HEPCloud: An FPGA-Based Multicore Processor for FV Somewhat Homomorphic Function Evaluation

In this paper, we present an FPGA based hardware accelerator '<inline-formula><tex-math notation="LaTeX"> \mathsf{HEPCloud}</tex-math> <inline-graphic xlink:href="sinharoy-ieq1-2816640.gif"/> </inline-formula>' for homomorphic evaluations o...

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Veröffentlicht in:IEEE transactions on computers Jg. 67; H. 11; S. 1637 - 1650
Hauptverfasser: Sinha Roy, Sujoy, Jarvinen, Kimmo, Vliegen, Jo, Vercauteren, Frederik, Verbauwhede, Ingrid
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.11.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Acceleration
Algorithms
Cloud computing
Computer architecture
Computer memory
Cybersecurity
Encryption
Feasibility studies
Field programmable gate arrays
Hardware
hardware implementation
Homomorphic encryption
lattice-based cryptography
Microprocessors
number theoretic transform
Parallel processing
Parameters
Pipelining (computers)
polynomial multiplication
Polynomials
ring-LWE
Rings (mathematics)
ISSN:0018-9340, 1557-9956
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Zusammenfassung:In this paper, we present an FPGA based hardware accelerator '<inline-formula><tex-math notation="LaTeX"> \mathsf{HEPCloud}</tex-math> <inline-graphic xlink:href="sinharoy-ieq1-2816640.gif"/> </inline-formula>' for homomorphic evaluations of medium depth functions which has applications in cloud computing. Our <inline-formula><tex-math notation="LaTeX">\mathsf{HEPCloud}</tex-math> <inline-graphic xlink:href="sinharoy-ieq2-2816640.gif"/> </inline-formula> architecture supports the polynomial ring based homomorphic encryption scheme FV for a ring-LWE parameter set of dimension <inline-formula> <tex-math notation="LaTeX">2^{15}</tex-math> <inline-graphic xlink:href="sinharoy-ieq3-2816640.gif"/> </inline-formula>, modulus size 1,228-bit, and a standard deviation 50. This parameter-set offers a multiplicative depth 36 and at least 85 bit security. The processor of <inline-formula><tex-math notation="LaTeX"> \mathsf{HEPCloud}</tex-math> <inline-graphic xlink:href="sinharoy-ieq4-2816640.gif"/> </inline-formula> is composed of multiple parallel cores. To achieve fast computation time for such a large parameter-set, various optimizations in both algorithm and architecture levels are performed. For fast polynomial multiplications, we use CRT with NTT and achieve two dimensional parallelism in <inline-formula> <tex-math notation="LaTeX">\mathsf{HEPCloud}</tex-math> <inline-graphic xlink:href="sinharoy-ieq5-2816640.gif"/> </inline-formula>. We optimize the BRAM access, use a fast Barrett like polynomial reduction method, optimize the cost of CRT, and design a fast divide-and-round unit. Beside parallel processing, we apply pipelining strategy in several of the sequential building blocks to reduce the impact of sequential computations. Finally, we implement <inline-formula><tex-math notation="LaTeX"> \mathsf{HEPCloud}</tex-math> <inline-graphic xlink:href="sinharoy-ieq6-2816640.gif"/> </inline-formula> on a medium-size Xilinx Virtex 6 FPGA board ML605 board and measure its on-board performance. To store the ciphertexts during a homomorphic function evaluation, we use the large DDR3 memory of the ML605 board. Our FPGA-based implementation of <inline-formula><tex-math notation="LaTeX">\mathsf{HEPCloud}</tex-math> <inline-graphic xlink:href="sinharoy-ieq7-2816640.gif"/> </inline-formula> computes a homomorphic multiplication in 26.67 s, of which the actual computation takes only 3.36 s and the rest is spent for off-chip memory access. It requires about 37,551 s to evaluate the SIMON-64/128 block cipher, but the per-block timing is only about 18 s because <inline-formula><tex-math notation="LaTeX">\mathsf{HEPCloud}</tex-math> <inline-graphic xlink:href="sinharoy-ieq8-2816640.gif"/> </inline-formula> processes 2,048 blocks simultaneously. The results show that FPGA-based acceleration of homomorphic function evaluations is feasible, but fast memory interface is crucial for the performance.
Bibliographie:ObjectType-Article-1
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ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2018.2816640