In multi-prover interactive proofs (MIPs), the verifier is usually non-adaptive. This stems from an implicit problem which we call ``contamination'' by the verifier. We make explicit the verifier contamination problem, and identify a solution by constructing a generalization of the MIP model. This new model quantifies non-locality as a new dimension in the characterization of MIPs. A new property of zero-knowledge emerges naturally as a result by also quantifying the non-locality of the simulator.
In multi-prover interactive proofs (MIPs), the verifier can provide non-local resources for the provers intrinsically. In most cases, this is undesirable. Existing proofs of soundness do not account for the verifier's non-local potential. We show that this may be a problem for many MIPs. We provide a solution by constructing a generalization of the MIP model, of which standard MIPs are a special case. This new model accounts for both the prover and the verifier's non-local correlations. A new property of multi-prover zero-knowledge naturally emerges as a result.
Homomorphic Cryptography raised as a new solution used in electronic voting systems. In this research, Fully Homomorphic encryption used to design and implement an e-voting system. The purpose of the study is to examine the applicability of Fully Homomorphic encryption in real systems and to evaluate the performance of fully homomorphic encryption in evoting systems. Most of homomorphic cryptography evoting systems based on additive or multiplicative homomorphic encryption. In this research, fully homomorphic encryption used to provide both operations additive and multiplication, which ease the demonstration of none interactive zero-knowledge proof NIZKP. The proposed e-voting system achieved most of the important security issues of the internet-voting systems such as eligibility, privacy, accuracy, verifiability, fairness, and others. One of the most important properties of the implemented internet voting system its applicability to work on cloud infrastructure, while preserving its security characteristics. The implementation is done using homomorphic encryption library HELib. Addition and multiplication properties of fully homomorphic encryption were used to verify the correctness of vote structure as a NIZKP, and for calculating the results of the voting process in an encrypted way. The results show that the implemented internet voting system is secure and applicable for a large number of voters up to 10 million voters.
Open access
Internet Traffic Analysis and Secure E-voting
Advanced Steganography and Watermarking Techniques
Digital identities and credentials are gradually replacing physical documents, as they can be verified with more accuracy and efficiency. Since online privacy is becoming more crucial than ever, it is essential to preserve the privacy of individuals whenever possible. Therefore, anonymous attestation of digital credentials should be feasible, where provers can selectively disclose attributes and create abstractions over attributes in their credential, in order to solely disclose the minimum amount of information required to complete the goal of verification.<br/><br/>Many schemes in the field of attribute-based credentials consider a single root authority issuing credentials to provers. This is coherent to the traditional way of the issuance of credentials since the process of producing physical documents is costly to distribute to multiple issuers. Digital identities provide the opportunity for authorities to distribute credential issuance rights (consecutively) to smaller entrusted entities.<br/><br/>To the best of our knowledge, we propose the first protocol which combines both anonymous attestation with attribute-based credentials and the delegation of selective signing rights for the issuance of these credentials. Root authorities could delegate signing rights for selective attributes consecutively to trustees, which are able to create anonymous attribute-based credentials with the acquired attributes for provers. Verifiers are able to verify presentation tokens with solely the public key of the root authority, without gaining knowledge about the identities of the prover and intermediate delegators. We introduce three adapted signature schemes based on existing work in order to realize a concrete instantiation of the protocol. Anonymity is achieved by incorporating Schnorr's zero-knowledge proof of knowledge with bilinear pairings to efficiently prove the correctness of presentation tokens.<br/><br/>We realized a prototype of our concrete instantiation and optimized the verification algorithm in order to achieve optimal pairing performance. Complexity analysis of the protocol shows improvement in efficiency by aggregating attribute signatures throughout signing right delegation. Experimental results demonstrate a degree of practical feasibility for the verification of presentation tokens on commodity hardware within the challenging public transportation access control time bound of 300 ms.<br/>
The notion of simulation is central to cryptography: often, to demonstrate that an adversary did not recover any information about private inputs of other participants, we exhibit the existence of a simulator that generates the adversary's view without access to inputs of honest participants. The primary method used to build simulators is rewinding, where a simulator resets the adversary to a previous point in the protocol and tries to complete the protocol tree multiple times until it achieves a favorable outcome.First introduced in the context of zero-knowledge proof systems and secure computation, today the rewinding technique is synonymous with protocol security and polynomial simulation. Prior to this work, all known rewinding techniques in the plain model required multiple rounds of back-and-forth interaction between participants.In this thesis, we demonstrate the first rewinding techniques that require only a single message from each participant. Using these techniques, we overcome several barriers from literature to construct for the first time, based on standard sub-exponential cryptographic assumptions, the following core protocols, and several subsequent applications:- Two message commitments satisfying non-malleability (with respect to commitment).- Two-message delayed-input weak zero-knowledge arguments for NP. These imply arguments for NP satisfying witness hiding and strong witness indistinguishability.
Asynchronous iterative algorithms are parallel iterative algorithms in which communications and iterations are not synchronized among processors. Thus, as soon as a processing unit finishes its own calculations, it starts the next cycle with the latest data received during a previous cycle, without waiting for any other processing unit to complete its own calculation. These algorithms increase the number of updates in some processors (as compared to the synchronous case) but suppress most idle times. This usually results in a reduction of the (execution) time to achieve convergence. Optimized Schwarz methods (OSM) are domain decomposition methods in which the transmission conditions between subdomains contain operators of the form \linebreak $\partial/\partial \nu +\Lambda$, where $\partial/\partial \nu$ is the outward normal derivative and $\Lambda$ is an optimized local approximation of the global Steklov-Poincar\'e operator. There is more than one family of transmission conditions that can be used for a given partial differential equation (e.g., the $OO0$ and $OO2$ families), each of these families containing a particular approximation of the Steklov-Poincar\'e operator. These transmission conditions have some parameters that are tuned to obtain a fast convergence rate. Optimized Schwarz methods are fast in terms of iteration count and can be implemented asynchronously. In this thesis we analyze the convergence behavior of the synchronous and asynchronous implementation of OSM applied to solve partial differential equations with a shifted Laplacian operator in bounded rectangular domains. We analyze two cases. In the first case we have a shift that can be either positive, negative or zero, a one-way domain decomposition and transmission conditions of the $OO2$ family. In the second case we have Poisson's equation, a domain decomposition with cross-points and $OO0$ transmission conditions. In both cases we reformulate the equations defining the problem into a fixed point iteration that is suitable for our analysis, then derive convergence proofs and analyze how the convergence rate varies with the number of subdomains, the amount of overlap, and the values of the parameters introduced in the transmission conditions. Additionally, we find the optimal values of the parameters and present some numerical experiments for the second case illustrating our theoretical results. To our knowledge this is the first time that a convergence analysis of optimized Schwarz is presented for bounded subdomains with multiple subdomains and arbitrary overlap. The analysis presented in this thesis also applies to problems with more general domains which can be decomposed as a union of rectangles.
Open access
Advanced Numerical Methods in Computational Mathematics
The goal of this thesis is to provide a mathematical rigorous derivation of the Schrödinger-Klein-Gordon equations, the Maxwell-Schrödinger equations and the defocusing cubic nonlinear Schrödinger equation in two dimensions. We study the time evolution of the Nelson model (with ultraviolet cutoff) in a limit where the number N of charged particles gets large while the coupling of each particle to the radiation field is of order N^{â1/2}. At time zero it is assumed that almost all charges are in the same one-body state (a Bose-Einstein condensate) and that the radiation field is close to a coherent state. We show the persistence of condensation over time and prove that the time evolution is approximately described by the Schrödinger-Klein-Gordon system of equations in the large N limit. Subsequently, we consider the spinless Pauli-Fierz Hamiltonian which models the interaction between charged bosons and the quantized electromagnetic field. We discuss the limit previously described and prove that the time evolution is approximated by the Maxwell-Schrödinger equations. To our knowledge, this is the first rigorous result concerning a mean-field limit of the Pauli-Fierz Hamiltonian. We then turn to the evolution of Bose-Einstein condensates in two dimensions and consider N bosons which interact by a repulsive two-body potential. The interaction is given either by N^{â1+2ÎČ}V(N^{ÎČ}x) with ÎČâR^{+}_{0} or by e^{2N}V(e^{N}x), for some spherical symmetric, positive and compactly supported VâL_{â}(R^{2},R). We prove that the dynamics is approximated by the defocusing two-dimensional cubic nonlinear Schrödinger equation in the large N limit. In case of the exponential scaling, we show that a short-scale correlation structure affects the dynamics of the condensate. This is the first rigorous derivation that considers an exponential scaling of the interaction. All derivations rely on a method developed by Pickl in [Lett. Math. Phys. 97(2), 151â164 (2011)]. The first two results are obtained by an extension of the method to systems which interact with quantized radiation fields. The latter is derived by an appropriate adaption of the proof in three space dimensions [Rev. Math. Phys., 27, 1550005 (2015)]. The crucial insight to derive the Maxwell-Schrödinger equations is to restrict the class of many-body wave functions to a subspace of states whose energy per particle only fluctuates little around the energy functional of the Maxwell-Schrödinger system. To derive the two-dimensional Gross-Pitaevskii equation it is essential to define a measure of condensation which properly incorporates the correlations that arise from the exponential scaling of the interaction. This thesis is based on the preprints [54, 47].
Sweden has as the first welfare state signed the petition of having net zero GHG emissions 2045. The construction industry is a large contributor to Swedenâs current GHG emissions and an action plan signed by several construction companies, including Veidekke, has stated several partial goals and one end goal of a construction industry with net zero emissions 2045. At the same time the demand of new residential houses is high. The choice of material affects the GHG emissions during the entire lifetime, making it a key parameter when planning a construction. 80 % of the emissions during a construction origin from the production of the materials used. The R&amp;D intensity in the construction industry is low and the sector is ruled by a high level of competition and low margins. This thesis aimed to investigate more sustainable building materials for bearing parts of multifamily houses, how they compare with conventional materials and challenges facing them. The materials investigated was compared to a reference wall with KPI:s from one construction made by Veidekke. The GHG emission from the reference wall was calculated to be 107 kg CO2-eq/m2wall. The materials were evaluated with the method of Industrial Dynamics to investigate salient and reverse salient properties, lock-ins and important stakeholders. The materials investigated were Cross-laminated timber (CLT) and different types of sustainable concretes. Creating timber concrete hybrids were also explored. CLT currently has a small market share but is a promising material with several beneficial properties. The current development of more sustainable concrete resulted in the investigation of Recycled Aggregates Concrete, Alkali Activated Concrete and the Eco-concrete with reduced amount of cement in favor for limestone powder. A second step was to explore the social and economic challenges for integrating new building materials into the construction industry. As the industry is heavily project based, the timeframe and lack of budget to explore new options acts as barrier. The processes also tend to be repetitive. As of now the industry has made itself path dependent to concrete in a large extent. However, the social acceptance towards CLT is rising and making sustainability a strategic business goal is becoming more important to appeal to the customers. Interviews at Veidekke showed the rising interest of mixing timber and concrete, but also the difficulties of pushing development forward in the industry. The materials and their KPI:s resulted in the further investigation of CLT and Eco-concrete. By stating the salient and reverse salient properties of the materials further analysis could be done. CLT showed the greatest reduction of GHG emissions due to the embodied carbon resulting in a negative GHG emission of -66.2 kg CO2-eq/m2wall. In addition to this the construction time and several other beneficial properties were found. The reduction of GHG emissions of the Eco-concrete is great too, about 50 % comparing with the concrete used in the reference wall. As a concrete the Eco-concrete should also face less barriers as the industry is familiar with the product. Further analysis with tools from industrial dynamics showed the importance of creating incitements for developing the knowledge of a sustainable construction industry. Results also showed that new networks between the manufactures and the building sector is of essence to find and use new materials. Timber and concrete industries have the main responsibility of developing new and more sustainable products. The building sector also have a responsibility of choosing sustainable options. Advocating a diversity of solutions will create a more robust and resilient industry with fewer lock-ins and path dependencies occurring today. The key stakeholders identified from stakeholder mapping was the business developers, the department of purchase, the timber and concrete industry and lastly the customers. Business developers need to pursue projects with clear and tough goals of sustainability. This will increase the chance of succeeding. The department of purchase need to have incitements for mapping sustainable materials and the ability to explore new subcontractors. The results of the analysis show that not a single innovation will solve the goal of having a construction industry with net zero emissions 2045. The key innovation opportunities for CLT is to develop a standardization and modularization comparable with the concrete industry. Improving the fire safety of CLT is also of essence and the development of fire proofing plasterboards and insulation could be a solution. Further research on modified design mixing and the usage of pozzolanic materials like limestone in concrete is also an important way forward. Constructing timber concrete hybrids have also raised great potential both in the literature, analysis and from the interviews to simplify the integration of timber into the market.
The existing multi-prover interactive proof framework suffers from incompleteness in terms of soundness and zero-knowledge that is not completely addressed in the literature. The problem is that the existing definitions of what is local, entangled and no-signalling are not rich enough to capture the full generality of multi-prover interaction. In general, existing proofs do not take into account possible changes in locality either during a protocol's execution or when protocols are composed together. This is especially problematic for zero-knowledge, as composing commitments is the only known way of achieving zero-knowledge outside of some NP-intermediate languages.
In this work, we introduce the locality hierarchy for multiparty (multi-round) interaction, and for the first time a complete definition of multi-round multiparty no-signalling distributions and strategies. Within this framework, we define the locality of a protocol which involves the provers, verifiers, simulators and distinguishers. We show that an existing protocol for NEXP [BFL90] and a zero-knowledge variant we introduce are sound in a local sense, but are zero-knowledge in a sense that is even stronger than usually understood. All prior claims of zero-knowledge proofs in the multi-prover model were actually incorrect. Finally, we present similar constructions for entangled and no-signalling prover sets for NEXP and EXP based on [IV12] and [KRR14] using new multi-prover commitment schemes.
Radio Frequency Identification (RFID) technology has been expanded to be used in different fields that need automatic identifying and verifying of tagged objects without human intervention. RFID technology offers a great advantage in comparison with barcodes by providing accurate information, ease of use and reducing of labour cost. These advantages have been utilised by using passive RFID tags. Although RFID technology can enhance the efficiency of different RFID applications systems, researchers have reported issues regarding the use of RFID technology. These issues are making the technology vulnerable to many threats in terms of security and privacy. Different RFID solutions, based on different cryptography primitives, have been developed. Most of these protocols focus on the use of passive RFID tags. However, due to the computation feasibility in passive RFID tags, these tags might be vulnerable to some of the security and privacy threats. , e.g. unauthorised reader can read the information inside tags, illegitimate tags or cloned tags can be accessed by a reader. Moreover, most consideration of reserchers is focus on single tag authentication and mostly do not consider scenarios that need multi-tag such as supply chain management and healthcare management. Secret sharing schemes have been also proposed to overcome the key management problem in supply chain management. However, secret sharing schemes have some scalability limitations when applied with high numbers of RFID tags. This work is mainly focused on solving the problem of the security and privacy in multi-tag RFID based system. In this work firstly, we studied different RFID protocols such as symmetric key authentication protocols, authentication protocols based on elliptic curve cryptography, secret sharing schemes and multi-tag authentication protocols. Secondly, we consider the significant research into the mutual authentication of passive RFID tags. Therefore, a mutual authentication scheme that is based on zero-knowledge proof have been proposed . The main object of this work is to develop an ECC- RFID based system that enables multi-RFID tags to be authenticated with one reader by using different versions of ECC public key encryption schemes. The protocol are relied on using threshold cryptosystems that operate ECC to generate secret keys then distribute and stored secret keys among multi RFID tags. Finally, we provide performance measurement for the implementation of the proposed protocols.
Verifiable computation (VC) protocols enable clients to outsource computations to untrusted servers in the cloud without compromising the integrity of the computation. Although cryptographic approaches for verifiable computation were mostly of theoretical interest in the past, there has been great progress in the area during the past few years. In particular, efficient constructions for Zero-Knowledge Succinct Non-interactive ARguments of Knowledge (zk-SNARKs) were proposed and adopted in practice. These techniques enable an untrusted server to prove the correctness of computations in zero-knowledge using a succinct proof that can be verified efficiently by the client. This thesis aims at addressing some challenges in such VC protocols, and developing practical protocols for cryptocurrency applications. The challenges we address include the proof computation overhead at the prover's side, and the level of expertise expected from the programmers to write secure and efficient programs for VC. More specifically, current protocols require the programmer to carefully express the computation as an arithmetic circuit, in a way that minimizes the proof computation overhead and prevents malicious behavior by the prover, which is a non-trivial task. To address the above challenges, we present a framework that aims to reduce the proof computation overhead, and offer more programmability to non-specialist developers, while automating the task of circuit minimization through a combination of techniques. The framework includes new circuit-friendly algorithms for frequent operations, which achieve constant to asymptotic savings over algorithms used in previous compilers. In addition, we explore and optimize cryptographic primitives that have efficient arithmetic circuit representations. Furthermore, we explore different settings where VC can be used in practice. We present the design of Hawk, a system for privacy-preserving smart contracts. Hawk enables custom decentralized applications in the smart contract setting to run verifiably on top of a public blockchain system, while not revealing the participants' inputs to the network. To achieve practical performance, Hawk relies on a special party per contract (a manager) that is only trusted for posterior privacy, but not for correctness. Finally, we explore how VC techniques and smart contracts could enable practical crimes in the future, which highlights the importance of working on countermeasures.
We consider natural ways to extend the notion of Zero-Knowledge (ZK) Proofs beyond decision problems. Specifically, we consider search problems, and define zero-knowledge proofs in this context as interactive protocols in which the prover can establish the correctness of a solution to a given instance without the verifier learning anything beyond the intended solution, even if it deviates from the protocol. The goal of this work is to initiate a study of Search Zero-Knowledge (search-ZK), the class of search problems for which such systems exist. This class trivially contains search problems where the validity of a solution can be efficiently verified (using a single message proof containing only the solution). A slightly less obvious, but still straightforward, way to obtain zero-knowledge proofs for search problems is to let the prover send a solution and prove in zero-knowledge that the instance-solution pair is valid. However, there may be other ways to obtain such zero-knowledge proofs, and they may be more advantageous. In fact, we prove that there are search problems for which the aforementioned approach fails, but still search zero-knowledge protocols exist. On the other hand, we show sufficient conditions for search problems under which some form of zero-knowledge can be obtained using the straightforward way.
Cardâbased physical access control systems are used by most people on a daily basis, for example, at work, in public transportation, or at hotels. Yet these systems have often very poor cryptographic protection. User identifiers and keys can be easily eavesdropped on and counterfeited. The privacyâpreserving features are almost missing in these systems. To improve this state, we propose a novel cryptographic scheme based on efficient zeroâknowledge proofs and BonehâBoyen signatures. The proposed scheme is provably secure and provides the full set of privacyâenhancing features, that is, the anonymity, untraceability, and unlinkability of users. Furthermore, our scheme supports distributed multidevice authentication with multiple RFID (RadioâFrequency IDentification) user devices. This feature is particularly important in applications for controlling access to dangerous sites where the presence of protective equipment is checked during each access control session. Besides the full cryptographic specification, we also show the results of our implementation on devices commonly used in access control applications, particularly the smart cards and embedded verification terminals. By avoiding costly operations on user devices, such as bilinear pairings, we were able to achieve times comparable to existing systems (around 500 ms), while providing significantly higher security, privacy protection, and features for RFID multidevice authentication.
This dissertation consists of three essays that design and evaluate the continuous audit analytics and fraud prevention systems using three emerging technologies (i.e., the blockchain, in-memory cloud computing, and deep learning). The first essay designs a framework of Blockchain-based Transaction Processing System using the homomorphic encryption and zero-knowledge proof mechanisms. Furthermore, this study develops a prototype of the designed system to demonstrate its applications in real-time accounting, continuous monitoring, and fraud prevention. Although the simulation tests show the Blockchain-based Transaction Processing System consumes more computational overhead than the conventional database-based ERP system, the blockchain should be considered as a promising technology for future accounting and auditing practice. The second essay introduces the database architecture that manages data in main physical memory and columnar format. This essay proposes a conceptual framework for applying the in-memory columnar database system to support high-speed continuous audit analytics. Moreover, this study develops a prototype and conducts the simulation tests to evaluate the proposed framework. The test results show the high efficiency and effectiveness of the in-memory columnar database relative to the conventional ERP system regarding the computational time and the storage volume. Furthermore, the deployment of the in-memory columnar database to the cloud shows great promise of applying the in-memory columnar database for continuous audit analytics. The third essay designs a continuous fraud detection system based on modified deep learning technology. Specifically, this essay builds an accounting layer on top of the deep learning architecture to process financial data for predicting the fraudulent financial statements. A prototype is developed to evaluate the prediction accuracy of the proposed design. The test results show the deep learning-based continuous fraud detection system provides high prediction accuracy relative to the existing studies of financial statement fraud detection.
We study the problem of argument systems, where a computationally weak verifier outsources the execution of a computation to a powerful but untrusted prover, while being able to validate that the result was computed correctly through a proof generated by the prover. In addition, the zero-knowledge property guarantees that proof leaks no information about the potential secret input from the prover. Existing efficient zero-knowledge arguments with sublinear verification time require an expensive preprocessing phase that depends on a particular computation, and incur big overhead on the prover time and prover memory consumption. This thesis proposes new constructions for zero-knowledge arguments that overcome the above problems. The new constructions require only a one time preprocessing and can be used to validate any computations later. They also reduce the overhead on the prover time and memory by orders of magnitude. We apply our new constructions to build a verifiable database system and verifiable RAM programs, leading to significant improvements over prior work.
Privacy in online applications has drawn tremendous attention in recent years. With the development of cloud-based applications, protecting users' privacy while guaranteeing the expected service from the server has become a significant issue. This paper surveyed the most popular cryptographic algorithms in privacy-preserving online applications to provide a tutorial-like introduction to researchers in this area. Specifically, this paper focuses on introduction to homomorphic encryption, secret sharing, secure multi-party computation and zero-knowledge proof.
Eli BenâSasson, Iddo Bentov, Yinon Horesh, Michael Riabzev
The family of Reed-Solomon (RS) codes plays a prominent role in the construction of quasilinear probabilistically checkable proofs (PCPs) and interactive oracle proofs (IOPs) with perfect zero knowledge and polylogarithmic verifiers. The large concrete computational complexity required to prove membership in RS codes is one of the biggest obstacles to deploying such PCP/IOP systems in practice. To advance on this problem we present a new interactive oracle proof of proximity (IOPP) for RS codes; we call it the Fast RS IOPP (FRI) because (i) it resembles the ubiquitous Fast Fourier Transform (FFT) and (ii) the arithmetic complexity of its prover is strictly linear and that of the verifier is strictly logarithmic (in comparison, FFT arithmetic complexity is quasi-linear but not strictly linear). Prior RS IOPPs and PCPs of proximity (PCPPs) required super-linear proving time even for polynomially large query complexity. For codes of block-length N, the arithmetic complexity of the (interactive) FRI prover is less than 6 * N, while the (interactive) FRI verifier has arithmetic complexity <= 21 * log N, query complexity 2 * log N and constant soundness - words that are delta-far from the code are rejected with probability min{delta * (1-o(1)),delta_0} where delta_0 is a positive constant that depends mainly on the code rate. The particular combination of query complexity and soundness obtained by FRI is better than that of the quasilinear PCPP of [Ben-Sasson and Sudan, SICOMP 2008], even with the tighter soundness analysis of [Ben-Sasson et al., STOC 2013; ECCC 2016]; consequently, FRI is likely to facilitate better concretely efficient zero knowledge proof and argument systems. Previous concretely efficient PCPPs and IOPPs suffered a constant multiplicative factor loss in soundness with each round of "proof composition" and thus used at most O(log log N) rounds. We show that when delta is smaller than the unique decoding radius of the code, FRI suffers only a negligible additive loss in soundness. This observation allows us to increase the number of "proof composition" rounds to Theta(log N) and thereby reduce prover and verifier running time for fixed soundness.
Jan 1, 2018·Proceedings of the ... Annual Hawaii International Conference on System Sciences/Proceedings of the Annual Hawaii International Conference on System Sciences
Blockchains permit to store information in a tamper-resistant and irrevocable manner by reverting to distributed computing and cryptographic technologies. The primary purpose is to keep track of the ownership of tangible and intangible assets. In the paper at hand we apply these concepts and technologies to the domain of knowledge management. Based on the explication of knowledge in the form of enterprise models this permits the application of so-called knowledge proofs for a. enabling the transparent monitoring of knowledge evolution, b. tracking the provenance, ownership, and relationships of knowledge in an organization, c. establishing delegation schemes for knowledge management, and d. ensuring the existence of patterns in models via zero-knowledge proofs. To validate the technical feasibility of the approach a first technical implementation is described and applied to a fictitious use case.
A treasury system is a community-controlled and decentralized collaborative decision-making mechanism for sustainable funding of blockchain development and maintenance. During each treasury period, project proposals are submitted, discussed, and voted for; top-ranked projects are funded from the treasury. The Dash governance system is a real-world example of such kind of systems. In this work, we, for the first time, provide a rigorous study of the treasury system. We modelled, designed, and implemented a provably secure treasury system that is compatible with most existing blockchain infrastructures, such as Bitcoin, Ethereum, etc. More specifically, the proposed treasury system supports liquid democracy/delegative voting for better collaborative intelligence. Namely, the stake holders can either vote directly on the proposed projects or delegate their votes to experts. Its core component is a distributed universally composable secure end-to-end verifiable voting protocol. The integrity of the treasury voting decisions is guaranteed even when all the voting committee members are corrupted. To further improve efficiency, we proposed the world's first honest verifier zero-knowledge proof for unit vector encryption with logarithmic size communication. This partial result may be of independent interest to other cryptographic protocols. A pilot system is implemented in Scala over the Scorex 2.0 framework, and its benchmark results indicate that the proposed system can support tens of thousands of treasury participants with high efficiency.
Recent work, including ZKBoo, ZKB++, and Ligero, has developed efficient non-interactive zero-knowledge proofs of knowledge (NIZKPoKs) for Boolean circuits based on symmetric-key primitives alone, using the "MPC-in-the-head" paradigm of Ishai et al. We show how to instantiate this paradigm with MPC protocols in the preprocessing model; once optimized, this results in an NIZKPoK with shorter proofs (and comparable computation) as in prior work for circuits containing roughly 300--100,000 AND~gates. In contrast to prior work, our NIZKPoK also supports witness-independent preprocessing, which allows the prover to shift most of its work to an offline phase before the witness is known. We use our NIZKPoK to construct a signature scheme based only on symmetric-key primitives (and hence with "post-quantum" security). The resulting scheme has shorter signatures than the scheme built using ZKB++ (and comparable signing/verification time), and is even competitive with hash-based signature schemes. To further highlight the flexibility and power of our NIZKPoK, we also use it to build efficient ring and group signatures based on symmetric-key primitives alone. To our knowledge, the resulting schemes are the most efficient constructions of these primitives that offer post-quantum security.