Abstract
Is it possible to measure a physical object in a way that makes the measurement signals unintelligible to an external observer? Alternatively, can one learn a natural concept by using a contrived training set that makes the labeled examples useless without the line of thought that has led to their choice? We initiate a study of “cryptographic sensing” problems of this type, presenting definitions, positive and negative results, and directions for further research.
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- 1.
The requirement that \(b<1\) is what rules out the trivial solution where h is just the list of labels for the m points in S and forces actual “learning”.
- 2.
In the case of proper PAC-learning (i.e., when \(\mathcal{H}=\mathcal{F}\)), [18] present a condition (called “closure under exception lists”) on \(\mathcal{F}\) under which PAC still implies OCCAM learning.
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Acknowledgements
We thank Brent Waters for helpful discussions.
Research supported by NSF-BSF grant 2015782. Y. Ishai and E. Kushilevitz were additionally supported by ISF grant 1709/14 and a grant from the Ministry of Science and Technology, Israel and Department of Science and Technology, Government of India. Y. Ishai was additionally supported by ERC Project NTSC (742754). R. Ostrovsky was additionally supported by NSF grant 1619348, DARPA SafeWare subcontract to Galois Inc., DARPA SPAWAR contract N66001-15-C-4065, JP Morgan Faculty Research Award, OKAWA Foundation Research Award, IBM Faculty Research Award, Xerox Faculty Research Award, B. John Garrick Foundation Award, Teradata Research Award, and Lockheed-Martin Corporation Research Award. A. Sahai was additionally supported by a DARPA/ARL SAFEWARE award, NSF Frontier Award 1413955, and NSF grant 1619348, a Xerox Faculty Research Award, a Google Faculty Research Award, an equipment grant from Intel, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through the ARL under Contract W911NF-15-C-0205. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense, the National Science Foundation or the U.S. Government.
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Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A. (2019). Cryptographic Sensing. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11694. Springer, Cham. https://doi.org/10.1007/978-3-030-26954-8_19
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