Implementation and performance evaluation of RNS variants of the BFV homomorphic encryption scheme

Ahmad Al Badawi, Yuriy Polyakov, Khin Mi Mi Aung, Bharadwaj Veeravalli, Kurt Rohloff

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


Homomorphic encryption is an emerging form of encryption that provides the ability to compute on encrypted data without ever decrypting them. Potential applications include aggregating sensitive encrypted data on a cloud environment and computing on the data in the cloud without compromising data privacy. There have been several recent advances resulting in new homomorphic encryption schemes and optimized variants. We implement and evaluate the performance of two optimized variants, namely Bajard-Eynard-Hasan-Zucca (BEHZ) and Halevi-Polyakov-Shoup (HPS), of the most promising homomorphic encryption scheme in CPU and GPU. The most interesting (and also unexpected) result of our performance evaluation is that the HPS variant in practice scales significantly better (typically by 15-30 percent) with increase in multiplicative depth of the computation circuit than BEHZ, implying that the HPS variant will always outperform BEHZ for most practical applications. For the multiplicative depth of 98, our fastest GPU implementation performs homomorphic multiplication in 51 ms for 128-bit security settings, which is faster by two orders of magnitude than prior results and already practical for cloud environments supporting GPU computations. Large multiplicative depths supported by our implementations are required for applications involving deep neural networks, logistic regression learning, and other important machine learning problems.

Original languageEnglish (US)
Article number8657794
Pages (from-to)941-956
Number of pages16
JournalIEEE Transactions on Emerging Topics in Computing
Issue number2
StatePublished - Apr 1 2021

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Information Systems
  • Human-Computer Interaction
  • Computer Science Applications


  • Secure computation
  • homomorphic encryption
  • lattice-based cryptography
  • parallel processing
  • residue number system


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