Daniel Escudero, Hong Cheng, H. M. Liu, Chaoping Xing · 5 authors
Reverse multiplication-friendly embeddings have played a crucial role in secure multiparty computation and zero-knowledge proofs. In this work, we generalize the notion of RMFEs todegree-DRMFEs. We present a general construction of degree-DRMFEs by generalizing the ideas on algebraic geometry used to construct traditional degree-2 RMFEs. Furthermore, our theory is given in a unified manner for general Galois rings, which include both rings of the form Zpkand fields like Fpk, which have been treated separately in prior works. We present multiple concrete sets of parameters for degree-DRMFEs (includingD= 2), which can be useful for future works. In the recent work of (Cheon & Lee, Eurocryptâ22), the concept of adegree-D packing methodwas formally introduced, which captures the idea of embedding multiple elements of a smaller ring into a larger ring. We show that the generalized notion of RMFEs todegree-D RMFEswhich, in spite of being âmore algebraicâ than packing methods, turn out to be essentially equivalent. Thus, our constructions of degree-DRMFEs are also degree-Dpacking methods.
Scalability remains a major challenge in blockchain technology, particularly for Layer-1 networks like Ethereum, where high transaction volumes cause congestion and high gas fees. Zero-Knowledge (ZK) Rollups have emerged as scalable Layer-2 solutions, offering enhanced security and lower transaction costs. However, existing zk-Rollups such as zkSync Era, dYdX, and StarkNet each have their advantages and limitations in terms of efficiency, cost, and decentralization. This paper proposes zkFusion, a hybrid zk-Rollup protocol that combines the most effective features of these rollups to achieve faster transaction rates, improved cost-effectiveness, and enhanced security. zkFusion employs a flexible proof mechanism, optimized transaction batching, and a modular data throughput method, allowing users to balance between cost and security. Additionally, it integrates a decentralized sequencer to enhance network reliability and mitigate centralization risks. Comparative evaluation with existing zk-Rollups demonstrates that zkFusion significantly reduces transaction fees, improves throughput, and maintains high security assurances. By blending the innovations of zkSync Era, dYdX, and StarkNet, zkFusion aims to set a new benchmark for scalability, efficiency, and cost reduction in Layer-2 blockchain solutions.
Alexandr Kuznetsov, Emanuele Frontoni, Alexandr Kuznetsov, Ruslan Shevchuk · 5 authors
In the rapidly evolving field of digital asset management, centralized and decentralized global registries have become essential tools for organizing, tracking, and distributing digital assets. However, existing systems often face challenges regarding security, censorship resistance, interoperability, customizability, and scalability. This research paper aims to address these gaps by proposing a novel decentralized global registry system based on blockchain technology and non-fungible tokens (NFTs). The research paper makes several key contributions to the field of digital asset management. First, it provides a detailed system design for the proposed decentralized global registry, outlining its architectural components, functional modules, and integration with blockchain and NFT technologies. Second, it offers a thorough comparative analysis of the advantages and limitations of the proposed system in relation to existing centralized and decentralized registries. Finally, the paper presents potential use cases and practical applications of the proposed system in various industries, demonstrating its versatility and adaptability to different contexts and requirements. In conclusion, this research paper contributes significantly to the ongoing efforts to improve digital asset management by presenting a novel, decentralized global registry system based on blockchain technology and NFTs. The proposed system addresses the key limitations of existing solutions and offers a promising direction for future research and development in this critical field.
A connected loopless graph is 2-edge-connected if it remains connected after the removal of at most one of its edges. Many combinatorial optimization problems seek, for a given graph with costs on its edges, a spanning subgraph satisfying certain connectivity constraints. The minimum 2-edge-connected spanning subgraph problem (2-ECSSP) is a problem of this type. It can be formulated as an integer linear program that selects edges of minimum total cost satisfying the restriction that every cut of the given graph is covered by at least two of the selected edges. This problem is known to be NP-hard. This thesis develops rounding algorithms for three variants of 2-ECSSP, focusing on rounding half-integral solutions of the corresponding linear relaxation. This family of solutions often yields the largest known integrality ratio for various subproblems of 2-ECSSP. The first problem we investigate is the half-integral 2-ECSSP with unrestricted costs. We develop a novel 5/3-rounding that, to the best of our knowledge, is the first one with a factor better than 2. Moreover, we design a reduction scheme, restricting the problem to 4-edge-connected graphs with maximum degree at most five. Then, we study the matching augmentation problem (MAP), a subproblem of 2-ECSSP in which the edge costs are either 0 or 1 and the zero cost edges define a matching. We survey a better-than-2-approximation, obtained in 2022 by Bamas, Drygala, and Svensson, presenting a comprehensive proof of their result and determining an improved factor. Additionally, we address conjectures posed in their work and present computational experiments to support our findings. Finally, we discuss the 2-edge-connected spanning multisubgraph problem (2-ECSMP), a variation of 2-ECSSP in which multiple copies of the same edge can be selected. We survey a recent work by Boyd et al. on a 4/3-rounding for the half-integral 2-ECSMP and leverage their techniques to prove novel decomposition theorems for 4-regular 4-edge-connected graphs. Finally, we pose two conjectures concerning extensions of the decomposition results, suggesting new research directions.
Behzad Abdolmaleki, Noemi Glaeser, Sebastian Ramacher, Daniel Slamanig
Non-interactive zero-knowledge proofs (NIZKs) and in particular succinct NIZK arguments of knowledge (zk-SNARKs) increasingly see real-world adoption in large and complex systems. Many zk-SNARKs require a trusted setup, i.e., a common reference string (CRS), and for practical use it is desirable to reduce the trust in the CRS generation. The latter can be achieved via the notions of subversion or updatable CRS. Another important property when deployed in large systems is the ability to securely compose them to obtain more complex protocols, e.g., via the Universal Composability (UC) framework. Relying on the UC framework allows arbitrary and secure composition of protocols in a modular way. In this work, we investigate whether zk-SNARKs can provide updatability and composability simultaneously. This is a challenging task as the UC framework rules out several natural techniques for such a construction. As our main result, we show that it is indeed possible to achieve these properties in a generic and modular way if we relax the succinctness properties of zk-SNARKs slightly to those of a circuit-succinct NIZK which is not witness-succinct, i.e., by increasing the proof size of the underlying zk-SNARK by the size of the witness$w$. We argue that for various practical applications of zk-SNARKs this overhead is acceptable. Our starting point is the Lamassu framework (ACM CCS'20), which we extend in several directions. Our new generic compiler adds only minimal overhead, which we demonstrate by benchmarking its application to the Sonic proof system (ACM CCS'19).
After more than three decades of electronic design automation, most layouts for analog integrated circuits are still handcrafted in a laborious manual fashion today. This book presents Self-organized Wiring and Arrangement of Responsive Modules (SWARM), a novel interdisciplinary methodology addressing the design problem with a decentralized multi-agent system. Its basic approach, similar to the roundup of a sheep herd, is to let autonomous layout modules interact with each other inside a successively tightened layout zone. Considering various principles of self-organization, remarkable overall solutions can result from the individual, local, selfish actions of the modules. Displaying this fascinating phenomenon of emergence, examples demonstrate SWARMâs suitability for floorplanning purposes and its application to practical place-and-route problems. From an academic point of view, SWARM combines the strengths of procedural generators with the assets of optimization algorithms, thus p...
After more than three decades of electronic design automation, most layouts for analog integrated circuits are still handcrafted in a laborious manual fashion today. This book presents Self-organized Wiring and Arrangement of Responsive Modules (SWARM), a novel interdisciplinary methodology addressing the design problem with a decentralized multi-agent system. Its basic approach, similar to the roundup of a sheep herd, is to let autonomous layout modules interact with each other inside a successively tightened layout zone. Considering various principles of self-organization, remarkable overall solutions can result from the individual, local, selfish actions of the modules. Displaying this fascinating phenomenon of emergence, examples demonstrate SWARMâs suitability for floorplanning purposes and its application to practical place-and-route problems. From an academic point of view, SWARM combines the strengths of procedural generators with the assets of optimization algorithms, thus p...
After more than three decades of electronic design automation, most layouts for analog integrated circuits are still handcrafted in a laborious manual fashion today. This book presents Self-organized Wiring and Arrangement of Responsive Modules (SWARM), a novel interdisciplinary methodology addressing the design problem with a decentralized multi-agent system. Its basic approach, similar to the roundup of a sheep herd, is to let autonomous layout modules interact with each other inside a successively tightened layout zone. Considering various principles of self-organization, remarkable overall solutions can result from the individual, local, selfish actions of the modules. Displaying this fascinating phenomenon of emergence, examples demonstrate SWARMâs suitability for floorplanning purposes and its application to practical place-and-route problems. From an academic point of view, SWARM combines the strengths of procedural generators with the assets of optimization algorithms, thus p...
After more than three decades of electronic design automation, most layouts for analog integrated circuits are still handcrafted in a laborious manual fashion today. This book presents Self-organized Wiring and Arrangement of Responsive Modules (SWARM), a novel interdisciplinary methodology addressing the design problem with a decentralized multi-agent system. Its basic approach, similar to the roundup of a sheep herd, is to let autonomous layout modules interact with each other inside a successively tightened layout zone. Considering various principles of self-organization, remarkable overall solutions can result from the individual, local, selfish actions of the modules. Displaying this fascinating phenomenon of emergence, examples demonstrate SWARMâs suitability for floorplanning purposes and its application to practical place-and-route problems. From an academic point of view, SWARM combines the strengths of procedural generators with the assets of optimization algorithms, thus p...
After more than three decades of electronic design automation, most layouts for analog integrated circuits are still handcrafted in a laborious manual fashion today. This book presents Self-organized Wiring and Arrangement of Responsive Modules (SWARM), a novel interdisciplinary methodology addressing the design problem with a decentralized multi-agent system. Its basic approach, similar to the roundup of a sheep herd, is to let autonomous layout modules interact with each other inside a successively tightened layout zone. Considering various principles of self-organization, remarkable overall solutions can result from the individual, local, selfish actions of the modules. Displaying this fascinating phenomenon of emergence, examples demonstrate SWARMâs suitability for floorplanning purposes and its application to practical place-and-route problems. From an academic point of view, SWARM combines the strengths of procedural generators with the assets of optimization algorithms, thus p...
After more than three decades of electronic design automation, most layouts for analog integrated circuits are still handcrafted in a laborious manual fashion today. This book presents Self-organized Wiring and Arrangement of Responsive Modules (SWARM), a novel interdisciplinary methodology addressing the design problem with a decentralized multi-agent system. Its basic approach, similar to the roundup of a sheep herd, is to let autonomous layout modules interact with each other inside a successively tightened layout zone. Considering various principles of self-organization, remarkable overall solutions can result from the individual, local, selfish actions of the modules. Displaying this fascinating phenomenon of emergence, examples demonstrate SWARMâs suitability for floorplanning purposes and its application to practical place-and-route problems. From an academic point of view, SWARM combines the strengths of procedural generators with the assets of optimization algorithms, thus p...