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Revisiting Single-Server Algorithms for Outsourcing Modular Exponentiation

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Progress in Cryptology – INDOCRYPT 2018 (INDOCRYPT 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11356))

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Abstract

We investigate the problem of securely outsourcing modular exponentiations to a single, malicious computational resource. We revisit recently proposed schemes using single server and analyse them against two fundamental security properties, namely privacy of inputs and verifiability of outputs. Interestingly, we observe that the chosen schemes do not appear to meet both the security properties. In fact we present a simple polynomial-time attack on each algorithm, allowing the malicious server either to recover a secret input or to convincingly fool the client with wrong outputs. Then we provide a fix to the identified problem in the ExpSOS scheme. With our fix and without pre-processing, the improved scheme becomes the best to-date outsourcing scheme for single-server case. Finally we present the first precomputation-free single-server algorithm, \(\pi \)ExpSOS for simultaneous exponentiations, thereby solving an important problem formulated in [6].

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Authors and Affiliations

  1. Society for Electronic Transactions and Security (SETS), Chennai, India

    Jothi Rangasamy & Lakshmi Kuppusamy

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  1. Jothi Rangasamy
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  2. Lakshmi Kuppusamy
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Correspondence to Jothi Rangasamy .

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Editors and Affiliations

  1. Indian Statistical Institute, Kolkata, India

    Debrup Chakraborty

  2. Nagoya University, Nagoya, Japan

    Tetsu Iwata

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Rangasamy, J., Kuppusamy, L. (2018). Revisiting Single-Server Algorithms for Outsourcing Modular Exponentiation. In: Chakraborty, D., Iwata, T. (eds) Progress in Cryptology – INDOCRYPT 2018. INDOCRYPT 2018. Lecture Notes in Computer Science(), vol 11356. Springer, Cham. https://doi.org/10.1007/978-3-030-05378-9_1

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  • DOI: https://doi.org/10.1007/978-3-030-05378-9_1

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