Accelerating NTRU based homomorphic encryption using GPUs

Wei Dai; Yarkin Doroz; Berk Sunar

doi:10.1109/HPEC.2014.7041001

Accelerating NTRU based homomorphic encryption using GPUs

Wei Dai, Yarkin Doroz, Berk Sunar

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

44 Scopus citations

Abstract

We introduce a large polynomial arithmetic library optimized for Nvidia GPUs to support fully homomorphic encryption schemes. To realize the large polynomial arithmetic library we convert polynomials with large coefficients using the Chinese Remainder Theorem into many polynomials with small coefficients, and then carry out modular multiplications in the residue space using a custom developed discrete Fourier transform library. We further extend the library to support the homomorphic evaluation operations, i.e. addition, multiplication, and relinearization, in an NTRU based somewhat homomorphic encryption library. Finally, we put the library to use to evaluate homomorphic evaluation of two block ciphers: Prince and AES, which show 2.57 times and 7.6 times speedup, respectively, over an Intel Xeon software implementation.

Original language	English (US)
Title of host publication	2014 IEEE High Performance Extreme Computing Conference, HPEC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781479962334
DOIs	https://doi.org/10.1109/HPEC.2014.7041001
State	Published - Feb 11 2014
Externally published	Yes
Event	2014 IEEE High Performance Extreme Computing Conference, HPEC 2014 - Waltham, United States Duration: Sep 9 2014 → Sep 11 2014

Publication series

Name	2014 IEEE High Performance Extreme Computing Conference, HPEC 2014

Other

Other	2014 IEEE High Performance Extreme Computing Conference, HPEC 2014
Country/Territory	United States
City	Waltham
Period	9/9/14 → 9/11/14

All Science Journal Classification (ASJC) codes

Software

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10.1109/HPEC.2014.7041001

Cite this

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title = "Accelerating NTRU based homomorphic encryption using GPUs",

abstract = "We introduce a large polynomial arithmetic library optimized for Nvidia GPUs to support fully homomorphic encryption schemes. To realize the large polynomial arithmetic library we convert polynomials with large coefficients using the Chinese Remainder Theorem into many polynomials with small coefficients, and then carry out modular multiplications in the residue space using a custom developed discrete Fourier transform library. We further extend the library to support the homomorphic evaluation operations, i.e. addition, multiplication, and relinearization, in an NTRU based somewhat homomorphic encryption library. Finally, we put the library to use to evaluate homomorphic evaluation of two block ciphers: Prince and AES, which show 2.57 times and 7.6 times speedup, respectively, over an Intel Xeon software implementation.",

author = "Wei Dai and Yarkin Doroz and Berk Sunar",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 IEEE High Performance Extreme Computing Conference, HPEC 2014 ; Conference date: 09-09-2014 Through 11-09-2014",

year = "2014",

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doi = "10.1109/HPEC.2014.7041001",

language = "English (US)",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

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}

Dai, W, Doroz, Y & Sunar, B 2014, Accelerating NTRU based homomorphic encryption using GPUs. in 2014 IEEE High Performance Extreme Computing Conference, HPEC 2014., 7041001, 2014 IEEE High Performance Extreme Computing Conference, HPEC 2014, Institute of Electrical and Electronics Engineers Inc., 2014 IEEE High Performance Extreme Computing Conference, HPEC 2014, Waltham, United States, 9/9/14. https://doi.org/10.1109/HPEC.2014.7041001

Accelerating NTRU based homomorphic encryption using GPUs. / Dai, Wei; Doroz, Yarkin; Sunar, Berk.
2014 IEEE High Performance Extreme Computing Conference, HPEC 2014. Institute of Electrical and Electronics Engineers Inc., 2014. 7041001 (2014 IEEE High Performance Extreme Computing Conference, HPEC 2014).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Dai, Wei

AU - Doroz, Yarkin

AU - Sunar, Berk

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N2 - We introduce a large polynomial arithmetic library optimized for Nvidia GPUs to support fully homomorphic encryption schemes. To realize the large polynomial arithmetic library we convert polynomials with large coefficients using the Chinese Remainder Theorem into many polynomials with small coefficients, and then carry out modular multiplications in the residue space using a custom developed discrete Fourier transform library. We further extend the library to support the homomorphic evaluation operations, i.e. addition, multiplication, and relinearization, in an NTRU based somewhat homomorphic encryption library. Finally, we put the library to use to evaluate homomorphic evaluation of two block ciphers: Prince and AES, which show 2.57 times and 7.6 times speedup, respectively, over an Intel Xeon software implementation.

AB - We introduce a large polynomial arithmetic library optimized for Nvidia GPUs to support fully homomorphic encryption schemes. To realize the large polynomial arithmetic library we convert polynomials with large coefficients using the Chinese Remainder Theorem into many polynomials with small coefficients, and then carry out modular multiplications in the residue space using a custom developed discrete Fourier transform library. We further extend the library to support the homomorphic evaluation operations, i.e. addition, multiplication, and relinearization, in an NTRU based somewhat homomorphic encryption library. Finally, we put the library to use to evaluate homomorphic evaluation of two block ciphers: Prince and AES, which show 2.57 times and 7.6 times speedup, respectively, over an Intel Xeon software implementation.

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Accelerating NTRU based homomorphic encryption using GPUs

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