Pseudo-signatures, Broadcast, and Multi-party Computation from Correlated Randomness

Fitzi, Matthias; Wolf, Stefan; Wullschleger, Jiirg

doi:10.1007/978-3-540-28628-8_34

Cited by 20 publications

(18 citation statements)

References 26 publications

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“…This area has a rich history (see [35,36,21,28,5,22,40] and references therein). However, most of the work in this area has been restricted to the two-party setting, and known results for the multi-party setting are not general enough to apply to the case of the anonymity functionality.…”

Section: Related Workmentioning

confidence: 99%

Cryptography from Anonymity

Ishai

Kushilevitz

Ostrovsky

et al. 2006

2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)

113

109

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There is a vast body of work on implementing anonymous communication. In this paper, we study the possibility of using anonymous communication as a building block, and show that one can leverage on anonymity in a variety of cryptographic contexts. Our results go in two directions.• Feasibility. We show that anonymous communication over insecure channels can be used to implement unconditionally secure point-to-point channels, broadcast, and general multi-party protocols that remain unconditionally secure as long as less than half of the players are maliciously corrupted. • Efficiency. We show that anonymous channels can yield substantial efficiency improvements for several natural secure computation tasks. In particular, we present the first solution to the problem of private information retrieval (PIR) which can handle multiple users while being close to optimal with respect to both communication and computation.

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Section: Related Workmentioning

confidence: 99%

Cryptography from Anonymity

Ishai

Kushilevitz

Ostrovsky

et al. 2006

2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)

113

109

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“…The type of correlated randomness needed for realizing multiparty computation with unconditional security in the presence of an honest majority is studied in [17,18]. Statistically secure commitment protocol from correlated randomness are constructed in [31].…”

Section: Related Workmentioning

confidence: 99%

On the Power of Correlated Randomness in Secure Computation

Ishai

Kushilevitz

Meldgaard

et al. 2013

Lecture Notes in Computer Science

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Abstract. We investigate the extent to which correlated secret randomness can help in secure computation with no honest majority. It is known that correlated randomness can be used to evaluate any circuit of size s with perfect security against semi-honest parties or statistical security against malicious parties, where the communication complexity grows linearly with s. This leaves open two natural questions: (1) Can the communication complexity be made independent of the circuit size? (2) Is it possible to obtain perfect security against malicious parties?We settle the above questions, obtaining both positive and negative results on unconditionally secure computation with correlated randomness. Concretely, we obtain the following results.Minimizing communication. Any multiparty functionality can be realized, with perfect security against semi-honest parties or statistical security against malicious parties, by a protocol in which the number of bits communicated by each party is linear in its input length. Our protocol uses an exponential number of correlated random bits. We give evidence that super-polynomial randomness complexity may be inherent.Perfect security against malicious parties. Any finite "senderreceiver" functionality, which takes inputs from a sender and a receiver and delivers an output only to the receiver, can be perfectly realized given correlated randomness. In contrast, perfect security is generally impossible for functionalities which deliver outputs to both parties. We also show useful functionalities (such as string equality) for which there are efficient perfectly secure protocols in the correlated randomness model.Perfect correctness in the plain model. We present a general approach for transforming perfectly secure protocols for sender-receiver On the Power of Correlated Randomness in Secure Computation 601 functionalities in the correlated randomness model into secure protocols in the plain model which offer perfect correctness against a malicious sender. This should be contrasted with the impossibility of perfectly sound zero-knowledge proofs.

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“…In the context of cryptography, the notions have first been used in [10], [12], [18]. Both notions have appeared previously in other information-theoretic contexts [11], the latter under the name of sufficient statistics.…”

Section: Preliminaries: Common and Dependent Partsmentioning

confidence: 99%

New Monotones and Lower Bounds in Unconditional Two-Party Computation

Wolf

Wullschleger

2008

IEEE Trans. Inform. Theory

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Abstract. Since bit and string oblivious transfer and commitment, two primitives of paramount importance in secure two-and multi-party computation, cannot be realized in an unconditionally secure way for both parties from scratch, reductions to weak information-theoretic primitives as well as between different variants of the functionalities are of great interest. In this context, we introduce three independent monotones-quantities that cannot be increased by any protocol-and use them to derive lower bounds on the possibility and efficiency of such reductions. An example is the transition between different versions of oblivious transfer, for which we also propose a new protocol allowing to increase the number of messages the receiver can choose from at the price of a reduction of their length. Our scheme matches the new lower bound and is, therefore, optimal.

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Pseudo-signatures, Broadcast, and Multi-party Computation from Correlated Randomness

Cited by 20 publications

References 26 publications

Cryptography from Anonymity

Cryptography from Anonymity

On the Power of Correlated Randomness in Secure Computation

New Monotones and Lower Bounds in Unconditional Two-Party Computation

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