Private Computation — k-Connected versus 1-Connected Networks

Bläser, Markus; Jakoby, Andreas; Liśkiewicz, Maciej; Siebert, Bodo

doi:10.1007/3-540-45708-9_13

Cited by 14 publications

(19 citation statements)

References 27 publications

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“…We give an exact characterization of the functions that can be computed privately in such a network. This result generalizes the result of Bläser et al [4] characterizing the Boolean functions that can be privately computed in such a network with 2 two-connected components. While Boolean functions that can be privately computed in such networks have a very simple structure ("if then else" functions), the non-Boolean functions that can be privately computed in such networks have a richer structure.…”

Section: Our Resultssupporting

confidence: 86%

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On private computation in incomplete networks

Beimel

2006

Distrib. Comput.

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Suppose that some parties are connected by an incomplete network of reliable and private channels. The parties cooperate to execute some protocol. However, the parties are curious -after the protocol terminates each party tries to learn information from the communication it heard. We say that a function can be computed privately in a network if there is a protocol in which each processor learns only the information implied by its input and the output of the function (in the information theoretic sense).The question we address in this paper is what functions can be privately computed in a given incomplete network. Every function can be privately computed in two-connected networks with at least three parties. Thus, the question is interesting only for non two-connected networks. Generalizing results of [Bläser et al. CRYPTO 2002], we characterize the functions that can be computed privately in simple networks -networks with one separating vertex and no leaves. We then deal with private computations in arbitrary non two-connected networks: we reduce this question to private computations of related functions on trees, and give some sufficient conditions and necessary conditions on the functions that can be privately computed on trees.

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Section: Our Resultssupporting

confidence: 86%

“…Bläser et al [4] characterize the Boolean functions that can be privately computed in simple non twoconnected networks, that is, in connected networks with one separating vertex and 2 two-connected components. We consider the more general question that naturally arises.…”

Section: Theorem 11 If N > 3 and The Network G Is Two-connected Thementioning

confidence: 99%

On private computation in incomplete networks

Beimel

2006

Distrib. Comput.

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“…From [3,1] we can conclude that most auction protocols cannot be run privately on non-2-connected networks. Therefore, we demand a communication network to be at least 2-connected.…”

Section: Privacy and Securitymentioning

confidence: 98%

“…Franklin and Yung [13] investigated the role of the connectivity of the underlying network in private computations. Bläser et al [3] completely characterized the class of privately computable Boolean functions, if the underlying network is connected but not 2-connected. In particular, no non-degenerate function can be computed privately if the network consists of three or more blocks.…”

Section: Related Work Concerning Private Computationmentioning

confidence: 99%

t-Private and t-Secure Auctions

Hinkelmann

Jakoby

Stechert

2008

J. Comput. Sci. Technol.

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In most of the used auction systems the values of bids are known to the auctioneer. This allows him to manipulate the outcome of the auction. Hence, one is interested in hiding these values. Some cryptographically secure protocols for electronic auctions have been presented in the last decade. Our work extends these protocols in several ways. Based on garbled circuits, i.e., encrypted circuits, we present protocols for sealed-bid auctions that fulfill the following requirements:1. Protocols are information-theoretically t-private for honest but curious parties.2. The number of bits that can be learned by malicious adversaries is bounded by the output length of the auction.3. The computational requirements for participating parties are very low: only random bit choices and bitwise computation of the XOR-function are necessary.Note that one can distinguish between the protocol that generates a garbled circuit for an auction and the protocol to evaluate the auction. In this paper we address both problems. We will present a t-private protocol for the construction of a garbled circuit that reaches the lower bound of 2t + 1 parties, and a more randomness efficient protocol for (t + 1) 2 parties. Finally, we address the problem of bid changes in an auction.

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“…In this section, we consider the more general case where, typically, the number of parties is significantly smaller than the circuit size. The randomness complexity of general t-private computations was studied by Canetti et al [18] (other works, such as [38,37,36,24,14], concentrated on special values of t or on special tasks).…”

Section: Secure Multiparty Computationmentioning

confidence: 99%

Robust Pseudorandom Generators

Ishai

Kushilevitz

et al. 2013

Automata, Languages, and Programming

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Let G : {0, 1} n → {0, 1} m be a pseudorandom generator. We say that a circuit implementation of G is (k, q)-robust if for every set S of at most k wires anywhere in the circuit, there is a set T of at most q|S| outputs, such that conditioned on the values of S and T the remaining outputs are pseudorandom. We initiate the study of robust PRGs, presenting explicit and non-explicit constructions in which k is close to n, q is constant, and m >> n. These include unconditional constructions of robust r-wise independent PRGs and small-bias PRGs, as well as conditional constructions of robust cryptographic PRGs.In addition to their general usefulness as a more resilient form of PRGs, our study of robust PRGs is motivated by cryptographic applications in which an adversary has a local view of a large source of secret randomness. We apply robust r-wise independent PRGs towards reducing the randomness complexity of private circuits and protocols for secure multiparty computation, as well as improving the "black-box complexity" of constant-round secure two-party computation.

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Private Computation — k-Connected versus 1-Connected Networks

Cited by 14 publications

References 27 publications

On private computation in incomplete networks

On private computation in incomplete networks

t-Private and t-Secure Auctions

Robust Pseudorandom Generators

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