We propose a novel distortion-theoretic approach to a secure three-party computation problem. Alice and Bob have deterministic sequences, and Charlie wishes to compute a normalized sum-type function of those sequences. We construct three-party protocols that allow Charlie to compute the function with arbitrarily high accuracy, while maintaining unconditional privacy for Alice and Bob and achieving vanishing communication cost. This work leverages a striking dimensionality reduction that allows a high accuracy estimate to be produced from only a random subsampling of the sequences. The worst-case distortion of the estimate, across all arbitrary deterministic sequences of any length, is independent of the dimensionality (length) of the sequences and proportional to inverse square root of the number of samples that the estimate is based upon.
We propose a novel distortion-theoretic approach to a secure three-party computation problem. Alice and Bob have deterministic sequences, and Charlie wishes to compute a normalized sum-type function of those sequences. We construct three-party protocols that allow Charlie to compute the function with arbitrarily high accuracy, while maintaining unconditional privacy for Alice and Bob and achieving vanishing communication cost. This work leverages a striking dimensionality reduction that allows a high accuracy estimate to be produced from only a random subsampling of the sequences. The worst-case distortion of the estimate, across all arbitrary deterministic sequences of any length, is independent of the dimensionality (length) of the sequences and proportional to inverse square root of the number of samples that the estimate is based upon.
Consider a network of k parties, each holding a long sequence of n entries (a database), with minimum vertex-cut greater than t. We show that any empirical statistic across the network of databases can be computed by each party with perfect privacy, against any set of t < k/2 passively colluding parties, such that the worst-case distortion and communication cost (in bits per database entry) both go to zero as n, the number of entries in the databases, goes to infinity. This is based on combining a striking dimensionality reduction result for random sampling with unconditionally secure multi-party computation protocols.
Consider a network of k parties, each holding a long sequence of n entries (a database), with minimum vertex-cut greater than t. We show that any empirical statistic across the network of databases can be computed by each party with perfect privacy, against any set of t ¡ k=2 passively colluding parties, such that the worst-case distortion and communication cost (in bits per database entry) both go to zero as n, the number of entries in the databases, goes to infinity. This is based on combining a striking dimensionality reduction result for random sampling with unconditionally secure multi-party computation protocols. arXiv.org
In the problem of Secure Multi-party Computation, the objective is to design a protocol that allows a group of parties to securely compute functions of their collective private data, while ensuring that no party reveals any more information about its private data other than what must be inherently revealed by the computation results (privacy) and that no parties can disrupt or influence the computation results beyond the effects of changing their input data (correctness and consistency). Information theoretic approaches toward this problem, that provide provable (unconditional) security guarantees even against adversarial parties that have unbounded computational power, have established that general computation is possible in a variety of scenarios. However, these general solutions are not always efficient or finely tuned to the requirements of specific problems and applications.
The focus of this thesis is on the development of information theoretic approaches for multi-party computation applications with the common theme of secure and efficient computation and inference over a distributed data network. Specific applications include: 1) private information retrieval, where the objective is to privately retrieve data without revealing what was selected; 2) secure statistical analysis, the problem of extracting statistics without revealing anything else about the underlying data; 3) secure sampling, which is the secure generation of new data with a given distribution; and 4) secure authentication, where the identity of a party needs to authenticated via inference on his/her credentials and stored registration data.
The contributions of this thesis toward addressing these applications include the following: The development of an Oblivious Transfer (OT) protocol, applicable to private information retrieval, that trades off a small amount of privacy while being several times more efficient than other OT protocols. The efficiency of general se- cure two-party computation via OT realized from noisy channels is also analyzed. A technique for approximate secure multi-party computation applicable to secure statistical analysis of large scale distributed databases is developed. By exploiting a dimensionality reduction and the structure of a broad class of functions based on the computed statistics, the feasibility of simultaneously achieving both arbitrarily high accuracy and arbitrarily high communication efficiency is demonstrated. The region of distributions that can be securely sampled in the two-party scenario is characterized. It is further established that for those distributions, it can be accomplished with a protocol that only sends one message. Inner and outer bounds on the region of distributions that can be securely sampled in the general multi-party scenario are also developed. A new three-party protocol, applicable to the problem of secure biometric authentication, that securely computes the Hamming distance even when one of the parties arbitrarily deviates from the protocol is proposed and analyzed. A two-factor secure biometric authentication system that is robust against the compromise of registered biometric data, allowing for revocability and resistance against cross-enrollment attacks is also proposed.
In the problem of secure multi-party sampling, n parties wish to securely sample an n-variate joint distribution, with each party receiving a sample of one of the correlated variables. The objective is to correctly produce the samples using a distributed message passing protocol, while maintaining privacy against a coalition of passively cheating parties. In the two-party case, we fully characterize the joint distributions that can be securely sampled under perfect correctness and privacy requirements as well as under weakened correctness and privacy requirements. Furthermore, we show that the distributions that can be securely sampled can be produced with a protocol that only uses one round of unidirectional communication. For the n-party case, any distribution can be securely sampled with privacy against a strict minority coalition, due to well-known results in secure multi-party computation. However, when privacy against a majority coalition is required, not all distributions can be securely sampled. We give necessary conditions and sufficient conditions for distributions that can be securely sampled. However, the exact characterization of the distributions that can be securely sampled remains open.
We show that some problems in information security can be solved without using one-way functions.The latter are usually regarded as a central concept of cryptography, but the very existence of one-way functions depends on difficult conjectures in complexity theory, most notably on the notorious "P = N P " conjecture.This is why cryptographic primitives that do not employ one-way functions are often called "unconditionally secure".In this paper, we suggest protocols for secure computation of the sum, product, and some other functions of two or more elements of an arbitrary constructible ring, without using any one-way functions.A new input that we offer here is that, in contrast with other proposals, we conceal "intermediate results" of a computation.For example, when we compute the sum of k numbers, only the final result is known to the parties; partial sums are not known to anybody.Other applications of our method include voting/rating over insecure channels and a rather elegant and efficient solution of the "two millionaires problem".Then, while it is fairly obvious that a secure (bit) commitment between two parties is impossible without a one-way function, we show that it is possible if the number of parties is at least 3.We also show how our unconditionally secure (bit) commitment scheme for 3 parties can be used to arrange an unconditionally secure (bit) commitment between just two parties if they use a "dummy" (e.g., a computer) as the third party.We explain how our concept of a "dummy" is different from a wellknown concept of a "trusted third party".Based on a similar idea, we also offer an unconditionally secure k-n oblivious transfer protocol between two parties who use a "dummy".We also suggest a protocol, without using a one-way function, for the so-called "mental poker", i.e., a fair card dealing (and playing) over distance.Finally, we propose a secret sharing scheme where an advantage over Shamir's and other known secret sharing schemes is that nobody, including the dealer, ends up knowing the shares (of the secret) owned by any particular player.It should be mentioned that computational cost of our protocols is negligible to the point that all of them can be executed without a computer.
We consider a two-user secure computation problem in which Alice and Bob communicate interactively in order to compute some deterministic functions of the inputs. The privacy requirement is that each user should not learn any additional information about a function of the inputs other than what can be inferred from its own input and output. For the distribution-free setting, i.e., when the protocol must be correct and private for any joint input distribution, we completely characterize the set of all securely computable functions. When privacy is required only against Bob who computes a function based on a single transmission from Alice, we show that asymptotically secure computability is equivalent to perfectly secure computability. Separately, we consider an eavesdropper who has access to all the communication and should not learn any information about some function of the inputs (possibly different from the functions to be computed by the users) and show that interaction may be necessary for secure computation.