Cryptology ePrint Archive: Report 2018/1053

Revisiting Single-server Algorithms for Outsourcing Modular Exponentiation

Jothi Rangasamy and Lakshmi Kuppusamy

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.

Category / Keywords: cryptographic protocols / modular exponentiations, secure outsourcing

Original Publication (in the same form): INDOCRYPT2018

Date: received 31 Oct 2018, last revised 31 Oct 2018

Contact author: jothi rangasamy at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20181102:011008 (All versions of this report)

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