A Bound For Multiparty Secret Key Agreement And Implications For A Problem Of Secure Computing

We consider secret key agreement by multiple parties observing correlated data and communicating interactively over an insecure communication channel. Our main contribution is a single-shot upper bound on the length of the secret keys that can be generated, without making any assumptions on the distribution of the underlying data. Heuristically, we bound the secret key length in terms of ``how far is the joint distribution of the initial observations of the parties and the eavesdropper from a distribution that renders the observations of the parties conditionally independent across some partition, when conditioned on the eavesdropper\u27s side information. The closeness of the two distributions is measured in terms of the exponent of the probability of error of type II for a binary hypothesis testing problem, thus bringing out a structural connection between secret key agreement and binary hypothesis testing. When the underlying data consists of an independent and identically distributed sequence, an application of our bound recovers several known upper bounds for the asymptotic rate of a secret key that can be generated, without requiring the agreement error probability or the security index to vanish to 0 asymptotically. Also, we consider the following problem of secure function computation with trusted parties: Multiple parties observing correlated data seek to compute a function of their collective data. To this end, they communicate interactively over an insecure communication channel. It is required that the value of the function be concealed from an eavesdropper with access to the communication. When is such a secure computation of a given function feasible? Using the aforementioned upper bound, we derive a necessary condition for the existence of a communication protocol that allows the parties to reliably recover the value of a given function, while keeping this value concealed from an eavesdropper with access to (only) the communication

Converses for Secret Key Agreement and Secure Computing

We consider information theoretic secret key agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the secret key length, which is derived using a reduction of binary hypothesis testing to multiparty secret key agreement. Building on this basic result, we derive new converses for multiparty secret key agreement. Furthermore, we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to secret key agreement. Finally, we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data, using an interactive public communication that by itself does not give away the value of the function. In many cases, we strengthen and improve upon previously known converse bounds. Our results are single-shot and use only the given joint distribution of the correlated observations. For the case when the correlated observations consist of independent and identically distributed (in time) sequences, we derive strong versions of previously known converses

ARPA Whitepaper

We propose a secure computation solution for blockchain networks. The correctness of computation is verifiable even under malicious majority condition using information-theoretic Message Authentication Code (MAC), and the privacy is preserved using Secret-Sharing. With state-of-the-art multiparty computation protocol and a layer2 solution, our privacy-preserving computation guarantees data security on blockchain, cryptographically, while reducing the heavy-lifting computation job to a few nodes. This breakthrough has several implications on the future of decentralized networks. First, secure computation can be used to support Private Smart Contracts, where consensus is reached without exposing the information in the public contract. Second, it enables data to be shared and used in trustless network, without disclosing the raw data during data-at-use, where data ownership and data usage is safely separated. Last but not least, computation and verification processes are separated, which can be perceived as computational sharding, this effectively makes the transaction processing speed linear to the number of participating nodes. Our objective is to deploy our secure computation network as an layer2 solution to any blockchain system. Smart Contracts\cite{smartcontract} will be used as bridge to link the blockchain and computation networks. Additionally, they will be used as verifier to ensure that outsourced computation is completed correctly. In order to achieve this, we first develop a general MPC network with advanced features, such as: 1) Secure Computation, 2) Off-chain Computation, 3) Verifiable Computation, and 4)Support dApps' needs like privacy-preserving data exchange

Strong Converse for a Degraded Wiretap Channel via Active Hypothesis Testing

We establish an upper bound on the rate of codes for a wiretap channel with public feedback for a fixed probability of error and secrecy parameter. As a corollary, we obtain a strong converse for the capacity of a degraded wiretap channel with public feedback. Our converse proof is based on a reduction of active hypothesis testing for discriminating between two channels to coding for wiretap channel with feedback.Comment: This paper was presented at Allerton 201

On the Communication Complexity of Secure Computation

Information theoretically secure multi-party computation (MPC) is a central primitive of modern cryptography. However, relatively little is known about the communication complexity of this primitive. In this work, we develop powerful information theoretic tools to prove lower bounds on the communication complexity of MPC. We restrict ourselves to a 3-party setting in order to bring out the power of these tools without introducing too many complications. Our techniques include the use of a data processing inequality for residual information - i.e., the gap between mutual information and G\'acs-K\"orner common information, a new information inequality for 3-party protocols, and the idea of distribution switching by which lower bounds computed under certain worst-case scenarios can be shown to apply for the general case. Using these techniques we obtain tight bounds on communication complexity by MPC protocols for various interesting functions. In particular, we show concrete functions that have "communication-ideal" protocols, which achieve the minimum communication simultaneously on all links in the network. Also, we obtain the first explicit example of a function that incurs a higher communication cost than the input length in the secure computation model of Feige, Kilian and Naor (1994), who had shown that such functions exist. We also show that our communication bounds imply tight lower bounds on the amount of randomness required by MPC protocols for many interesting functions.Comment: 37 page