TY - GEN

T1 - Private interactive communication across an adversarial channel

AU - Gelles, Ran

AU - Sahai, Amit

AU - Wadia, Akshay

PY - 2014

Y1 - 2014

N2 - Consider two parties Alice and Bob, who hold private inputs x and y, and wish to compute a function f(x,y) privately in the information theoretic sense; that is, each party should learn nothing beyond f(x, y). However, the communication channel available to them is noisy. This means that the channel can introduce errors in the transmission between the two parties. Moreover, the channel is adversarial in the sense that it knows the protocol that Alice and Bob are running, and maliciously introduces errors to disrupt the communication, subject to some bound on the total number of errors. A fundamental question in this setting is to design a protocol that remains private in the presence of large number of errors. If Alice and Bob are only interested in computing f(x, y) correctly, and not privately, then quite robust protocols are known that can tolerate a constant fraction of errors. However, none of these solutions is applicable in the setting of privacy, as they inherently leak information about the parties' inputs. This leads to the question whether we can simultaneously achieve privacy and error-resilience against a constant fraction of errors. We show that privacy and error-resilience are contradictory goals. In particular, we show that for every constant c > 0, there exists a function f which is privately computable in the error-less setting, but for which no private and correct protocol is resilient against a c-fraction of errors. The same impossibility holds also for sub-constant noise rate, e.g., when c is exponentially small (as a function of the input size).

AB - Consider two parties Alice and Bob, who hold private inputs x and y, and wish to compute a function f(x,y) privately in the information theoretic sense; that is, each party should learn nothing beyond f(x, y). However, the communication channel available to them is noisy. This means that the channel can introduce errors in the transmission between the two parties. Moreover, the channel is adversarial in the sense that it knows the protocol that Alice and Bob are running, and maliciously introduces errors to disrupt the communication, subject to some bound on the total number of errors. A fundamental question in this setting is to design a protocol that remains private in the presence of large number of errors. If Alice and Bob are only interested in computing f(x, y) correctly, and not privately, then quite robust protocols are known that can tolerate a constant fraction of errors. However, none of these solutions is applicable in the setting of privacy, as they inherently leak information about the parties' inputs. This leads to the question whether we can simultaneously achieve privacy and error-resilience against a constant fraction of errors. We show that privacy and error-resilience are contradictory goals. In particular, we show that for every constant c > 0, there exists a function f which is privately computable in the error-less setting, but for which no private and correct protocol is resilient against a c-fraction of errors. The same impossibility holds also for sub-constant noise rate, e.g., when c is exponentially small (as a function of the input size).

KW - Adversarial noise

KW - Coding

KW - Information-theoretic security

KW - Interactive communication

KW - Private function evaluation

UR - http://www.scopus.com/inward/record.url?scp=84893315824&partnerID=8YFLogxK

U2 - 10.1145/2554797.2554812

DO - 10.1145/2554797.2554812

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AN - SCOPUS:84893315824

SN - 9781450322430

T3 - ITCS 2014 - Proceedings of the 2014 Conference on Innovations in Theoretical Computer Science

SP - 135

EP - 144

BT - ITCS 2014 - Proceedings of the 2014 Conference on Innovations in Theoretical Computer Science

PB - Association for Computing Machinery

T2 - 2014 5th Conference on Innovations in Theoretical Computer Science, ITCS 2014

Y2 - 12 January 2014 through 14 January 2014

ER -