TY - GEN
T1 - On the power of correlated randomness in secure computation
AU - Ishai, Yuval
AU - Kushilevitz, Eyal
AU - Meldgaard, Sigurd
AU - Orlandi, Claudio
AU - Paskin-Cherniavsky, Anat
PY - 2013
Y1 - 2013
N2 - 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 "sender-receiver" 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 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.
AB - 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 "sender-receiver" 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 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.
UR - http://www.scopus.com/inward/record.url?scp=84873953976&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-36594-2_34
DO - 10.1007/978-3-642-36594-2_34
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AN - SCOPUS:84873953976
SN - 9783642365935
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 600
EP - 620
BT - Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Proceedings
T2 - 10th Theory of Cryptography Conference, TCC 2013
Y2 - 3 March 2013 through 6 March 2013
ER -