Founding crytpography on oblivious transfer
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A zero-one law for Boolean privacy
SIAM Journal on Discrete Mathematics
Privacy and communication complexity
SIAM Journal on Discrete Mathematics
Deterministic coding for interactive communication
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A coding theorem for distributed computation
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A mathematical theory of communication
ACM SIGMOBILE Mobile Computing and Communications Review
Achieving oblivious transfer using weakened security assumptions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Privacy and communication complexity
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Towards coding for maximum errors in interactive communication
Proceedings of the forty-third annual ACM symposium on Theory of computing
Efficient and Explicit Coding for Interactive Communication
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Coding for interactive communication
IEEE Transactions on Information Theory - Part 1
Efficient Interactive Coding against Adversarial Noise
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
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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).