Modular arithmetic, particularly modular reduction, is widely used in cryptographic applications such as homomorphic encryption (HE) and zero-knowledge proofs (ZKP). High-bit-width operations are crucial for enhancing security; however, they are computationally intensive due to the large number of modular operations required. The lookup-table-based (LUT-based) approach, a ``space-for-time'' technique, reduces computational load by segmenting the input number into smaller bit groups, pre-computing modular reduction results for each segment, and storing these results in LUTs. While effective, this method incurs significant hardware overhead due to extensive LUT usage. In this paper, we introduce ALLMod, a novel approach that improves the area efficiency of LUT-based large-number modular reduction by employing hybrid workloads. Inspired by the iterative method, ALLMod splits the bit groups into two distinct workloads, achieving lower area costs without compromising throughput. We first develop a template to facilitate workload splitting and ensure balanced distribution. Then, we conduct design space exploration to evaluate the optimal timing for fusing workload results, enabling us to identify the most efficient design under specific constraints. Extensive evaluations show that ALLMod achieves up to $1.65\times$ and $3\times$ improvements in area efficiency over conventional LUT-based methods for bit-widths of $128$ and $8,192$, respectively.
Multi-scalar multiplication (MSM) is the primary building block in many pairing-based zero-knowledge proof (ZKP) systems. MSM at large scales has become the main bottleneck in ZKP implementations. Inspired by existing SIMD-accelerated work, we are focused on accelerating MSM computing efficiency using SIMD instructions in a single CPU environment. First, we propose a SIMD-accelerated MSM computing architecture with no write conflicts and constant memory overheads. This architecture utilizes multithreading to achieve task-level and loop-level parallelism and employs a three-tier buffer mechanism to maximize the utilization of the SIMD engine. Instanced with AVX512-IFMA instructions, we implement six SIMD elliptic curve arithmetic engines for different point addition in three coordinate systems and two groups. Moreover, we integrate our AVX-MSM implementation into the libsnark library, naming it AVX-ZK. In more detail, point deduplication and “Three-Stage” memory optimization are proposed to address problems existing in practical applications. Based on the RELIC library, our performance results on the BLS12-381 curve show that our AVX-MSM achieves up to 27.86x speedup over the most popular Pippenger algorithm. Compared with libsnark, our AVX-ZK implementation achieves over 11.53x (up to 20.26x) speedup under standard benchmarks.
Zhengbang Yang, Lutan Zhao, Peinan Li, Han Liu · 8 authors
Zero-knowledge proof (ZKP) allows a prover to convince a verifier of the truth of a statement without revealing any secret information. This property is utilized in numerous privacy-preserving applications. However, the huge overhead of proof generation impedes the widespread adoption of ZKP. As a result, many ZKP accelerators have been developed to speed up proof generation. However, existing accelerators are designed at the granularity of core operators and exhibit low hardware resource utilization and limited adaptability. In this paper, we identify the commonality of all computation stages in proof generation at the level of basic finite field arithmetic operations. Based on this insight, we propose LegoZK, a dynamically reconfigurable hardware accelerator for ZKP. LegoZK employs finite field arithmetic units (FAUs) as its fundamental components and integrates these FAUs with a hierarchical on-chip network (NoC). By dynamically configuring the FAUs and the NoC, LegoZK can effectively accelerate the entire proof generation process, achieving higher overall performance. Additionally, for the most time-consuming MSM, this paper proposes a fast, fully pipelined bucket reduction algorithm based on lookup tables, which significantly reduces the latency of MSM. Experimental results demonstrate that LegoZK achieves on average speedup of $31.96 \times$ and $11.30 \times$ in proof generation compared to the state-of-the-art ZKP ASIC accelerator PipeZK and the GPU accelerator GZKP, respectively. And compared to PipeZK, LegoZK achieves $\mathbf{5 0. 1 \%}$ area reduction and $\mathbf{3 7. 7 \%}$ power consumption reduction.
Tao Lu, Yuxun Chen, Zonghui Wang, Xiaohang Wang · 6 authors
Zero-knowledge proof (ZKP) is a cryptographic primitive that enables one party to prove the validity of a statement to other parties without disclosing any secret information. With its widespread adoption in applications such as blockchain and verifiable machine learning, the demand for generating zero-knowledge proofs has increased dramatically. In recent years, considerable efforts have been directed toward developing GPU-accelerated systems for proof generation. However, these previous systems only explored efficiently generating a single proof by reducing latency rather than batch generation to provide high throughput.
Zero-knowledge proof (ZKP) is an important cryptographic tool that sees wide applications in real-world scenarios where privacy must be protected, including privacy-preserving blockchains and zero-knowledge machine learning. Existing ZKP acceleration approaches using GPUs, FPGAs, and ASICs focus only on classic protocols that rely on expensive elliptic curve arithmetics. Emerging ZKP protocols based on hash functions can greatly reduce the algorithmic complexity, but they also introduce much more diverse computation kernels that cannot be efficiently handled by a single accelerator chip if dedicated units for each kernel are used. Our approach is to leverage a unified hardware architecture that is able to efficiently support the common primitives in ZKP, and then use smart mapping strategies to flexibly map various kernels to such hardware while ensuring high resource utilization. We design UniZK as such a ZKP accelerator, with a systolic-array-based hardware architecture enhanced with extra local links and a new vector processing mode. We propose novel mapping strategies to support diverse kernels including number theoretic transforms, hash functions, and general polynomial computations. UniZK provides 97x and 46x speedups on average compared to the CPU and GPU implementations of the same protocols, and is also 840x faster than previous ZKP accelerators using different protocols.
This survey provides a comprehensive examination of verifiable computing, tracing its evolution from foundational complexity theory to modern zero-knowledge succinct non-interactive arguments of knowledge (ZK-SNARKs). We explore key developments in interactive proof systems, knowledge complexity, and the application of low-degree polynomials in error detection and verification protocols. The survey delves into essential mathematical frameworks such as the Cook-Levin Theorem, the sum-check protocol, and the GKR protocol, highlighting their roles in enhancing verification efficiency and soundness. By systematically addressing the limitations of traditional NP-based proof systems and then introducing advanced interactive proof mechanisms to overcome them, this work offers an accessible step-by-step introduction for newcomers while providing detailed mathematical analyses for researchers. Ultimately, we synthesize these concepts to elucidate the GKR protocol, which serves as a foundation for contemporary verifiable computing models. This survey not only reviews the historical and theoretical advancements in verifiable computing over the past three decades but also lays the groundwork for understanding recent innovations in the field.
Due to the strong untraceability of mixing services, numerous criminals exploit these services to engage in illicit activities, posing a significant threat to the blockchain ecosystem. This paper addresses the challenge of linking transaction addresses in Tornado Cash, a popular mixing service on Ethereum. While existing state-of-the-art solutions like MixBroker attempt to address this problem, two fundamental limitations persist: insufficient utilization of neighbor information and neglect of address information asymmetry. To address these gaps, a novel framework termed “MixLinker” is proposed, which enhances neighbor information utilization and models information asymmetry. Specifically, a Normalized Adjusted Personal PageRank (NAPPR) module is designed to prioritize significant neighbor nodes while mitigating interference from super and irrelevant addresses. Additionally, tensors are employed to model transactions, capturing rich interaction features related to transaction attributes. Based on historical transaction sequences, Tensor Long Short-Term Memory (TLSTM) is used to obtain high-quality initial input features for the Graph Neural Network (GNN) module, enabling effective learning of nonlinear dynamics. To ensure symmetric output results and model asymmetric information, a temporal-aware symmetry classifier is constructed that leverages asymmetric information through permutation operations and an order-aware classifier. Extensive experiments demonstrate that MixLinker outperforms other methods, validating the effectiveness of the proposed approach and confirming the two underlying motivations.
Zero-knowledge proof (ZKP) is a widely used privacy-preserving technology, where multiscalar multiplication (MSM) accounts for over 70% of the computational workload. The acceleration of MSM can enhance the overall performance of ZKP, making it a focal point of community attention. However, in practical applications involving the deployment of multiple MSM accelerators, existing designs often overlook strategies for optimizing bandwidth and area efficiency. To address this, we propose Myosotis, an efficiently pipelined and parameterized MSM architecture. By sharing input data and allocating cache effectively, it mitigates average transmission bandwidth in runtime. Myosotis also supports the use of multiple point addition (PADD) units to achieve performance gains, balancing area overhead and latency for improved area efficiency. Different parameter selection enables a tradeoff between the performance, area, and bandwidth of the MSM accelerator. When benchmarking with MSM degrees between$2^{18}$and$2^{26}$, our proposed baseline design achieves up to$3.32\times $and$6.72\times $speedups over state-of-the-art FPGA and ASIC designs. Compared to the baseline, Myosotis with two window MSMs and one PADD unit reduces bandwidth demand by 43% while maintaining similar area and latency. On the other hand, Myosotis with three window MSMs and two PADD units decreases latency by 43% and bandwidth by 17%, with only a 9% area increase.
Shahzad Ahmad Butt, Benjamin Reynolds, V. Ramamurthy, Xiao Xiao · 8 authors
Zero-Knowledge Proofs (ZKPs) have emerged as an important cryptographic technique allowing one party (prover) to prove the correctness of a statement to some other party (verifier) and nothing else. ZKPs give rise to user's privacy in many applications such as blockchains, digital voting, and machine learning. Traditionally, ZKPs suffered from poor scalability but recently, a sub-class of ZKPs known as Zero-knowledge Succinct Non-interactive ARgument of Knowledges (zk-SNARKs) have addressed this challenge. They are getting significant attention and are being implemented by many public libraries. In this paper, we present a novel scalable architecture that is suitable for accelerating the zk-SNARK prover compute on FPGAs. We focus on the multi-scalar multiplication (MSM) that accounts for the majority of computation time spent in zk-SNARK systems. The MSM calculations extensive rely on modular arithmetic so highly optimized Intel IP Libraries for modular arithmetic are used. The proposed architecture exploits the parallelism inherent to MSM and is implemented using the Intel OneAPI framework for FPGAs. Our implementation runs 110x-150x faster compared to reference software library, uses a generic curve form in Jacobian coordinates and is the first to report FPGA hardware acceleration results for BLS12-381 and BN128 family of elliptic curves.
Over the last few decades, a large body of research was carried out covering Byzantine Fault Tolerance (BFT) systems. This research has brought forward new techniques, including but not limited, for ordering operations (Abraham et al., 2018; Buchman, 2016; Guo et al., 2020; Bessani et al., 2014; Duan et al., 2018) and state transfer (Bessani et al., 2013; Distler, 2021 , Eischer et al., 2019 ), on networks that suffer from byzantine faults. More recently, the ongoing research on distributed ledgers re-ignited the interest on BFT, due to its high throughput when compared to other alternatives of byzantine consensus ( Vukolić, 2016 ). In this paper we present three contributions covering several aspects, including modular and extensible framework design and implementation, system optimization through development of better networking alternatives, a greater use of parallelism, several ordering protocol improvements and extensive comparative assessment of previous state-of-the-art approaches. First, we introduce Atlas, an open-source modular BFT framework that aims to support the research and development of highly efficient BFT protocols, by decoupling traditionally entangled sub-protocols, e.g., consensus primitive from the execution (Bessani et al., 2014), and deferment of log management to replicated services from state transfer. Atlas allows to further provide modules that can be re-used across different BFT approaches, such as deterministic and probabilistic/randomized models. Second, we present FeBFT, a new BFT implementation developed upon Atlas that combines pre-existing proven ideas from PBFTs, namely its 3-phase consensus and view-change protocol. This base approach is then extended with novel optimizations of the protocol, namely, multi-leader proposals (Stathakopoulou et al., 2019), multi-instance consensus execution (Stathakopoulou et al., 2022; Behl et al., 2015), and configurable batching solution that allow us to reduce the latency while improving throughput at the same time. Third, we offer a comprehensive evaluation amongst our work and other state-of-the-art BFT-SMR implementations, namely, Atlas ( Anon, 2024a ) with FeBFT (Official febft repository 2024), BFT-SMaRt (Bessani et al., 2014) and Themis (Rüsch et al., 2019). With these contributions, we aim to lay the ground work to: (i) improve reusability and hence productivity in BFT(-SMR) development; (ii) increase system safety, performance, scalability and reduce recovery time with the optimizations proposed; (iii) draw insights on the bottlenecks preventing order-of-magnitude improvements in BFT processing from a system’s perspective; and lastly, (iv) improve reproducibility between different BFT (sub-)protocols by allowing for true apples-to-apples comparisons. • Atlas, an open-source, modular BFT framework designed to support the efficient development of BFT protocols by separating traditionally intertwined sub-protocols and allowing for reusable modules across different BFT approaches. • FeBFT, introduces a novel BFT implementation leveraging the Atlas framework, which boosts protocol efficiency via multi-leader proposals and multi-instance consensus execution. It incorporates a batching solution designed to scale with network throughput, prioritizing this over network latency while maintaining the configurability to be tuned for low latency if needed. • Focusing on the essential need for reproducibility in scientific evaluation, Atlas provides a critical framework for accurate comparisons between different protocols. By offering a modular and reusable architecture, it significantly reduces the workload for system researchers in developing and testing implementations. This approach ensures a true apple-to-apple comparison, enabling a more precise and reliable assessment of protocol performance and efficacy. • And lastly, a comprehensive evaluation comparison with two well-known BFT-SMR (deterministic) implementations, namely, BTF-SMaRt and Themis, against FeBFT, our PBFT implementation that uses Atlas.
Conner Fulford, Sai Medury, Amani Altarawneh, Anthony Skjellum
Distributed systems and blockchain consensus protocols rely on a clock synchronization algorithm to resolve any conflicts related to the state of data or resources. Faulty and adversarial peers make it challenging to achieve clock synchronization in a peer-to-peer distributed system. Clock-synchronization protocols such as the Network Time Protocol (NTP) and the Precision Time Protocol (PTP) are effective but only in a partially or fully trusted network. They fail to synchronize clocks in the presence of misbehaving peers who try to rewind or fast-forward time or introduce deadlocks purposely.This paper introduces BFT-Metronome, a Byzantine fault-tolerant clock synchronization algorithm for peer-to-peer distributed systems. The novel BFT-Metronome algorithm combines a sensor-fusion algorithm with a statistical outlier detection algorithm to enable participating peers to determine the most likely skew based on broadcast timestamps. The algorithm is designed to withstand up to $\frac{N}{3} - 1$ misbehaving participants in a network of N total participants, and the independently calculated offset is observed to be within 10 ms of precision vs. 40-100 ms in peer-to-peer distributed systems.The BFT-Metronome clock synchronization algorithm can also be applied to blockchain consensus protocols (such as Proof-of-Stake) that rely on weakly synchronized clocks. This is shown by integrating BFT-Metronome with the Lightweight Mining Algorithm to achieve consensus-round synchronization and timeouts. Then, generalization to other protocols is argued qualitatively. It can also be applied to large distributed systems to secure against insider threats during clock synchronization.
This paper presents a comprehensive analysis of storage proofs in the Ethereum ecosystem, examining their role in addressing historical and cross-chain state access challenges. We systematically review existing approaches to historical state verification, comparing Merkle Mountain Range (MMR) and Merkle-Patricia trie (MPT) architectures. An analysis involves their respective performance characteristics within zero-knowledge contexts, where performance challenges related to Keccak-256 are explored. The paper also examines the cross-chain verification, particularly focusing on the interactions between Ethereum and Layer 2 networks. Through careful analysis of storage proof patterns across different network configurations, we identify and formalize three architectures for cross-chain verification. By organizing this complex technical landscape, this analysis provides a structured framework for understanding storage proof implementations in the Ethereum ecosystem, offering insights into their practical applications and limitations.
This chapter delves into the future of the complex and evolving world of non-fungible tokens (NFTs), focusing on their potential to drive mass adoption of blockchain technology. Beginning with some historical context, the chapter explores the rapid growth of NFTs in the digital art and collectibles space, most notably during the speculative boom in 2021–2022 and the subsequent crash. The chapter then investigates how NFTs might expand beyond these initial use cases. It describes major developments in technology, business models, and financial infrastructure that will support further evolution of NFTs. Using real-world examples, the chapter then discusses emerging categories of NFT use cases, such as tokenization of physical assets, ticketing, and digital identity. It concludes by emphasizing that the true mass adoption of NFTs will occur when the technology becomes invisible and the primary draw becomes the value of use cases, not the novelty of NFTs themselves. While one should be skeptical about specific predictions for massive NFT adoption, this chapter shows that the capabilities NFTs provide are poised to add value in a wide variety of contexts.
Parallel Computing and Optimization Techniques
Music Technology and Sound Studies
Physical Unclonable Functions (PUFs) and Hardware Security
Super-instructions are a crucial optimization method for interpreters, as they combine multiple basic instructions into single specialized operations. The optimization technique reduces dispatch overhead and enables further optimizations in the synthesized operation code for a super-instruction. However, due to combinatorial explosion, identifying super-instructions is a complex selection problem. This paper presents a novel approach for the automated synthesis of super-instructions using a combination of offline dictionary-based compression algorithms and greedy heuristics. Our method addresses the common issue of overlap between super-instructions, which previous approaches often overlook. Additionally, we introduce a meta-compiler for the Ethereum Virtual Machine (EVM) that automatically generates a new interpreter incorporating the super-instructions. The super-instructions generated with our approach result in an 8.45% speedup for the interpreter component of the EVM.
Decompilation of binary code has arisen as a highly-important application in the space of Ethereum VM (EVM) smart contracts. Major new decompilers appear nearly every year and attain popularity, for a multitude of reverse-engineering or tool-building purposes. Technically, the problem is fundamental: it consists of recovering high-level control flow from a highly-optimized continuation-passing-style (CPS) representation. Architecturally, decompilers can be built using either static analysis or symbolic execution techniques. We present Shrnkr, a static-analysis-based decompiler succeeding the state-of-the-art Elipmoc decompiler. Shrnkr manages to achieve drastic improvements relative to the state of the art, in all significant dimensions: scalability, completeness, precision. Chief among the techniques employed is a new variant of static analysis context: shrinking context sensitivity. Shrinking context sensitivity performs deep cuts in the static analysis context, eagerly “forgetting” control-flow history, in order to leave room for further precise reasoning. We compare Shrnkr to state-of-the-art decompilers, both static-analysis- and symbolic-execution-based. In a standard benchmark set, Shrnkr scales to over 99.5% of contracts (compared to ∼95% for Elipmoc), covers (i.e., reaches and manages to decompile) 67% more code than Heimdall-rs, and reduces key imprecision metrics by over 65%, compared again to Elipmoc.
Xudong Zhu, Haoqi He, Zhengbang Yang, Yi Deng · 6 authors
Zero-knowledge proof (ZKP) is a cryptographic primitive that enables a prover to convince a verifier that a statement is true, without revealing any other information beyond the correctness of the statement itself. Due to its powerful capabilities, its most practical type, called zero-knowledge Succinct Non-interactive ARgument of Knowledge (zkSNARK), has been widely deployed in various privacypreserving applications such as cryptocurrencies and verifiable computation. Although state-of-the-art zkSNARKs are highly efficient for the verifier, the computational overhead for the prover is still orders of magnitude too high to warrant use in many applications. This overhead arises from several time-consuming operations, including large-scale matrix-vector multiplication (MUL), number-theoretic transform (NTT), and especially the multi-scalar multiplication (MSM) which constitutes the largest proportion. Therefore, further efficiency improvements are needed.In this paper, we focus on comprehensive optimization of running time and storage space required by the MSM algorithm on GPUs. Specifically, we propose a novel, modular and adaptive parameter configuration technique—elastic MSM to enable us to adjust the scale of MSM according to our own wishes by performing a corresponding amount of preprocessing. This technique enables us to fully unleash the potential of various efficient parallel MSM algorithms. We have implemented and tested elastic MSM over three prevailing parallel Pippenger algorithms on GPUs. Across various preprocessing space limitations (across various MSM scales), our constructions achieve up to about 1.90×, 1.08× and 1.36× (2.58×, 1.39× and 1.91×) speedup versus three state-of-the-art parallel Pippenger algorithms on GPUs, respectively.From another perspective, elastic MSM could also be regarded as a preprocessing technique over the well-known Pippenger algorithm, which is modular and could be used to accelerate almost all the most advanced parallel Pippenger algorithms on GPUs. Meanwhile, elastic MSM provides an adaptive trade-off between the running time and the extra storage space needed by parallel Pippenger algorithms on GPUs. This is the first preprocessing technique to retain the improved MSM computation brought by preprocessing under varying storage space limitations. Specifically, across various preprocessing space limitations (across various MSM scales), our constructions achieve up to about 192× and 223× (159× and 174×) speedup versus two state-ofthe- art preprocessing parallel Pippenger algorithms on GPUs, respectively.
Proposals for Ultra-Large-Scale-System (ULSS), particularly the grid’s energy management systems (EMSs), to adopt the Ethereum blockchain are increasing as its support for privacy-preserving, encrypted, decentralized computing via sharding, rollups, Smart-Contracts (SC), and Zero-Knowledge-proofs (ZK) address the increasing topological, behavioral, and data-processing challenges. In this context, the aggregation and verification of aggregated, ZK Kate-Zaverucha-Goldberg constant-sized polynomials commitments (KZG) are a bottleneck limiting deployment to Internet-of-Things (IoT) nodes used by the EMS due to high O(b G+blog2b F) computationincurred when aggregating or verifying by recreation. The alternative, expensive pairing checks involve two pairings, three exponentiations (Exp), three multiplications (Mul), and one addition (Add), a security factor S times for the n aggregated KZG. The proposed pairing checks significantly reduce costs for both: 1) Verifiers: two pairings, no Exp, one Mul, and one Add, and 2) Provers: one pairing check, no Exp, four Mul, and one Add. The aggregation method, based on multidimensional differential addition chains, costs only O(ℓ) computation, where ℓ is the bit length of the scalars. This approach demonstrates the feasibility of operating a KZG-centric blockchain with KZG rollups on IoT networks, marking a significant advancement in ULSS.
Changxu Liu, Hao Zhou, Patrick Dai, Li Shang · 5 authors
Multi-Scalar Multiplication (MSM) is a computationally intensive task that operates on elliptic curves based on GF(P) . It is commonly used in zero-knowledge proof (ZKP), where it accounts for a significant portion of the computation time required for proof generation. In this article, we present PriorMSM, an efficient acceleration architecture for MSM. We propose a Priority-Based Scheduling Mechanism (PBSM) based on a multi-FIFO and multi-bank architecture to accelerate the implementation of MSM. By increasing the pairing success rate of internal points, PBSM reduces the number of bubbles in the pipeline of point addition (PADD), consequently improving the data throughput of the pipeline. We also introduce an advanced parallel bucket aggregation algorithm, leveraging PADD’s fully pipelined characteristics to significantly accelerate the implementation of bucket aggregation. We perform a sensitivity analysis on the crucial parameter of window size in MSM. The results indicate that the window size of the MSM significantly impacts its latency. Area-Time Product (ATP) metric is introduced to guide the selection of the optimal window size, balancing the performance and cost for practical applications of subsequent MSM implementations. PriorMSM is evaluated using the TSMC 28 nm process. It achieves a maximum speedup of 10.9× compared to the previous custom hardware implementations and a maximum speedup of 3.9× compared to the GPU implementations.
Bruno Farias, Rafael Menezes, Eddie B. de Lima Filho, Youcheng Sun · 5 authors
This paper introduces a tool for verifying Python programs, which, using type annotation and front-end processing, can harness the capabilities of a bounded model-checking (BMC) pipeline. It transforms an input program into an abstract syntax tree to infer and add type information. Then, it translates Python expressions and statements into an intermediate representation. Finally, it converts this description into formulae evaluated with satisfiability modulo theories (SMT) solvers. The proposed approach was realized with the efficient SMT-based bounded model checker (ESBMC), which resulted in a tool called ESBMC-Python, the first BMC-based Python-code verifier. Experimental results, with a test suite specifically developed for this purpose, showed its effectiveness, where successful and failed tests were correctly evaluated. Moreover, it found a real problem in the Ethereum Consensus Specification.
Shasha Yu, Yanan Qiao, Junge Bo, Fan Yang · 5 authors
Proof-of-Work (PoW) is a consensus mechanism widely applied in blockchain applications such as Bitcoin and Ethereum. In PoW, only the first miner solving the PoW puzzle by Hash Collisions wins the reward. Thus, PoW-powered cryptocurrencies have become increasingly energy inefficient due to the fierce competition among the participants. Additionally, PoW can cause centralization in blockchain networks. To address these challenges, this research proposes an incentive mechanism named EPoW. EPoW has been proven to generally benefit the conservation of energy in Bitcoin mining by giving miners no incentive to devote a higher hash rate. Moreover, EPoW is an instrument for decentralization by discouraging the collusion among miners. Then, a dual security verification mechanism is proposed to enhance the security of blockchain networks. Finally, extensive comparative experiments are conducted to validate the effectiveness of EPoW in energy efficiency. The research indicates that EPoW eliminates the miner's incentive to devote a higher hash-rate than all their counterparts, thus relieving the malignant competition and conserving expensive energy. Additionally, EPoW alleviates the problem of centralization caused by mining pools.
Vladlen D. Afonin, Sergey Zapechnikov, Igor A. Prostov
Zero-knowledge proofs are being increasingly applied to a wide range of tasks in modern distributed information systems. Of particular interest are such areas of activity as digital asset management systems, anonymous electronic voting systems, and anonymous credentials. Nevertheless, within the framework of the desire of Russian developers to localize the developed products, there is a question of compliance of the used algorithms with the legislative framework of the Russian Federation, which obliges developers to use local cryptographic standards. As our analysis shows, insufficient attention has been paid in the literature to the applicability of these standards to the scenario of use in zero-knowledge proof systems. In particular, the complexity of proof generation, parameters of arithmetic schemes are not analyzed, there is no comparison of computational complexity and cryptographic properties with foreign alternatives. In this paper we consider in detail the peculiarities of implementation of the arithmetic scheme for the function of GOST 34.11-2018 in the most widespread language for arithmetic circuit programming Circom. The developed program code is open and available for use and modification. The characteristics of the scheme, compilation and generation times are analyzed. The obtained results were compared with other popular hash functions: the cryptographic hash function SHA256 included in the standard language library, and the hash function Poseidon, specialized and optimized for use in zero-knowledge proof systems. The results show that while the use of the Russian hash function is possible, it is not desirable in applications that do not require the use of local cryptographic standards, due to the greater time complexity of witness generation and consequently proof generation. Recommendations on usage scenarios are given and further research directions are suggested.