Abstract
Secure computation (i.e., performing computation while keeping inputs private) is a fundamental problem in cryptography. In this paper, we present an efficient and secure 2-party computation protocol for any function computable via a monotone formula over equality statements between data blocks, under standard cryptographic assumptions. Our result bypasses roadblocks in previous general solutions, like Yao’s garbled circuits and Gentry’s lattice-based fully homomorphic encryption, by performing secure computations over data blocks (instead of bits) and using typical-size (instead of impractically large) cryptographic keys. An important efficiency property achieved is that the number of cryptographic operations in the protocol is sublinear in the size of the circuit representing the computed function. Even though not as general as in the two mentioned techniques, the class of formulae in our result contains a large number of well-known computational problems (while previously, only single specific problems were known to satisfy the mentioned sublinear efficiency property). Our main underlying technique is a new cryptographic primitive, perhaps of independent interest, that we call real-or-random conditional transfer, built as a variant of the well-known Rabin’s oblivious transfer primitive.
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Acknowledgements
This work was supported by the Defense Advanced Research Projects Agency (DARPA) via Air Force Research Laboratory (AFRL), contract number FA8750-14-C-0057. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation hereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of DARPA, AFRL or the U.S. Government.
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Di Crescenzo, G., Coan, B., Kirsch, J. (2015). Efficient Computations over Encrypted Data Blocks . In: Italiano, G., Pighizzini, G., Sannella, D. (eds) Mathematical Foundations of Computer Science 2015. MFCS 2015. Lecture Notes in Computer Science(), vol 9235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48054-0_23
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DOI: https://doi.org/10.1007/978-3-662-48054-0_23
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