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Round and Communication Efficient Unconditionally-Secure MPC with \(t<n/3\) in Partially Synchronous Network

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Information Theoretic Security (ICITS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10681))

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Abstract

In this work, we study unconditionally-secure multi-party computation (MPC) tolerating \(t < n/3\) corruptions, where n is the total number of parties involved. In this setting, it is well known that if the underlying network is completely asynchronous, then one can achieve only statistical security; moreover it is impossible to ensure input provision and consider inputs of all the honest parties. The best known statistically-secure asynchronous MPC (AMPC) with \(t<n/3\) requires a communication of \(\varOmega (n^5)\) field elements per multiplication. We consider a partially synchronous setting, where the parties are assumed to be globally synchronized initially for few rounds and then the network becomes completely asynchronous. In such a setting, we present a MPC protocol, which requires \(\mathcal {O}(n^2)\) communication per multiplication while ensuring input provision. Our MPC protocol relies on a new four round, communication efficient statistical verifiable secret-sharing (VSS) protocol with broadcast communication complexity independent of the number of secret-shared values.

A. Choudhury—Financial support from Infosys Foundation acknowledged.

A. Patra—Work partially supported by INSPIRE Faculty Fellowship (DST/INSPIRE/04/2014/015727) from Department of Science & Technology, India.

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Notes

  1. 1.

    The outcome of a perfectly-secure protocol is error-free, while a negligible error is allowed in a statistically-secure protocol.

  2. 2.

    Informally such a scheme ensures that the shared value remains information-theoretically secure even if upto t shares are revealed. Shamir sharing of a secret with threshold t is done by selecting a random polynomial of degree at most t with the secret as the constant term and defining the individual shares as distinct evaluations of the polynomial.

  3. 3.

    The amortized communication complexity is derived under the assumption that the circuit is large enough so that the terms that are independent of the circuit size can be ignored.

  4. 4.

    We say a protocol requires \((r, r')\) (synchronous) rounds, if it requires a total of r rounds of interaction among the parties and out of these r rounds, \(r'\) rounds require broadcast by the parties, where \(r' \le r\).

  5. 5.

    The actual complexity (communication, computation and round) of these protocols are of the form \(\mathcal {O}((\log ^k n\; \cdot \text{ poly }(\log |C|)) \cdot |C|) + \mathcal {O}(\text{ poly }(n, \log |C|, \mathcal {D}))\), where \(\mathcal {D}\) is the multiplicative depth of the underlying circuit C.

  6. 6.

    The interpretation of a proof corresponding to a set of values will be clear later during the formal presentation of our ICPoP.

  7. 7.

    This explains the need for two masking polynomials: one is used to preserve the privacy of the secret-encoding polynomials during the authentication phase while the other is used to maintain the privacy during the revelation phase.

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Authors and Affiliations

  1. International Institute of Information Technology, Bangalore, India

    Ashish Choudhury

  2. Indian Institute of Science, Bangalore, India

    Arpita Patra & Divya Ravi

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  1. Ashish Choudhury
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  2. Arpita Patra
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Correspondence to Ashish Choudhury .

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  1. Yokohama National University , Yokohama, Japan

    Junji Shikata

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Choudhury, A., Patra, A., Ravi, D. (2017). Round and Communication Efficient Unconditionally-Secure MPC with \(t<n/3\) in Partially Synchronous Network. In: Shikata, J. (eds) Information Theoretic Security. ICITS 2017. Lecture Notes in Computer Science(), vol 10681. Springer, Cham. https://doi.org/10.1007/978-3-319-72089-0_6

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  • DOI: https://doi.org/10.1007/978-3-319-72089-0_6

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