Optimised Multiplication Architectures for Accelerating Fully Homomorphic Encryption

Xiaolin Cao, Ciara Moore, Maire O'Neill, Elizabeth O'Sullivan, Neil Hanley

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)
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Large integer multiplication is a major performance bottleneck in fully homomorphic encryption (FHE) schemes over the integers. In this paper two optimised multiplier architectures for large integer multiplication are proposed. The first of these is a low-latency hardware architecture of an integer-FFT multiplier. Secondly, the use of low Hamming weight (LHW) parameters is applied to create a novel hardware architecture for large integer multiplication in integer-based FHE schemes. The proposed architectures are implemented, verified and compared on the Xilinx Virtex-7 FPGA platform. Finally, the proposed implementations are employed to evaluate the large multiplication in the encryption step of FHE over the integers. The analysis shows a speed improvement factor of up to 26.2 for the low-latency design compared to the corresponding original integer-based FHE software implementation. When the proposed LHW architecture is combined with the low-latency integer-FFT accelerator to evaluate a single FHE encryption operation, the performance results show that a speed improvement by a factor of approximately 130 is possible.
Original languageEnglish
Pages (from-to)2794-2806
JournalIEEE Transactions on Computers
Issue number9
Early online date06 Nov 2015
Publication statusPublished - 01 Sept 2016


  • Fully homomorphic encryption
  • Large integer multiplication
  • low Hamming weight
  • FPGA
  • cryptography


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