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On hiding information from an oracle

Authors:

J. KilianAuthors Info & Claims

STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

Pages 195 - 203

https://doi.org/10.1145/28395.28417

Published: 01 January 1987 Publication History

Abstract

We consider the problem of computing with encrypted data. Player A wishes to know the value ƒ(x) for some x but lacks the power to compute it. Player B has the power to compute ƒ and is willing to send ƒ(y) to A if she sends him y, for any y. Informally, an encryption scheme for the problem ƒ is a method by which A, using her inferior resources, can transform the cleartext instance x into an encrypted instance y, obtain ƒ(y) from B, and infer ƒ(x) from ƒ(y) in such a way that B cannot infer x from y. When such an encryption scheme exists, we say that ƒ is encryptable.

The framework defined in this paper enables us to prove precise statements about what an encrypted instance hides and what it leaks, in an information-theoretic sense. Our definitions are cast in the language of probability theory and do not involve assumptions such as the intractability of factoring or the existence of one-way functions. We use our framework to describe encryption schemes for some natural problems in NP ⋒ CoNP.

We also consider the following generalization of encryption schemes. Player A, who is limited to probabilistic polynomial time, wishes to guess the value ƒ(x) with probability at least 1/2 + 1/|x|^c of being correct, for some constant c. Player B can compute any function and generate arbitrary probability distributions. Players A and B can interact for a polynomial number of rounds by sending polynomial-sized messages. We prove a strong negative result: there is no such generalized encryption scheme for SAT that leaks no more than the size of x (unless the polynomial hierarchy collapses at the second level).

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cover image ACM Conferences

STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

January 1987

471 pages

ISBN:0897912217

DOI:10.1145/28395

Editor:
Alfred V. Aho

Copyright © 1987 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 January 1987

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STOC87: 19th Annual ACM Conference on Theory of Computing

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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https://doi.org/10.1109/JSAC.2022.3142358
Ding QWeng GZhao GHu C(2021)Efficient and Secure Outsourcing of Large-Scale Linear System of EquationsIEEE Transactions on Cloud Computing10.1109/TCC.2018.28801819:2(587-597)Online publication date: 1-Apr-2021
https://doi.org/10.1109/TCC.2018.2880181
Huang YSong ZLi KArora SDaumé HSingh A(2020)InstaHideProceedings of the 37th International Conference on Machine Learning10.5555/3524938.3525357(4507-4518)Online publication date: 13-Jul-2020
https://dl.acm.org/doi/10.5555/3524938.3525357
Jia ZJafar S(2020) X -Secure T -Private Information Retrieval From MDS Coded Storage With Byzantine and Unresponsive Servers IEEE Transactions on Information Theory10.1109/TIT.2020.301315266:12(7427-7438)Online publication date: Dec-2020
https://doi.org/10.1109/TIT.2020.3013152
Bicer OBingol MKiraz MLevi A(2020)Highly Efficient and Re-executable Private Function Evaluation with Linear ComplexityIEEE Transactions on Dependable and Secure Computing10.1109/TDSC.2020.3009496(1-1)Online publication date: 2020
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