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Blind Polynomial Evaluation and Data Trading

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Applied Cryptography and Network Security (ACNS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12726))

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Abstract

Data trading is an emerging business, in which data sellers provide buyers with, for example, their private datasets and get paid from buyers. In many scenarios, sellers prefer to sell pieces of data, such as statistical results derived from the dataset, rather than the entire dataset. Meanwhile, buyers wish to hide the results they retrieve. Since it is not preferable to rely on a trusted third party (TTP), we are wondering, in the absence of TTP, whether there exists a practical mechanism satisfying the following requirements: the seller Sarah receives the payment if and only if she obliviously returns the buyer Bob the correct evaluation result of a function delegated by Bob on her dataset, and Bob can only derive the result for which he pays. Despite a lot of attention data trading has received, a desirable mechanism for this scenario is still missing. This is due to the fact that general solutions are inefficient when the size of datasets is considerable or the evaluated function is complicated, and that existing efficient cryptographic techniques cannot fully capture the features of our scenario or can only address very limited computing tasks.

In this paper, we propose the first desirable mechanism that is practical and supports a wide variety of computing tasks—evaluation of arbitrary functions that can be represented as polynomials. We introduce a new cryptographic notion called blind polynomial evaluation and instantiate it with an explicit protocol. We further combine this notion with the blockchain paradigm to provide a practical framework that can satisfy the requirements mentioned above.

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Notes

  1. 1.

    Such an approach is similar to that of [6]. However, their security goal indeed cannot be achieved since the random coins of the ElGamal encryption cannot be extracted and the group order is hidden. We overcome the security faults for our scenario.

  2. 2.

    Assume that the gas price is 10 Gwei (a common price, albeit lower fees is possible). The total transaction fees (of US dollar) are calculated according to the average price of gas and coin on April 12th, 2020 (see more in https://etherscan.io/chart/gasprice). For the total fee, we take into account the total gas consumption of all functions for active verification and all functions except complain for passive verification.

  3. 3.

    Note that since our implementation involves big integers and Ethereum today can only support integers represented by 256 bits, we have to use an external library. However, library instructions from therein will be pulled into the calling contract in the compilation. Hence, once a new version of Ethereum has better support of external library call, the cost of our protocol can further be dramatically reduced.

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Acknowledgments

We thank the reviewers for their detailed and helpful comments. Y. Liu and Q. Wang were partially supported by the National Science Foundation of China under Grant No. 61672015 and Guangdong Provincial Key Laboratory (Grant No. 2020B121201001). Y. Liu and S.-M. Yiu were also partially supported by ITF, Hong Kong (ITS/173/18FP).

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Authors and Affiliations

  1. Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Yi Liu & Qi Wang

  2. National Center for Applied Mathematics (Shenzhen), Southern University of Science and Technology, Shenzhen, 518055, China

    Qi Wang

  3. Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong SAR, China

    Yi Liu & Siu-Ming Yiu

Authors
  1. Yi Liu
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  2. Qi Wang
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  3. Siu-Ming Yiu
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Correspondence to Qi Wang .

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Editors and Affiliations

  1. Waseda University, Tokyo, Japan

    Kazue Sako

  2. CISPA Helmholtz Center for Information Security, SaarbrĂĽcken, Germany

    Nils Ole Tippenhauer

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Liu, Y., Wang, Q., Yiu, SM. (2021). Blind Polynomial Evaluation and Data Trading. In: Sako, K., Tippenhauer, N.O. (eds) Applied Cryptography and Network Security. ACNS 2021. Lecture Notes in Computer Science(), vol 12726. Springer, Cham. https://doi.org/10.1007/978-3-030-78372-3_5

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  • DOI: https://doi.org/10.1007/978-3-030-78372-3_5

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