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Efficient and Secure Delegation of Exponentiation in General Groups to a Single Malicious Server

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Abstract

Group exponentiation is an important and relatively expensive operation used in many public-key cryptosystems and, more generally, cryptographic protocols. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that this operation is delegated from a computationally weaker client to a computationally stronger server. In the case of a single, possibly malicious, server, this problem has remained open since the introduction of a formal model. In previous work we have proposed practical and secure solutions applicable to two classes of specific groups, related to well-known cryptosystems. In this paper, we investigate this problem in a general class of multiplicative groups, possibly going beyond groups currently subject to quantum cryptanalysis attacks. Our main results are efficient delegation protocols for exponentiation in these general groups. The main technique in our results is a reduction of the protocol’s security probability (i.e., the probability that a malicious server convinces a client of an incorrect exponentiation output) that is more efficient than by standard parallel repetition. The resulting protocols satisfy natural requirements such as correctness, security, privacy and efficiency, even if the adversary uses the full power of quantum computers. In particular, in our protocols the client performs a number of online group multiplications smaller by 1–2 orders of magnitude than in a non-delegated computation.

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Authors and Affiliations

  1. Perspecta Labs, Basking Ridge, NJ, USA

    Giovanni Di Crescenzo

  2. CUNY John Jay College of Criminal Justice, New York, NY, USA

    Matluba Khodjaeva

  3. University of York, Heslington, UK

    Delaram Kahrobaei

  4. City University of New York, New York, NY, USA

    Vladimir Shpilrain

Authors
  1. Giovanni Di Crescenzo
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  2. Matluba Khodjaeva
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  3. Delaram Kahrobaei
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  4. Vladimir Shpilrain
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Correspondence to Giovanni Di Crescenzo.

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Di Crescenzo, G., Khodjaeva, M., Kahrobaei, D. et al. Efficient and Secure Delegation of Exponentiation in General Groups to a Single Malicious Server. Math.Comput.Sci. 14, 641–656 (2020). https://doi.org/10.1007/s11786-020-00462-4

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