sébastien Designolle · 8 authors
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.
Open access
3 source records
Cryptography and Data Security
Physical Unclonable Functions (PUFs) and Hardware Security
Due to intelligent electronic management, the smart grid has recently played a significant role in modern energy infrastructure. However, along with widespread deployment of the smart grid, many potential security threats (e.g., impersonation attack, replay attack, man-in-the-middle attack) rise to the surface. To defend against these possible attacks, numerous cryptography-based authentication schemes have been proposed for the smart grid. Most of the schemes investigate the secret key distribution problem, but the requirement of decentralized registration authority is neglected. In addition, over-complicated cryptographic primitives also strengthen the burden of authentication system. In contrast with previous researches, our proposed BlockSLAP utilizes cutting-edge blockchain technology as well as smart contract to decentralize the registration authority and reduce the interaction process to 2 steps. Moreover, our protocol is proved secure under computational hard assumption and informal security analysis. Finally, experimental results show that smart grid authentication performance in our protocol has been improved compared to the other existing ECC-related schemes.
Ran Canetti, Rosario Gennaro, Steven Goldfeder, Nikolaos Makriyannis · 5 authors
Building on the Gennaro & Goldfeder and Lindell & Nof protocols (CCS '18), we present two threshold ECDSA protocols, for any number of signatories and any threshold, that improve as follows over the state of the art: -- For both protocols, only the last round requires knowledge of the message, and the other rounds can take place in a preprocessing stage, lending to a non-interactive threshold ECDSA protocol. -- Both protocols withstand adaptive corruption of signatories. Furthermore, they include a periodic refresh mechanism and offer full proactive security. -- Both protocols realize an ideal threshold signature functionality within the UC framework, in the global random oracle model, assuming Strong RSA, DDH, semantic security of the Paillier encryption, and a somewhat enhanced variant of existential unforgeability of ECDSA. -- Both protocols achieve accountability by identifying corrupted parties in case of failure to generate a valid signature. The two protocols are distinguished by the round-complexity and the identification process for detecting cheating parties. Namely: -- For the first protocol, signature generation takes only 4 rounds (down from the current state of the art of 8 rounds), but the identification process requires computation and communication that is quadratic in the number of parties. -- For the second protocol, the identification process requires computation and communication that is only linear in the number of parties, but signature generation takes 7 rounds. These properties (low latency, compatibility with cold-wallet architectures, proactive security, identifiable abort and composable security) make the two protocols ideal for threshold wallets for ECDSA-based cryptocurrencies.
Zero-Knowledge (ZK) proofs (ZKP) are foundational in cryptography. Most recent ZK research focuses on non-interactive proofs (NIZK) of small statements, useful in blockchain scenarios. Another line, and our focus, instead targets proofs of large statements that are useful, e.g., in proving properties of programs in ZK. We specify a zero-knowledge processor that executes arbitrary programs written in a simple instruction set, and proves in ZK the correctness of the execution. Such an approach is well-suited for constructing ZK proofs of large statements as it efficiently supports complex programming constructs, such as loops and RAM access. Critically, we propose several novel ZK improvements that make our approach concretely efficient: (1) an efficient arithmetic representation with conversions to/from Boolean, (2) an efficient read-only memory that uses $2łog n$ OTs per access, and (3) an efficient read-write memory, øurram, which uses $\frac1 2 łog^2 n$ OTs per access. øurram beats linear scan for RAM of size $>3$ elements! Prior ZK systems used generic ORAM costing orders of magnitude more. We cast our system as a garbling scheme that can be plugged into the ZK protocol of [Jawurek et al, CCS'13]. Put together, our system is concretely efficient: for a processor instantiated with $512$KB of main memory, each processor cycle costs $24$KB of communication. We implemented our approach in \textttC++. On a 1Gbps LAN our implementation realizes a $2.1$KHz processor.
Basudeb Bera, Sourav Saha, Ashok Kumar Das, Athanasios V. Vasilakos
We design a new blockchain-based access control protocol in IoT-enabled smart-grid system, called DBACP-IoTSG. Through the proposed DBACP-IoTSG, the data is securely brought to the service providers from their respective smart meters (SMs). The peer-to-peer (P2P) network is formed by the participating service providers, where the peer nodes are responsible for creating the blocks from the gathered data securely from their corresponding SMs and adding them into the blockchain after validation of the blocks using the voting-based consensus algorithm. In our work, the blockchain is considered as private because the data collected from the consumers of the SMs are private and confidential. By the formal security analysis under the random oracle model, nonmathematical security analysis and software-based formal security verification, DBACP-IoTSG is shown to be resistant against various attacks. We carry out the experimental results of various cryptographic primitives that are needed for comparative analysis using the widely used multiprecision integer and rational arithmetic cryptographic library (MIRACL). A detailed comparative study reveals that DBACP-IoTSG supports more functionality features and provides better security apart from its low communication and computation costs as compared to recently proposed relevant schemes. In addition, the blockchain implementation of DBACP-IoTSG has been performed to measure computational time needed for the varied number of blocks addition and also the varied number of transactions per block in the blockchain.
J Dharani, K Sundarakantham, Kunwar Singh, S. Mercy Shalinie
Blockchain technology has gained its attention from its application in bitcoin which circumvented the problem of double spending that existed in the prior digital currencies, through validation. Particularly permissioned blockchain framework became popular with organizations forming consortium that allowed only authorized entities to participate in the network. Hyperledger Fabric, a popular distributed ledger technology hosted by Linux Foundation has remarkable features because of the fact that it is open source. It stands out from other frameworks as it focuses on the privacy-preserving requirements of the enterprises. Apart from only allowing authenticated organizations to participate in the network it implements channels that allows a subset of organizations to communicate concealing the existence of such a channel to other members. Optionally fabric also provides anonymity and unlinkability of the participating clients through a cryptographic protocol suite called Idemix that operates based on zero-knowledge proofs. Fabric follows the execute-order-validate transaction flow as opposed to order-execute flow that had certain limitations in other platforms. For executing the transactions submitted by the clients, fabric has designated endorsing peers which holds the smart contract - programmable business logic. Endorsing peers or endorsers execute the transactions and attach their signatures to the results for validation purpose. But revealing the endorser identities may be a problem when there is conflict of interest among the enterprises. Hence to have an unbiased flow of work it is important to conceal the endorser identity. According to [1] anonymization of endorsing peers is still a open problem in fabric community. We propose a solution to this problem which uses linkable threshold ring signatures that conceals the identity of endorsers. Ring signatures are known for preserving the privacy of the signer in a group. Threshold ring signature allows t-out-of-n signers to collaborate on the signing procedure. Employing threshold ring signature implicitly addresses one more problem stated in [10] where the verifiers need to manually count the valid ring signature that increases the verification time. This process of separately verifying each of the signatures and checking if the number of signatures is more than the threshold value is replaced by having just one threshold signature collaboratively signed by the required endorsers.
We introduce Xiphos and Kopis, new transparent zero-knowledge succinct non-interactive arguments of knowledge (zkSNARKs) for R1CS. They do not require a trusted setup, and their security relies on the standard SXDH problem. They achieve non-interactivity in the random oracle model using the Fiat-Shamir transform. Unlike prior transparent zkSNARKs, which support either a fast prover, short proofs, or quick verification, our work is the first to simultaneously achieve all three properties (both asymptotically and concretely) and in addition an inexpensive setup phase, thereby providing the first quadruple-efficient transparent zkSNARKs (Quarks). Under both schemes, for an R1CS instance of size n and security parameter $\lambda$, the prover incurs $Oλ(n)>O_{\lambda}(n)$ costs to produce a proof of size $Oλ(n)>O_{\lambda}(\log{n})$. In Xiphos, verification time is $Oλ(n)>O_{\lambda}(\log{n})$, and in Kopis it is $Oλ(n)>O_{\lambda}(\sqrt{n})$. In terms of concrete efficiency, compared to prior state-of-the-art transparent zkSNARKs, Xiphos offers the fastest verification; its proof sizes are competitive with those of SuperSonic [EUROCRYPT 2020], a prior transparent SNARK with the shortest proofs in the literature. Xiphos’s prover is fast: its prover is $\approx3.85×>\times$ of Spartan [CRYPTO 2020], a prior transparent zkSNARK with the fastest prover in the literature, and is $250> 376\times$ faster than SuperSonic. Kopis, at the cost of increased verification time (which is still concretely faster than SuperSonic), shortens Xiphos’s proof sizes further, thereby producing proofs shorter than SuperSonic. Xiphos and Kopis incur $10>10$–$10,000×>10,000\times$ lower preprocessing costs for the verifier in the setup phase depending on the baseline. Finally, a byproduct of Kopis is Lakonia, a NIZK for R1CS with $Oλ(n)>O_{\lambda}(\log{n})$-sized proofs, which provides an alternative to Bulletproofs [S&P 2018] with over an order of magnitude faster proving and verification times.
After the work of Impagliazzo and Rudich (STOC, 1989), the black box framework has become one of the main research domain of cryptography. However black box techniques say nothing about non-black box techniques such as making use of zero-knowledge proofs. Brakerski et al. introduced a new black box framework named augmented black box framework, in which they gave a zero-knowledge proof oracle in addition to a base primitive oracle (TCC, 2011). They showed a construction of a non-interactive zero knowledge proof system based on a witness indistinguishable proof system oracle. They presented augmented black box construction of chosen ciphertext secure public key encryption scheme based on chosen plaintext secure public key encryption scheme and augmented black box separation between one-way function and key agreement. In this paper we simplify the work of Brakerski et al. by introducing a proof system oracle without witness indistinguishability, named coin-free proof system oracle, that aims to give the same construction and separation results of previous work. As a result, the augmented black box framework becomes easier to handle. Since our oracle is not witness indistinguishable, our result encompasses the result of previous work.
While traditional symmetric algorithms like AES and SHA-3 are optimized for efficient hardware and software implementations, a range of emerging applications using advanced cryptographic protocols such as multi-party computation and zero knowledge proofs require optimization with respect to a different metric: arithmetic complexity. In this paper we study the design of secure cryptographic algorithms optimized to minimize this metric. We begin by identifying the differences in the design space between such arithmetization-oriented ciphers and traditional ones, with particular emphasis on the available tools, efficiency metrics, and relevant cryptanalysis. This discussion highlights a crucial point—the considerations for designing arithmetization-oriented ciphers are oftentimes different from the considerations arising in the design of software- and hardware-oriented ciphers. The natural next step is to identify sound principles to securely navigate this new terrain, and to materialize these principles into concrete designs. To this end, we present the Marvellous design strategy which provides a generic way to easily instantiate secure and efficient algorithms for this emerging domain. We then show two examples for families following this approach. These families — Vision and Rescue — are benchmarked with respect to three use cases: the ZK-STARK proof system, proof systems based on Rank-One Constraint Satisfaction (R1CS), and Multi-Party Computation (MPC). These benchmarks show that our algorithms achieve a highly compact algebraic description, and thus benefit the advanced cryptographic protocols that employ them.
Ethan Heilman, Neha Narula, Garrett Tanzer, James Peter Thomas. Lovejoy · 7 authors
We present attacks on the cryptography formerly used in the IOTA blockchain, including under certain conditions the ability to forge signatures. We developed practical attacks on IOTA’s cryptographic hash function Curl-P-27, allowing us to quickly generate short colliding messages. These collisions work even for messages of the same length. Exploiting these weaknesses in Curl-P-27, we broke the EUCMA security of the former IOTA Signature Scheme (ISS). Finally, we show that in a chosen-message setting we could forge signatures and multi-signatures of valid spending transactions (called bundles in IOTA).
How someone can get health insurance without sharing his health infor-mation? How you can get a loan without disclosing your credit score? There is a method to certify certain attributes of various data, either this is health metrics or finance information, without revealing the data itself or any other kind of personal data. This method is known as “zero-knowledge proofs”. Zero-Knowledge techniques are mathematical methods used to verify things without sharing or revealing underlying data. Zero-Knowledge protocols have vast applications from simple identity schemes and blockchains to de-fense research programs and nuclear arms control. In this article we present the basic principles behind ZKP technology, possible applications and the threats and vulnerabilities that it is subject to and we review proposed securi-ty solutions.
Abstract Bitcoin’s security relies solely on cryptographic primitives, namely on digital signatures, hash functions and Merkle trees. This chapter discusses the security of the Bitcoin system if some primitives become weaker due to advances in cryptanalysis, an increasing computing power of the adversaries or improper software implementations. The chapter starts with a general overview of the primitives in use, explaining possible attack strategies against each of them, which is followed by combined attack strategies. The chapter closes by showing the consequences of Grover’s and Shor’s quantum algorithms for Bitcoin’s security.
Sumaia Atiwa, Yunus Dawji, Ahmed Refaey, Sebastian Magierowski
Interest in the efficient implementations of hashing algorithms has received even more attention recently due to the growing application-space for blockchain technology. Consequently, a pressing need has arisen to develop high-performance hashing techniques to support these developments. In this paper, an architecture and VLSI implementation of the newest hashing standard, BLAKE2, is presented. The Equihash algorithm serves as a use case for BLAKE2 in Blockchain. An FPGA-based custom computing machine (FCCM) approach is used. This approach is producing an accelerated Equihash hashing-core system which is 5x faster than an ARM Cortex-A9 based system on a ZC706 SoC chip for 0.27 W. Indeed, this is the first BLAKE2 implementation allowing fast execution, and effective substitution of any previous hash families implementations.
Chaos-based Image/Signal Encryption
Cryptographic Implementations and Security
Advanced Steganography and Watermarking Techniques
Tato diplomová práce se zabývá technologii blockchain se zaměřením na konsenzus protokoly, zvláště protokoly typu proof-of-stake. V této práci naleznete popis těchto protokolů následovaný popisem konsenzu v technologii blockchain. Prvotní kapitoly detailněji popisují a porovnávají jednotlivé proof-of-stake protokoly na základě teoretických znalostí. Druhá část práce se zaobírá návrhem a implementací testbedu, který je následně použitý pro praktické porovnání proof-of-stake protokolů. V závěrečné částí práce je diskutováno nad zjištěnými výsledky pozorováním testbedu a zjištěnými vlatnostmi protokolů. Na tomto základě práce ve svém konci naznačuje další směřování consesus protokolů, ba jejich případné zlepšení, a zvláště proof-of-stake typu protokolů.
R. Indrakumari, T. Poongodi, Kavita Saini, B. Balamurugan
A blockchain is a cryptographically signed transactional record shared by the participating nodes in the network. Each record has a timestamp and link to earlier transactions, and it is a predominant architectural design of the distributed ledger concept. The authorized participant with proper access rights can track the history of transactional events belonging to any participant. However, a significant disconnect occurs between the expectation in the market sector and reality. Blockchain consensus protocols assure that the nodes in the network will be synchronized with each other. Consensus means the nodes in the blockchain network will agree on the same state for self-auditing across a distributed network. The main objective of the consensus protocol is to ensure a single chain is utilized and followed, and it is one of the significant revolutionary aspects of blockchain technology. Achieving consensus is an acceptance among nodes on the network for a data value even if some nodes are unreliable. The cryptocurrency must be secured against attacks in the blockchain, and it does not rely on a single centralized authority for security, where the users do not have any prior knowledge about the versions of the valid record. According to Gartner report, there will be an exponential growth of blockchain by 2020 due to the implementation of the smart contract which includes tokenization and decentralization. Furlonger said, “Blockchain is not just a technology, it is a societal change”. Consensus protocols provide rewards and incentives for the participants who are maintaining the blockchain. The rewards in blockchain will be in the form of tokens or cryptocurrencies, and the competition for confirming the next block in the chain is extremely high. The complete history of transaction is maintained in digital currencies to check the user’s balance at any time. Some of the significant objectives of blockchain consensus models are in achieving agreement, cooperation, collaboration, participation and activity. The different types of consensus algorithms are proof of work (PoW), proof of stake (PoS), delegated proof of stake (DPoS), leased proof of stake (LPoS), proof of elapsed time (PoET), practical Byzantine fault tolerance (PBFT), simplified Byzantine fault tolerance (SBFT), delegated Byzantine fault tolerance (DBFT), directed acyclic graphs (DAG), proof of activity (PoA), proof of importance (PoI), proof of capacity (PoC), proof of burn (PoB) and proof of weight (PoWeight). This chapter highlights the significance of consensus algorithms and their usage.
Zero-Knowledge Proofs (ZKPs) have emerged as a revolutionary cryptographic technique that enables one party to prove knowledge of a statement without revealing any underlying information. ZKPs play a crucial role in enhancing cybersecurity by enabling privacy-preserving authentication, secure transactions, and data integrity verification. This paper explores the fundamentals of zero-knowledge proofs, including their classifications—interactive, non-interactive, and succinct proofs—along with real-world applications in secure communications, blockchain security, and identity verification. Furthermore, we discuss the challenges of implementing ZKPs and the potential future advancements in this cryptographic field
The cryptographic algorithm has been gradually improved in design, but its implementations are vulnerable to side‐channel analysis (SCA). Generally speaking, adding a mask to the primitive is the best way to counteract SCA. In the high‐order mask, the key to affecting performance and security lies in the multiplication design. Based on the research of the advanced encryption standard (AES) algorithm, internal round function structure, and zero‐knowledge proof, a high‐order AES mask scheme is designed to optimise the implementation. In this scheme, the substitution‐box protects sensitive variables in the algorithm with the use of secure multiplication and secure inversion by column. The scheme named as in columns higher‐order mask (ICHM), features low cost and high security. The result of the experiment proves the security and effectiveness of the ICHM.
Cryptographic Implementations and Security
Chaos-based Image/Signal Encryption
Physical Unclonable Functions (PUFs) and Hardware Security
Alexander Frolov, Alexander Vinnikov, S.D. Polyakova
We present the IT solutions for educational modeling of non-interactive zero knowledge (NIZK) cryptographic public keys certification protocols. Certified public keys can then be used in a variety of non-interactive protocols, for example, in protocols using technique designated verifier proofs. The solution is based on algebraic means provided by MPEI algebraic processor. The IT solution supports the following educational purposes: obtaining practical skills of remote implementation of multiple non-interactive oblivious transfer and of non-interactive zero-knowledge proof protocol, mastering the methods of a remote automatic modeling of cryptographic protocols and of non-interactive public keys certification, and the technique designated verifier proofs.