Non-fungible tokens (NFTs) offer a unique method for representing digital and physical assets on the blockchain. However, the NFT market has recently experienced a downturn in interest, mainly due to challenges related to high entry barriers and limited market liquidity. Fractionalization emerges as a promising solution, allowing multiple parties to hold a stake in a single NFT. By breaking down ownership into fractional shares, this approach lowers the entry barrier for investors, enhances market liquidity, and democratizes access to valuable digital assets. Despite these benefits, the current landscape of NFT fractionalization is fragmented, with no standardized framework to guide the secure and interoperable implementation of fractionalization mechanisms. This paper contributions are twofold: first, we provide a detailed analysis of the current NFT fractionalization landscape focusing on security challenges; second, we introduce a standardized approach that addresses these challenges, paving the way for more secure, interoperable, and accessible NFT fractionalization platforms.
Zero-Knowledge Proofs (ZKPs) are cryptographic tools that enables one party, known as the prover, to prove to another party, the verifier, that a certain statement is true without revealing any information beyond the validity of the statement itself. We introduce the Neutrosophic One-Round Zero-Knowledge Proof protocol (N-1-R) ZKP, which is an extension of the One-Round (1-R) ZKP in the realm of Neutrosophic numbers. The N-1-R ZKP is the first Neutrosophic ZK protocol.
Multiple internet services rely on the Diffie–Hellman (DH) algorithm for security. In spite of this, a study from October 2015 reveals that many DH-based internet applications are not protected adequately from highly resourced attackers, including the security services of some nations. To improve the security of data while it is in transit over an unsecured network, a novel method for encrypting and decrypting voice signals is presented in this research. The Diffie–Hellman algorithm, a specific form of asymmetric key cryptography, is the basis of the presented technique. This method&s;s primary value is that it lets users encrypt and decode their conversations using an encrypted session key. To begin, the dispatcher uses the agreed-upon secret key to encrypt the incoming speech signal using this technique. Second, the encrypted voice signal is transmitted through a public network to reach its final destination. To begin, we implemented a client-side encryption system to better protect sensitive information while still allowing for secure communication between client and server. Key exchange is protected from man-in-the-middle and discrete logarithm attacks with the help of the modified Diffie–Hellman method and from unauthorized access with the help of the modified Zero Knowledge Proof (ZKP) method. Criteria for evaluation include file size, time to generate keys, time to encrypt and decode data, and time to execute the algorithm.
Zero Knowledge Proofs (ZKPs), cryptographic protocols that allow a party to authenticate a transaction to another without disclosing additional information beyond the authenticity of the transaction, continue to have a significant impact on privacy, security, and integrity in applications. It addresses constraints such as computing costs, trust dimensions, and integration complexity, and proposes possible methods and techniques for future research. It emphasizes the importance of ZKP for improving privacy and security in digital systems highlights, the article emphasizes the importance of continuous innovation and further development of their standardization efforts. Proofs (ZKPs) have emerged as a powerful tool in cryptography, offering innovative solutions to privacy, security, and authentication challenges. This article provides an in-depth review of ZKPs, exploring their progress, challenges and future prospects in cryptography. It examines the basic concepts of ZKPs, their applications, and their impact on cryptographic protocols.
Zero-Knowledge Proofs (ZKPs) are an emergent paradigm in verifiable computing. In the context of applications like cloud computing, ZKPs can be used by a client (called the verifier) to verify the service provider (called the prover) is in fact performing the correct computation based on a public input. A recently prominent variant of ZKPs is zkSNARKs, generating succinct proofs that can be rapidly verified by the end user. However, proof generation itself is very time consuming per transaction. Two key primitives in proof generation are the Number Theoretic Transform (NTT) and Multi-scalar Multiplication (MSM). These primitives are prime candidates for hardware acceleration, and prior works have looked at GPU implementations and custom RTL. However, both algorithms involve complex dataflow patterns -- standard NTTs have irregular memory accesses for butterfly computations from stage to stage, and MSMs using Pippenger's algorithm have data-dependent memory accesses for partial sum calculations. We present SZKP, a scalable accelerator framework that is the first ASIC to accelerate an entire proof on-chip by leveraging structured dataflows for both NTTs and MSMs. SZKP achieves conservative full-proof speedups of over 400$\times$, 3$\times$, and 12$\times$ over CPU, ASIC, and GPU implementations.
Blockchain adoption has surged with the rise of Decentralized Finance (DeFi) applications. However, the significant value of digital assets managed by DeFi protocols makes them prime targets for attacks. Current smart contract vulnerability detection tools struggle with DeFi protocols due to deep logical bugs arising from complex financial interactions between multiple smart contracts. These tools primarily analyze individual contracts and resort to brute-force methods for DeFi protocols crossing numerous smart contracts, leading to inefficiency. We introduce Foray, a highly effective attack synthesis framework against deep logical bugs in DeFi protocols. Foray proposes a novel attack sketch generation and completion framework. Specifically, instead of treating DeFis as regular programs, we design a domain-specific language (DSL) to lift the low-level smart contracts into their high-level financial operations. Based on our DSL, we first compile a given DeFi protocol into a token flow graph, our graphical representation of DeFi protocols. Then, we design an efficient sketch generation method to synthesize attack sketches for a certain attack goal (e.g., price manipulation, arbitrage, etc.). This algorithm strategically identifies candidate sketches by finding reachable paths in TFG, which is much more efficient than random enumeration. For each candidate sketch written in our DSL, Foray designs a domain-specific symbolic compilation to compile it into SMT constraints. Our compilation simplifies the constraints by removing redundant smart contract semantics. It maintains the usability of symbolic compilation, yet scales to problems orders of magnitude larger. Finally, the candidates are completed via existing solvers and are transformed into concrete attacks via direct syntax transformation.
Fischlin's transform (CRYPTO 2005) is an alternative to the Fiat-Shamir transform that enables straight-line extraction when proving knowledge. In this work we focus on the problem of using the Fischlin transform to construct UC-secure zero-knowledge from Sigma protocols, since UC security – that guarantees security under general concurrent composition – requires straight-line (non-rewinding) simulators. We provide a slightly simplified transform that is much easier to understand, and present algorithmic and implementation optimizations that significantly improve the running time. It appears that the main obstacles to the use of Fischlin in practice is its computational cost and implementation complexity (with multiple parameters that need to be chosen). We provide clear guidelines and a simple methodology for choosing parameters, and show that with our optimizations the running-time is far lower than expected. For just one example, on a 2023 MacBook, the cost of proving the knowledge of discrete log with Fischlin is only 0.41ms (on a single core). This is 15 times slower than plain Fiat-Shamir on the same machine, which is a significant multiple but objectively not significant in many applications. We also extend the transform so that it can be applied to batch proofs, and show how this can be much more efficient than individually proving each statement. We hope that this paper will both encourage and help practitioners implement the Fischlin transform where relevant.
As cryptographic technologies evolve, the need for specialized hash functions to operate efficiently over different computational environments becomes necessary. Traditional symmetric algorithms like AES and SHA-3 have been optimized for traditional hardware and software implementations, which are designed over binary fields. However, protocols like zero-knowledge proofs require hash functions that are optimised over large prime fields. This thesis addresses the growing demand for Arithmetization-Oriented (AO) cryptographic hash functions for zero-knowledge applications. The performance and efficiency of many zero-knowledge applications often depends on the efficiency of the hash function used. In response to this need, this work explores a selection of these hash functions and implements them within two zero-knowledge proving systems: Dusk Network?s Plonk and Polygon?s Plonky2, with a focus on assessing the different performance tradeoffs that these hash functions offer within these sytems.
Function-as-a-Service providers manage security devices that are shared among multiple tenants. It is undesirable to give them access to cleartext HTTP requests to perform tasks such as traffic inspection. The recent Zero-Knowledge Middlebox (ZKMB) can be used to enforce network policies on TLS traffic without revealing any information on the content to the policy verifier. In this paper, we describe a ZKMB implementation and a policy designed to check whether the HTTPS function invocations by the clients follow a legitimate pattern. We also present and compare two strategies to distribute allowed patterns, introducing a Moving-Target Defense approach for the function URI randomization, which shows a good tradeoff between detection effectiveness and confidentiality. Performance assessment in our prototype implementation shows that the ZK algorithms are not yet suitable for real-time execution, but current research interest in this technology is expected to narrow this gap.
Zixin Wang, Bin Cao, Yao Sun, Chenxi Liu · 6 authors
Ensuring secure access to cellular networks is of paramount importance, in which system information (SI) protection plays a crucial role at the initial access stage. While the 3rd generation partnership project (3GPP) released many standardizations to enhance SI protection for preventing users from false base station (FBS) attacks, most of them are centralized solutions which are vulnerable to potential attacks and single-point failures. To address the aforementioned issues, a blockchain-enabled SI protection (BeSI), as a compatible and effective secure access scheme, is developed in this work, which aims at guaranteeing the authenticity and reliability of SI by considering the features of blockchain in immutability, traceability, and decentralization. Then, we derive a mathematical framework to justify the superiority of using blockchain in SI protection. Moreover, by resorting to a Poisson point process as the geographical model for both base stations and FBSs, we thus theoretically analyze the security gain of blockchain and understand the impact of network parameters including redundancy rate, number of confirmation blocks, and the density of base stations. Finally, numerical results are demonstrated to validate the effectiveness of BeSI.
Venkata Naga Rani Bandaru, P. Visalakshi, L. N. Prakash Kumar Ponnuru, Shaik Mohammad Rafee · 5 authors
The synergy between machine learning and encryption fortifies data security and privacy. This comprehensive overview delves into pivotal encryption methods in ML, spotlighting their inherent adaptability and paramount role in shielding sensitive data. Differential privacy injects controlled noise, ensuring privacy preservation while upholding data utility, especially vital in healthcare and financial sectors. Federated learning facilitates decentralized training, while homomorphic encryption assures secure data processing. Secure multi-party computation (SMPC) empowers collaborative private computation, and zero-knowledge proofs authenticate veracity sans data exposure, pivotal in blockchain and identity validation. These sophisticated algorithms cater comprehensively to diverse security requisites, bolstering data protection across indispensable domains.
Jan Lauinger, Serhat Bezmez, Jens Ernstberger, Sebastian Steinhorst
Latest identity systems rely on public blockchains to enhance user autonomy and reduce tracking from conventional identity providers. At the same time, identity systems integrate novel technologies such as zero-knowledge proofs (ZKPs) to improve data privacy and data compliance. We show that a naive verification of ZKPs at smart contracts enables replay attacks: Attackers can replay ZKPs at arbitrary times without having access to the private inputs that are required for the computation of the ZKP. To solve this problem, we construct a transaction sequence which verifies time-bound and replay-resistant ZKPs at smart contracts. Our construction introduces an additional but constant fee of 0.14${\$}$ per verification of a ZKP on the public blockchain Ethereum. With our new construction, we propose Portal, a novel identity system for decentralized single sign-on.
The rapid development of modern cryptographic applications such as zero-knowledge, secure multi-party computation, fully homomorphic encryption has motivated the design of new so-called arithmetization-oriented symmetric primitives. As designing ciphers in this domain is relatively new and not well-understood, the security of these new ciphers remains to be completely assessed. In this paper, we revisit the security analysis of arithmetization-oriented cipher Grendel. Grendel uses the Legendre symbol as a component, which is tailored specifically for the use in zero-knowledge and efficiently-varifiable proof systems. At FSE 2022, the first preimage attack on some original full GrendelHash instances was proposed. As a countermeasure, the designer adds this attack into the security analysis and updates the formula to derive the secure number of rounds. In our work, we present new algebraic attacks on GrendelHash. For the preimage attack, we can reduce the complexity or attack one more round than previous attacks for some instances. In addition, we present the first collision attack on some round-reduced instances by solving the constrained input/constrained output problem for the underlying permutations.
Ulysse Pavloff, Yackolley Amoussou-Guenou, Sara Tucci-Piergiovanni
In May 2023, the Ethereum blockchain experienced its first inactivity leak, a mechanism designed to reinstate chain finalization amid persistent network disruptions. This mechanism aims to reduce the voting power of validators who are unreachable within the network, reallocating this power to active validators. This paper investigates the implications of the inactivity leak on safety within the Ethereum blockchain. Our theoretical analysis reveals scenarios where actions by Byzantine validators expedite the finalization of two conflicting branches, and instances where Byzantine validators reach a voting power exceeding the critical safety threshold of one-third. Additionally, we revisit the probabilistic bouncing attack, illustrating how the inactivity leak can result in a probabilistic breach of safety, potentially allowing Byzantine validators to exceed the one-third safety threshold. Our findings uncover how penalizing inactive nodes can compromise blockchain properties, particularly in the presence of Byzantine validators capable of coordinating actions.
Ruben De Smet, Robrecht Blancquaert, Tom Godden, Kris Steenhaut · 5 authors
Elliptic curve cryptography is a widely deployed technology for securing digital communication. It is the basis of many cryptographic primitives such as key agreement protocols, digital signatures, and zero-knowledge proofs. Fast elliptic curve cryptography relies on heavily optimised modular arithmetic operations, which are often tailored to specific micro-architectures. In this article, we study and evaluate optimisations of the popular elliptic curve Curve25519 for ARM processors. We specifically target the ARM NEON single instruction, multiple data (SIMD) architecture, which is a popular architecture for modern smartphones. We introduce a novel representation for 128-bit NEON SIMD vectors, optimised for SIMD parallelisation, to accelerate elliptic curve operations significantly. Leveraging this representation, we implement an extended twisted Edwards curve Curve25519 back-end within the popular Rust library "curve25519-dalek". We extensively evaluate our implementation across multiple ARM devices using both cryptographic benchmarks and the benchmark suite available for the Signal protocol. Our findings demonstrate a substantial back-end speed-up of at least 20% for ARM NEON, along with a noteworthy speed improvement of at least 15% for benchmarked Signal functions.
With the growing practical applications of fully homomorphic encryption (FHE), secure multi-party computation (MPC), and zero-knowledge proofs (ZK), there has been an increasing need to design and analyze symmetric primitives that have low multiplication complexity and depth. In this paper, we propose a permutation constructed upon a 4-round nonlinear feedback resistor over$ \mathbb {F}_{q}^{4}$. Our proposed permutation has a multiplication depth of 2 and a multiplication complexity of 4. Significantly, its maximum differential/linear probability is bounded by$q^{-2}$. Based on this nonlinear function, we propose a new family of block ciphers over$ \mathbb {F}_{q}^{16}$called$ \mathsf {YuX}$, whose decryption circuit is highly efficient for FHE evaluation. We further provide specific instantiations, denoted as$ \mathsf {Yu_{2}X}$and$ \mathsf {Yu_{\mathrm {p}}X}$, wherein$q$takes the form of either$2^{n}$or a prime$p$, respectively. Furthermore, we conduct a comprehensive security analysis of$ \mathsf {YuX}$within certain parameters against various cryptanalysis methods employing automatic analysis tools, including the differential attack, linear attack, impossible differential attack, zero-correlation attack, and integral attack, as well as Gröbner basis and linearization attacks. Our research indicates that$ \mathsf {YuX}$maintains a robust security margin against those attacks. Finally, we present a detailed implementation of$ \mathsf {Yu_{2}X}$and$ \mathsf {Yu_{\mathrm {p}}X}$employing the BGV homomorphic encryption scheme. In comparison to ciphers over a field of characteristic 2, the outcomes evince that$ \mathsf {Yu_{2}X}$-8 (over$ \mathbb {F}_{2^{8}}^{16}$) and$ \mathsf {Yu_{2}X}$-16 (over$ \mathbb {F}_{2^{16}}^{16}$) achieve remarkably competitive throughputs, boasting performance approximately 12 times, 17 times, and 9 times superior to AES-128, CHAGHRI, and LowMC-128 (under 128-bit security), respectively. Furthermore, when juxtaposed with ciphers over a field of characteristic$p$, the outcomes affirm that the throughput of$ \mathsf {Yu_{\mathrm {p}}X}$-65537 (over$ \mathbb {F}_{65537}^{16}$) retains considerable competitiveness, registering an approximate fivefold enhancement relative to HERA. Evidently,$ \mathsf {YuX}$exhibits superior throughput compared to a majority of symmetric ciphers within this category.
Zero-knowledge SNARKs have become an extremely studied topic in cryptography due to their recent applications in modern cryptocurrencies. Most of these protocols are created using Polynomial Commitment Schemes such as the KZG protocol by Kate, Zaverucha, and Goldberg (ASIACRYPT 2010). Until recently, the known proofs of ex- tractability of the KZG protocol were either in idealized models or under very strong assumptions. This year, Lipmaa, Parisella, and Siim (EUROCRYPT 2024) proved the KZG protocol to be Special Sound and Black-Box Extractable in the standard model under their new ARSDH assumption. In this thesis, we build upon the work of Lipmaa et al. to prove Special Soundness for the bivariate version of the KZG polynomial commitment. To this end, we generalise their ARSDH assumption and define Special Soundness for the Bivariate KZG polynomial commitment. We then prove that the Bivariate KZG polynomial commitment achieves the Special Soundness under the ARSDH assumption and our generalisation of the AR- SDH assumption. Finally, we give a more refined analysis of the running time of the black-box extractor from Lipmaa et al. 1