Paper 2018/1053

Revisiting Single-server Algorithms for Outsourcing Modular Exponentiation

Jothi Rangasamy and Lakshmi Kuppusamy


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.

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. INDOCRYPT2018
modular exponentiationssecure outsourcing
Contact author(s)
jothi rangasamy @ gmail com
2018-11-02: received
Short URL
Creative Commons Attribution


      author = {Jothi Rangasamy and Lakshmi Kuppusamy},
      title = {Revisiting Single-server Algorithms for Outsourcing Modular Exponentiation},
      howpublished = {Cryptology ePrint Archive, Paper 2018/1053},
      year = {2018},
      note = {\url{}},
      url = {}
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