Hardware/Software Co-Design of an Accelerator for FV Homomorphic Encryption Scheme Using Karatsuba Algorithm | IEEE Journals & Magazine | IEEE Xplore

Hardware/Software Co-Design of an Accelerator for FV Homomorphic Encryption Scheme Using Karatsuba Algorithm


Abstract:

Somewhat Homomorphic Encryption (SHE) schemes allow to carry out operations on data in the cipher domain. In a cloud computing scenario, personal information can be proce...Show More

Abstract:

Somewhat Homomorphic Encryption (SHE) schemes allow to carry out operations on data in the cipher domain. In a cloud computing scenario, personal information can be processed secretly, inferring a high level of confidentiality. For many years, practical parameters of SHE schemes were overestimated, leading to only consider the FFT algorithm to accelerate SHE in hardware. Nevertheless, recent work demonstrates that parameters can be lowered without compromising the security [1] . Following this trend, this work investigates the benefits of using Karatsuba algorithm instead of FFT for the Fan-Vercauteren (FV) Homomorphic Encryption scheme. The proposed accelerator relies on an hardware/software co-design approach, and is designed to perform fast arithmetic operations on degree 2,560 polynomials with 135 bits coefficients, allowing to compute small algorithms homomorphically. Compared to a functionally equivalent design using FFT, our accelerator performs an homomorphic multiplication in 11.9 ms instead of 15.46 ms, and halves the size of logic utilization and registers on the FPGA.
Published in: IEEE Transactions on Computers ( Volume: 67, Issue: 3, 01 March 2018)
Page(s): 335 - 347
Date of Publication: 26 December 2016

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1 Introduction

Homomorphic Encryption schemes are considered as promising in modern cryptography, because they directly allow to carry out operations on data in the cipher domain. Fig. 1 illustrates a basic client/server transaction in an homomorphic scenario. The most flexible ones, called Fully Homomorphic Encryption (FHE) schemes, are able to process unlimited additions and multiplications secretly, and so make possible to address a wide range of algorithms. To reduce computation times, many applications only consider Somewhat Homomorphic Encryption (SHE) schemes, which bound the number of operations to reduce the complexity.

References

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