We are interested in secure computation protocols in settings where the number of parties is huge and their data even larger. Assuming the existence of a single-use broadcast channel (per player), we demonstrate statistically secure computation protocols for computing (multiple) arbitrary dynamic RAM programs over parties ’ inputs, handling (1/3−) fraction static corrup-tions, while preserving up to polylogarithmic factors the computation and memory complexities of the RAM program. Additionally, our protocol is load balanced and has polylogarithmic communication locality.
We are interested in secure computation protocols in settings where the number of parties is huge and their data even larger. Assuming the existence of a single-use broadcast channel (per player), we demonstrate statistically secure computation protocols for computing (multiple) arbitrary dynamic RAM programs over parties ’ inputs, handling (1/3−) fraction static corrup-tions, while preserving up to polylogarithmic factors the computation and memory complexities of the RAM program. Additionally, our protocol is load balanced and has polylogarithmic communication locality.
Abstract. In secure multi-party shuffling, multiple parties, each holding an input, want to agree on a random permutation of their inputs while keeping the permutation secret. This problem is important as a primitive in many privacy-preserving applications such as anonymous communication, location-based services, and electronic voting. Known techniques for solving this problem suffer from poor scalability, load-balancing issues, trusted party assumptions, and/or weak security guarantees. In this paper, we propose an unconditionally-secure protocol for multi-party shuffling that scales well with the number of parties and is load-balanced. In particular, we require each party to send only a polylogarithmic number of bits and perform a polylogarithmic number of operations while incurring only a logarithmic round complexity. We show security under universal composability against up to about n/3 fully-malicious parties. We also provide simulation results showing that our protocol im-proves significantly over previous work. For example, for one million parties, when compared to the state of the art, our protocol reduces the communication and computation costs by at least three orders of magnitude and slightly decreases the number of communication rounds. 1
Secure multiparty computation (MPC) is perhaps the most popular paradigm in the area of cryptographic protocols. It allows several mutually untrustworthy parties to jointly compute a function of their private inputs, without revealing to each other information about those inputs. In the case of unconditional (information-theoretic) security, protocols are known which tolerate a dishonest minority of players, who may coordinate their attack and deviate arbitrarily from the protocol specification. It is typically assumed in these results that parties are connected pairwise by authenticated, private channels, and that in addition they have access to a “broadcast ” channel. Broadcast allows one party to send a consistent message to all other parties, guaranteeing consistency even if the broadcaster is corrupted. Because broadcast cannot be simulated on the point-to-point network when more than a third of the parties are corrupt, it is impossible to construct general MPC protocols in this setting without using a broadcast channel (or some equivalent addition to the model). A great deal of research has focused on increasing the efficiency of MPC, primarily in terms of round complexity and communication complexity. In this work we propose a refinement of the round complexity which we term broadcast complexity. We view the broadcast channel as an expensive resource
Traditional approaches to secure computation begin by representing the function f being computed as a circuit. For any function f that depends on each of its inputs, this implies a protocol with complexity at least linear in the input size. In fact, linear running time is inherent for secure computation of non-trivial functions, since each party must “touch” every bit of their input lest information about other party’s input be leaked. This seems to rule out many interesting applications of secure computation in scenarios where at least one of the inputs is huge and sublinear-time algorithms can be utilized in the insecure setting; private database search is a prime example. We present an approach to secure two-party computation that yields sublinear-time protocols, in an amortized sense, for functions that can be computed in sublinear time on a random access machine (RAM). Furthermore, a party whose input is “small” is required to maintain only small state. We provide a generic protocol that achieves the claimed complexity, based on any oblivious RAM and any protocol for secure two-party computation. We then present an optimized version of this protocol, where generic secure two-party computation is used only for evaluating a small number of simple operations.
In secure multi-party shuffling, multiple parties, each holding an input, want to agree on a random permutation of their inputs while keeping the permutation secret. This problem is important as a primitive in many privacy-preserving applications such as anonymous communication, location-based services, and electronic voting. Known techniques for solving this problem suffer from poor scalability, load-balancing issues, trusted party assumptions, and/or weak security guarantees. In this paper, we propose an unconditionally-secure protocol for multi-party shuffling that scales well with the number of parties and is load-balanced. In particular, we require each party to send only a polylogarithmic number of bits and perform a polylogarithmic number of operations while incurring only a logarithmic round complexity. We show security under universal compos ability against up to about n/3 fully-malicious parties. We also provide simulation results in the full version of this paper showing that our protocol improves significantly over previous work. For example, for one million parties, when compared to the state of the art, our protocol reduces the communication and computation costs by at least three orders of magnitude and slightly decreases the number of communication rounds.
We describe scalable protocols for solving the secure multi-party computation (MPC) problem among a large number of parties. We consider both the synchronous and the asynchronous communication models. In the synchronous setting, our protocol is secure against a static malicious adversary corrupting less than a 1/3 fraction of the parties. In the asynchronous setting, we allow the adversary to corrupt less than a 1/8 fraction of parties. For any deterministic function that can be computed by an arithmetic circuit with m gates, both of our protocols require each party to send a number of field elements and perform an amount of computation that is O~(m/n+n). We also show that our protocols provide perfect and universally-composable security. To achieve our asynchronous MPC result, we define the \emph{threshold counting problem} and present a distributed protocol to solve it in the asynchronous setting. This protocol is load balanced, with computation, communication and latency complexity of O(logn), and can also be used for designing other load-balanced applications in the asynchronous communication model.
The classical results in unconditional multi-party computation among a set of n players state that less than n/2 passive or Iess than n/3 active adversaries can be tolerated; assuming a broadcast channel the threshold for active adversaries is ta/2.Strictly generalizing these results we specify the set of potential y misbehaving players as an arbitrary set of subsets of the player set.We prove the necessary and sufficient conditions for the existence of secure multi-party protocols in terms of the potentially misbehaving player sets.For every function there exists a protocol secure against a set of potential passive collusions if and only if no two of these collusions add up to the full player set.The same condition applies for active adversaries when assuming a broadcast chzmnel.Without broadcast channels, for every function there exists a protocol secure against a set of potential active adverse player sets if and only if no three of these sets add up to the full player set.The complexities of the protocols not using a broadcast channel are polynomial, that of the protocol with broadcast is only slightly higher.