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Cryptanalysis of a Protocol for Efficient Sorting on SHE Encrypted Data

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Cryptography and Coding (IMACC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11929))

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Abstract

Sorting on encrypted data using Somewhat Homomorphic Encryption (SHE) schemes is currently inefficient in practice when the number of elements to be sorted is very large. Hence alternate protocols that can efficiently perform computation and sorting on encrypted data is of interest. Recently, Kesarwani et al. (EDBT 2018) proposed a protocol for efficient sorting on data encrypted using an SHE scheme in a model where one of the two non-colluding servers is holding the decryption key. The encrypted data to be sorted is transformed homomorphically by the first server using a randomly chosen monotonic polynomial with possibly large coefficients, and then the non-colluding server holding the decryption key decrypts, sorts, and conveys back the sorted order to the first server without learning the actual values except possibly for the order.

In this work we demonstrate an attack on the above protocol that allows the non-colluding server holding the decryption key to recover the original plaintext inputs (up to a constant difference). Though our attack runs in time exponential in the size of plaintext inputs and degree of the polynomial but polynomial in the size of coefficients, we show that our attack is feasible for 32-bit inputs, hence accounting for several real world scenarios. Of independent interest is our algorithm for recovering the integer inputs (up to a constant difference) by observing only the integer polynomial outputs.

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Acknowledgements

We thank Sonata Software Limited, Bengaluru, India for funding this work. We also thank Debdeep Mukhopadhyay and Sikhar Patranabis for helpful discussions.

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Authors and Affiliations

  1. IIIT Bangalore, Bangalore, India

    Shyam Murthy & Srinivas Vivek

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  1. Shyam Murthy
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  2. Srinivas Vivek
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Correspondence to Shyam Murthy .

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  1. Royal Holloway, University of London, London, UK

    Martin Albrecht

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Murthy, S., Vivek, S. (2019). Cryptanalysis of a Protocol for Efficient Sorting on SHE Encrypted Data. In: Albrecht, M. (eds) Cryptography and Coding. IMACC 2019. Lecture Notes in Computer Science(), vol 11929. Springer, Cham. https://doi.org/10.1007/978-3-030-35199-1_14

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  • DOI: https://doi.org/10.1007/978-3-030-35199-1_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-35198-4

  • Online ISBN: 978-3-030-35199-1

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