Unconditionally Secure Multiparty Set Intersection Re-Visited

In this paper, we re-visit the problem of unconditionally secure multiparty set intersection in information theoretic model. Li et.al \cite{LiSetMPCACNS07} have proposed a protocol for $n$-party set intersection problem, which provides unconditional security when $t < \frac{n}{3}$ players are corrupted by an active adversary having {\it unbounded computing power}. Moreover, they have claimed that their protocol takes six rounds of communication and incurs a communication complexity of ${\cal O}(n^4m^2)$, where each player has a set of size $m$. However, we show that the round complexity and communication complexity of the protocol in \cite{LiSetMPCACNS07} is much more than what is claimed in \cite{LiSetMPCACNS07}. We then propose a {\it novel} unconditionally secure protocol for multiparty set intersection problem with $n > 3t$ players, which significantly improves the actual round and communication complexity (as shown in this paper) of the protocol given in \cite{LiSetMPCACNS07}. To design our protocol, we use several tools which are of independent interest

Information Theoretically Secure Multi Party Set Intersection Re-Visited

We re-visit the problem of secure multiparty set intersection in information theoretic settings. In \cite{LiSetMPCACNS07}, Li et.al have proposed a protocol for multiparty set intersection problem with $n$ parties, that provides information theoretic security, when $t < \frac{n}{3}$ parties are corrupted by an active adversary having {\it unbounded computing power}. In \cite{LiSetMPCACNS07}, the authors claimed that their protocol takes six rounds of communication and communicates ${\cal O}(n^4m^2)$ field elements, where each party has a set containing $m$ field elements. However, we show that the round and communication complexity of the protocol in \cite{LiSetMPCACNS07} is much more than what is claimed in \cite{LiSetMPCACNS07}. We then propose a {\it novel} information theoretically secure protocol for multiparty set intersection with $n > 3t$, which significantly improves the actual round and communication complexity (as shown in this paper) of the protocol given in \cite{LiSetMPCACNS07}. To design our protocol, we use several tools which are of independent interest

Unconditionally Secure Multiparty Computation for Symmetric Functions with Low Bottleneck Complexity

Bottleneck complexity is an efficiency measure of secure multiparty computation (MPC) introduced by Boyle et al. (ICALP 2018) to achieve load-balancing. Roughly speaking, it is defined as the maximum communication complexity required by any player within the protocol execution. Since it is impossible to achieve sublinear bottleneck complexity in the number of players $n$ for all functions, a prior work constructed MPC protocols with low bottleneck complexity for specific functions including the AND function and general symmetric functions. However, the previous protocol for a symmetric function needs to assume a computational primitive of garbled circuits. Its unconditionally secure variant has exponentially large bottleneck complexity in the depth of an arithmetic formula computing the function, which limits the class of symmetric functions the protocol can compute with sublinear bottleneck complexity in $n$. In this paper, we propose for the first time unconditionally secure MPC protocols computing any symmetric function with sublinear bottleneck complexity in $n$. Our first protocol is an application of the one-time truth-table protocol by Ishai et al. (TCC 2013). We devise a novel technique to express the truth-table as an array of two or higher dimensions and obtain two other protocols with better trade-offs. We also propose an unconditionally secure protocol with lower bottleneck complexity tailored to the AND function. It avoids pseudorandom functions used by the previous protocol, preserving bottleneck complexity up to a logarithmic factor in $n$. As an application, we construct an unconditionally secure protocol for private set intersection (PSI), which computes the intersection of players\u27 private sets. This is the first PSI protocol with sublinear bottleneck complexity in $n$ and to the best of our knowledge, there has been no such protocol even under cryptographic assumptions

Private and Oblivious Set and Multiset Operations

Privacy-preserving set operations, and set intersection in particular, are a popular research topic. Despite a large body of literature, the great majority of the available solutions are two-party protocols and are not composable. In this work we design a comprehensive suite of secure multi-party protocols for set and multiset operations that are composable, do not assume any knowledge of the sets by the parties carrying out the secure computation, and can be used for secure outsourcing. All of our protocols have communication and computation complexity of $O(m \log m)$ for sets or multisets of size $m$, which compares favorably with prior work. Furthermore, we are not aware of any results that realize composable operations. Our protocols are secure in the information theoretic sense and are designed to minimize the round complexity. Practicality of our solutions is shown through experimental results

Studies on Verifiable Secret Sharing, Byzantine Agreement and Multiparty Computation

This dissertation deals with three most important as well as fundamental problems in secure distributed computing, namely Verifiable Secret Sharing (VSS), Byzantine Agreement (BA) and Multiparty Computation (MPC). VSS is a two phase protocol (Sharing and Reconstruction) carried out among $n$ parties in the presence of a centralized adversary who can corrupt up to $t$ parties. Informally, the goal of the VSS protocol is to share a secret $s$, among the $n$ parties during the sharing phase in a way that would later allow for a unique reconstruction of this secret in the reconstruction phase, while preserving the secrecy of $s$ until the reconstruction phase. VSS is used as a key tool in MPC, BA and many other secure distributed computing problems. It can take many different forms, depending on the underlying network (synchronous or asynchronous), the nature (passive or active) and computing power (bounded or unbounded) of the adversary, type of security (cryptographic or information theoretic) etc. We study VSS in information theoretic setting over both synchronous as well as asynchronous network, considering an active unbounded powerful adversary. Our main contributions for VSS are: \begin{itemize} \item In synchronous network, we carry out in-depth investigation on the round complexity of VSS by allowing a probability of error in computation and show that existing lower bounds for the round complexity of error-free VSS can be circumvented by introducing a negligible probability of error. \item We study the communication and round efficiency of VSS in synchronous network and present a robust VSS protocol that is simultaneously communication efficient and round efficient. In addition, our protocol is the best known communication and round efficient protocol in the literature. \item In asynchronous network, we study the communication complexity of VSS and propose a number of VSS protocols. Our protocols are highly communication efficient and show significant improvement over the existing protocols in terms of communication complexity. \end{itemize} The next problem that we deal with is Byzantine Agreement (BA). BA is considered as one of the most fundamental primitives for fault tolerant distributed computing and cryptographic protocols. BA among a set of $n$ parties, each having a private input value, allows them to reach agreement on a common value even if some of the malicious parties (at most $t$) try to prevent agreement among the parties. Similar to the case of VSS, several models for BA have been proposed during the last three decades, considering various aspects like the underlying network, the nature and computing power of adversary, type of security. One of these models is BA over asynchronous network which is considered to be more realistic network than synchronous in many occasions. Though important, research in BA in asynchronous network has received much less attention in comparison to the BA protocols in synchronous network. Even the existing protocols for asynchronous BA involve high communication complexity and in general are very inefficient in comparison to their synchronous counterparts. We focus on BA in information theoretic setting over asynchronous network tolerating an active adversary having unbounded computing power and mainly work towards the communication efficiency of the problem. Our contributions for BA are as follows: \begin{itemize} \item We propose communication efficient asynchronous BA protocols that show huge improvement over the existing protocols in the same setting. Our protocols for asynchronous BA use our VSS protocols in asynchronous network as their vital building blocks. \item We also construct a communication optimal asynchronous BA protocol for sufficiently long message size. Precisely, our asynchronous BA communicates O(\ell n) bits for \ell bit message, for sufficiently large \ell. \end{itemize} The studies on VSS and BA naturally lead one towards MPC problems. The MPC can model almost any known cryptographic application and uses VSS as well as BA as building blocks. MPC enables a set of $n$ mutually distrusting parties to compute some function of their private inputs, such that the privacy of the inputs of the honest parties is guaranteed (except for what can be derived from the function output) even in the presence of an adversary corrupting up to $t$ of the parties and making them misbehave arbitrarily. Much like VSS and BA, MPC can also be studied in various models. Here, we attempt to solve MPC in information theoretic setting over synchronous as well as asynchronous network, tolerating an active unbounded powerful adversary. As for MPC, our main contributions are: \begin{itemize} \item Using one of our synchronous VSS protocol, we design a synchronous MPC that minimizes the communication and round complexity simultaneously, where existing MPC protocols try to minimize one complexity measure at a time (i.e the existing protocols minimize either communication complexity or round complexity). \item We study the communication complexity of asynchronous MPC protocols and design a number of protocols for the same that show significant gain in communication complexity in comparison to the existing asynchronous MPC protocols. \item We also study a specific instance of MPC problem called Multiparty Set Intersection (MPSI) and provide protocols for the same. \end{itemize} In brief, our work in this thesis has made significant advancement in the state-of-the-art research on VSS, BA and MPC by presenting several inherent lower bounds and efficient/optimal solutions for the problems in terms of their key parameters such as communication complexity and time/round complexity. Thus our work has made a significant contribution to the field of secure distributed computing by carrying out a foundation research on the three most important problems of this field

Optimal Load-Balanced Scalable Distributed Agreement

We consider the fundamental problem of designing classical consensus-related distributed abstractions for large-scale networks, where the number of parties can be huge. Specifically, we consider tasks such as Byzantine Agreement, Broadcast, and Committee Election, and our goal is to design scalable protocols in the sense that each honest party processes and sends a number of bits which is sub-linear in $n$, the total number of parties. In this work, we construct the first such scalable protocols for all of the above tasks. In our protocols, each party processes and sends $\tilde O (\sqrt n)$ bits throughout $\tilde O (1)$ rounds of communication, and correctness is guaranteed for at most $1/3-\epsilon$ fraction of static byzantine corruptions for every constant $\epsilon>0$ (in the full information model). All previous protocols for the considered agreement tasks were non-scalable, either because the communication complexity was linear or because the computational complexity was super polynomial. We complement our result with a matching lower bound showing that any Byzantine Agreement protocol must have $\Omega(\sqrt n)$ complexity in our model. Previously, the state of the art was the well-known $\tilde\Omega(\sqrt[3]{n})$ lower bound of Holtby, Kapron, and King (Distributed Computing, 2008)

MPC with Synchronous Security and Asynchronous Responsiveness

Two paradigms for secure MPC are synchronous and asynchronous protocols. While synchronous protocols tolerate more corruptions and allow every party to give its input, they are very slow because the speed depends on the conservatively assumed worst-case delay $\Delta$ of the network. In contrast, asynchronous protocols allow parties to obtain output as fast as the actual network allows, a property called responsiveness, but unavoidably have lower resilience and parties with slow network connections cannot give input. It is natural to wonder whether it is possible to leverage synchronous MPC protocols to achieve responsiveness, hence obtaining the advantages of both paradigms: full security with responsiveness up to $t$ corruptions, and extended security (full security or security with unanimous abort) with no responsiveness up to $T \ge t$ corruptions. We settle the question by providing matching feasibility and impossibility results: -For the case of unanimous abort as extended security, there is an MPC protocol if and only if $T + 2t < n$. -For the case of full security as extended security, there is an MPC protocol if and only if $T < n/2$ and $T + 2t < n$. In particular, setting $t = n/4$ allows to achieve a fully secure MPC for honest majority, which in addition benefits from having substantial responsiveness

SoK: Privacy-Enhancing Technologies in Finance

Recent years have seen the emergence of practical advanced cryptographic tools that not only protect data privacy and authenticity, but also allow for jointly processing data from different institutions without sacrificing privacy. The ability to do so has enabled implementations a number of traditional and decentralized financial applications that would have required sacrificing privacy or trusting a third party. The main catalyst of this revolution was the advent of decentralized cryptocurrencies that use public ledgers to register financial transactions, which must be verifiable by any third party, while keeping sensitive data private. Zero Knowledge (ZK) proofs rose to prominence as a solution to this challenge, allowing for the owner of sensitive data (e.g. the identities of users involved in an operation) to convince a third party verifier that a certain operation has been correctly executed without revealing said data. It quickly became clear that performing arbitrary computation on private data from multiple sources by means of secure Multiparty Computation (MPC) and related techniques allows for more powerful financial applications, also in traditional finance. In this SoK, we categorize the main traditional and decentralized financial applications that can benefit from state-of-the-art Privacy-Enhancing Technologies (PETs) and identify design patterns commonly used when applying PETs in the context of these applications. In particular, we consider the following classes of applications: 1. Identity Management, KYC & AML; and 2. Markets & Settlement; 3. Legal; and 4. Digital Asset Custody. We examine how ZK proofs, MPC and related PETs have been used to tackle the main security challenges in each of these applications. Moreover, we provide an assessment of the technological readiness of each PET in the context of different financial applications according to the availability of: theoretical feasibility results, preliminary benchmarks (in scientific papers) or benchmarks achieving real-world performance (in commercially deployed solutions). Finally, we propose future applications of PETs as Fintech solutions to currently unsolved issues. While we systematize financial applications of PETs at large, we focus mainly on those applications that require privacy preserving computation on data from multiple parties

Implementation of a Secure Multiparty Computation Protocol

Secure multiparty computation (SMC) allows a set of parties to jointly compute a function on private inputs such that, they learn only the output of the function, and the correctness of the output is guaranteed even when a subset of the parties is controlled by an adversary. SMC allows data to be kept in an uncompromisable form and still be useful, and it also gives new meaning to data ownership, allowing data to be shared in a useful way while retaining its privacy. Thus, applications of SMC hold promise for addressing some of the security issues information-driven societies struggle with. In this thesis, we implement two SMC protocols. Our primary objective is to gain a solid understanding of the basic concepts related to SMC. We present a brief survey of the field, with focus on SMC based on secret sharing. In addition to the protocol im- plementations, we implement circuit randomization, a common technique for efficiency improvement. The implemented protocols are run on a simulator to securely evaluate some simple arithmetic functions, and the round complexities of the implemented protocols are compared. Finally, we attempt to extend the implementation to support more general computations