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Universally Composable Secure Computation with Corrupted Tokens

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Book cover Advances in Cryptology – CRYPTO 2019 (CRYPTO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11694))

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Abstract

We introduce the corrupted token model. This model generalizes the tamper-proof token model proposed by Katz (EUROCRYPT ’07) relaxing the trust assumption on the honest behavior of tokens. Our model is motivated by the real-world practice of outsourcing hardware production to possibly corrupted manufacturers. We capture the malicious behavior of token manufacturers by allowing the adversary to corrupt the tokens of honest players at the time of their creation.

We show that under minimal complexity assumptions, i.e., the existence of one-way functions, it is possible to UC-securely realize (a variant of) the tamper-proof token functionality of Katz in the corrupted token model with n stateless tokens assuming that the adversary corrupts at most \(n-1\) of them (for any \(n>0\)). We apply this result to existing multi-party protocols in Katz’s model to achieve UC-secure MPC in the corrupted token model assuming only the existence of one-way functions. Finally, we show how to obtain the above results using tokens of small size that take only short inputs. The technique in this result can also be used to improve the assumption of UC-secure hardware obfuscation recently proposed by Nayak et al. (NDSS ’17). While their construction requires the existence of collision-resistant hash functions, we can obtain the same result from only one-way functions. Moreover using our main result we can improve the trust assumption on the tokens as well.

W. Chongchitmate—Work done while the author was at Department of Computer Science, University of California, Los Angeles.

R. Ostrovsky—Research supported in part by NSF-BSF grant 1619348, DARPA SafeWare subcontract to Galois Inc., DARPA SPAWAR contract N66001-15-C-4065, US-Israel BSF grant 2012366, JP Morgan Faculty 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. The views expressed are those of the authors and do not reflect position of the Department of Defense or the U.S. Government.

I. Visconti—Work done in part while the author was visiting UCLA.

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Notes

  1. 1.

    A similar question for the case of Common Reference String (CRS) generation was answered in the multi-string model [30].

  2. 2.

    The correlated randomness is the key that allows us to avoid the impossibility of resettably-secure computation in the standard model proven in [25]. However, we stress that correlated randomness is not required by our main theorem for UC security with tamper-proof stateless corruptible tokens from OWFs.

  3. 3.

    Our ZK argument protocol also has a straight-line witness extractor, but it is not necessary for our applications.

  4. 4.

    Whenever, the state of the program (ORAM or otherwise) needs to be modified, this is done by appending encrypted \(\texttt {state}\) with \(\overline{{\mathsf {Header}}}\) and then authenticating, similar to Nayak et al. [39].

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Author information

Authors and Affiliations

  1. Microsoft Research India, Bengaluru, India

    Nishanth Chandran

  2. Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, Thailand

    Wutichai Chongchitmate

  3. Department of Computer Science and Department of Mathematics, University of California, Los Angeles, CA, USA

    Rafail Ostrovsky

  4. DIEM, University of Salerno, Fisciano, Italy

    Ivan Visconti

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  1. Nishanth Chandran
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  2. Wutichai Chongchitmate
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  3. Rafail Ostrovsky
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  4. Ivan Visconti
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Correspondence to Nishanth Chandran or Wutichai Chongchitmate .

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Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. University of California at San Diego, La Jolla, CA, USA

    Daniele Micciancio

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Chandran, N., Chongchitmate, W., Ostrovsky, R., Visconti, I. (2019). Universally Composable Secure Computation with Corrupted Tokens. 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_14

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