Citation: | BIAN Song, MAO Ran, ZHU Yongqing, FU Yunhao, ZHANG Zhou, DING Lin, ZHANG Jiliang, ZHANG Bo, CHEN Yi, DONG Jin, GUAN Zhenyu. A Survey on Software-hardware Acceleration for Fully Homomorphic Encryption[J]. Journal of Electronics & Information Technology, 2024, 46(5): 1790-1805. doi: 10.11999/JEIT230448 |
[1] |
GOLDREICH O, MICALI S, and WIGDERSON A. How to play any mental game[C]. The Nineteenth Annual ACM Symposium on Theory of Computing, New York, USA, 1987: 218–229. doi: 10.1145/28395.28420.
|
[2] |
YAO A C C. How to generate and exchange secrets[C]. The 27th Annual Symposium on Foundations of Computer Science, Toronto, Canada, 1986: 162–167. doi: 10.1109/SFCS.1986.25.
|
[3] |
GENTRY C. Fully homomorphic encryption using ideal lattices[C]. The Forty-First Annual ACM Symposium on Theory of Computing, Bethesda, USA, 2009: 169–178. doi: 10.1145/1536414.1536440.
|
[4] |
HUANG Zhicong, LU Wenjie, HONG Cheng, et al. Cheetah: Lean and fast secure two-party deep neural network inference[C]. The 31st USENIX Security Symposium, Boston, USA, 2022: 809–826.
|
[5] |
LU Wenjie, HUANG Zhicong, HONG Cheng, et al. PEGASUS: Bridging polynomial and non-polynomial evaluations in homomorphic encryption[C]. 2021 IEEE Symposium on Security and Privacy, San Francisco, USA, 2021: 1057–1073. doi: 10.1109/SP40001.2021.00043.
|
[6] |
韦韬, 潘无穷, 李婷婷, 等. 可信隐私计算: 破解数据密态时代“技术困局”[J]. 信息通信技术与政策, 2022, 48(5): 15–24. doi: 10.12267/j.issn.2096-5931.2022.05.003.
WEI Tao, PAN Wuqiong, LI Tingting, et al. Trusted-environment-based privacy preserving computing: Breaks the bottleneck of ciphertext-exchange era[J]. Information and Communications Technology and Policy, 2022, 48(5): 15–24. doi: 10.12267/j.issn.2096-5931.2022.05.003.
|
[7] |
FAN Junfeng and VERCAUTEREN F. Somewhat practical fully homomorphic encryption[R]. Cryptology ePrint Archive 2012/144, 2012.
|
[8] |
BRAKERSKI Z, GENTRY C, and VAIKUNTANATHAN V. (Leveled) fully homomorphic encryption without bootstrapping[J]. ACM Transactions on Computation Theory, 2014, 6(3): 13. doi: 10.1145/2633600.
|
[9] |
CHEON J H, KIM A, KIM M, et al. Homomorphic encryption for arithmetic of approximate numbers[C]. The 23rd International Conference on the Theory and Application of Cryptology and Information Security, Hong Kong, China, 2017: 409–437. doi: 10.1007/978-3-319-70694-8_15.
|
[10] |
GENTRY C, SAHAI A, and WATERS B. Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based[C]. The 33rd Annual Cryptology Conference, Santa Barbara, USA, 2013: 75–92. doi: 10.1007/978-3-642-40041-4_5.
|
[11] |
CHILLOTTI I, GAMA N, GEORGIEVA M, et al. TFHE: Fast fully homomorphic encryption over the torus[J]. Journal of Cryptology, 2020, 33(1): 34–91. doi: 10.1007/s00145-019-09319-x.
|
[12] |
BRAKERSKI Z and VAIKUNTANATHAN V. Fully homomorphic encryption from ring-LWE and security for key dependent messages[C]. The 31st Annual Cryptology Conference, Santa Barbara, USA, 2011: 505–524. doi: 10.1007/978-3-642-22792-9_29.
|
[13] |
COSTACHE A and SMART N P. Which ring based somewhat homomorphic encryption scheme is best?[C]. The Cryptographers' Track at the RSA Conference, San Francisco, USA, 2016: 325–340. doi: 10.1007/978-3-319-29485-8_19.
|
[14] |
CHEON J H, HAN K, KIM A, et al. Bootstrapping for approximate homomorphic encryption[C]. The 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Tel Aviv, Israel, 2018: 360–384. doi: 10.1007/978-3-319-78381-9_14.
|
[15] |
ALPERIN-SHERIFF J and PEIKERT C. Faster bootstrapping with polynomial error[C]. The 34th Annual Cryptology Conference, Santa Barbara, USA, 2014: 297–314. doi: 10.1007/978-3-662-44371-2_17.
|
[16] |
DUCAS L and MICCIANCIO D. FHEW: Bootstrapping homomorphic encryption in less than a second[C]. The 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, 2015: 617–640. doi: 10.1007/978-3-662-46800-5_24.
|
[17] |
GAMA N, IZABACHÈNE M, NGUYEN P Q, et al. Structural lattice reduction: Generalized worst-case to average-case reductions and homomorphic cryptosystems[C]. The 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Vienna, Austria, 2016: 528–558. doi: 10.1007/978-3-662-49896-5_19.
|
[18] |
SMART N P and VERCAUTEREN F. Fully homomorphic SIMD operations[J]. Designs, Codes and Cryptography, 2014, 71(1): 57–81. doi: 10.1007/s10623-012-9720-4.
|
[19] |
GARNER H L. The residue number system[C]. The Western Joint Computer Conference, San Francisco, USA, 1959: 146–153. doi: 10.1145/1457838.1457864.
|
[20] |
HALEVI S and SHOUP V. Algorithms in HElib[C]. The 34th Annual Cryptology Conference, Santa Barbara, USA, 2014: 554–571. doi: 10.1007/978-3-662-44371-2_31.
|
[21] |
HALEVI S and SHOUP V. Bootstrapping for HElib[J]. Journal of Cryptology, 2021, 34(1): 7. doi: 10.1007/s00145-020-09368-7.
|
[22] |
HALEVI S and SHOUP V. Faster homomorphic linear transformations in HElib[C]. The 38th Annual International Cryptology Conference, Santa Barbara, USA, 2018: 93–120. doi: 10.1007/978-3-319-96884-1_4.
|
[23] |
JUVEKAR C, VAIKUNTANATHAN V, and CHANDRAKASAN A. GAZELLE: A low latency framework for secure neural network inference[C]. The 27th USENIX Conference on Security Symposium, Baltimore, USA, 2018: 1651–1669.
|
[24] |
BIAN S, KUNDI D E S, HIROZAWA K, et al. APAS: Application-specific accelerators for RLWE-based homomorphic linear transformations[J]. IEEE Transactions on Information Forensics and Security, 2021, 16: 4663–4678. doi: 10.1109/TIFS.2021.3114032.
|
[25] |
BOSSUAT J P, MOUCHET C, TRONCOSO-PASTORIZA J, et al. Efficient bootstrapping for approximate homomorphic encryption with non-sparse keys[C]. The 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, 2021: 587–617. doi: 10.1007/978-3-030-77870-5_21.
|
[26] |
LEE Y, LEE J W, KIM Y S, et al. High-precision bootstrapping for approximate homomorphic encryption by error variance minimization[C]. The 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Trondheim, Norway, 2022: 551–580. doi: 10.1007/978-3-031-06944-4_19.
|
[27] |
JUTLA C S and MANOHAR N. Sine series approximation of the mod function for bootstrapping of approximate HE[C]. The 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Trondheim, Norway, 2022: 491–520. doi: 10.1007/978-3-031-06944-4_17.
|
[28] |
CHEN Hao, CHILLOTTI I, and SONG Y. Improved bootstrapping for approximate homomorphic encryption[C]. The 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Darmstadt, Germany, 2019: 34–54. doi: 10.1007/978-3-030-17656-3_2.
|
[29] |
LEE J W, LEE E, LEE Y, et al. High-precision bootstrapping of RNS-CKKS homomorphic encryption using optimal minimax polynomial approximation and inverse sine function[C]. The 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, 2021: 618–647. doi: 10.1007/978-3-030-77870-5_22.
|
[30] |
RATHEE D, RATHEE M, KUMAR N, et al. CrypTFlow2: Practical 2-party secure inference[C]. The 2020 ACM SIGSAC Conference on Computer and Communications Security, Virtual Event, USA, 2020: 325–342. doi: 10.1145/3372297.3417274.
|
[31] |
BAJARD J C, EYNARD J, HASAN M A, et al. A full RNS variant of FV like somewhat homomorphic encryption schemes[C]. The 23rd International Conference on Selected Areas in Cryptography, St. John's, Canada, 2017: 423–442. doi: 10.1007/978-3-319-69453-5_23.
|
[32] |
CHEON J H, HAN K, KIM A, et al. A full RNS variant of approximate homomorphic encryption[C]. The 25th International Conference on Selected Areas in Cryptography, Calgary, Canada, 2019: 347–368. doi: 10.1007/978-3-030-10970-7_16.
|
[33] |
HALEVI S, POLYAKOV Y, and SHOUP V. An improved RNS variant of the BFV homomorphic encryption scheme[C]. The Cryptographers’ Track at the RSA Conference, San Francisco, USA, 2019: 83–105. doi: 10.1007/978-3-030-12612-4_5.
|
[34] |
GENTRY C, HALEVI S, and SMART N P. Homomorphic evaluation of the AES circuit[C]. The 32nd Annual Cryptology Conference, Santa Barbara, USA, 2012: 850–867. doi: 10.1007/978-3-642-32009-5_49.
|
[35] |
CHEON J H, HAN K, KIM A, et al. A full RNS variant of approximate homomorphic encryption[C]. The 25th International Conference on Selected Areas in Cryptography, Calgary, Canada, 2019: 347–368. doi: 10.1007/978-3-030-10970-7_16.
|
[36] |
HAN K and KI D. Better bootstrapping for approximate homomorphic encryption[C]. The Cryptographers’ Track at the RSA Conference 2020, San Francisco, USA, 2020: 364–390. doi: 10.1007/978-3-030-40186-3_16.
|
[37] |
KIM A, PAPADIMITRIOU A, and POLYAKOV Y. Approximate homomorphic encryption with reduced approximation error[R]. Cryptology ePrint Archive 2022/1118, 2022: 120–144.
|
[38] |
MICCIANCIO D and POLYAKOV Y. Bootstrapping in FHEW-like cryptosystems[C]. The 9th on Workshop on Encrypted Computing & Applied Homomorphic Cryptography, Seoul, South Korea, 2021: 17–28. doi: 10.1145/3474366.3486924.
|
[39] |
BONNORON G, DUCAS L, and FILLINGER M. Large FHE gates from tensored homomorphic accumulator[C]. The 10th International Conference on Cryptology in Africa, Marrakesh, Morocco, 2018: 217–251. doi: 10.1007/978-3-319-89339-6_13.
|
[40] |
LEE Y, MICCIANCIO D, KIM A, et al. Efficient FHEW bootstrapping with small evaluation keys, and applications to threshold homomorphic encryption[R]. Cryptology ePrint Archive 2022/198, 2022.
|
[41] |
MICCIANCIO D and SORRELL J. Ring packing and amortized FHEW bootstrapping[R]. Cryptology ePrint Archive 2018/532, 2018.
|
[42] |
GUIMARÃES A, PEREIRA H V L, and VAN LEEUWEN B. Amortized bootstrapping revisited: Simpler, asymptotically-faster, implemented[J]. Cryptology ePrint Archive 2023/014, 2023.
|
[43] |
LIU Fenghao and WANG Han. Batch bootstrapping I: A new framework for SIMD bootstrapping in polynomial modulus[C]. The 42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Lyon, France, 2023: 321–352. doi: 10.1007/978-3-031-30620-4_11.
|
[44] |
BOURA C, GAMA N, GEORGIEVA M, et al. Simulating homomorphic evaluation of deep learning predictions[C]. The 3rd International Symposium on Cyber Security Cryptography and Machine Learning, Beer-Sheva, Israel, 2019: 212–230. doi: 10.1007/978-3-030-20951-3_20.
|
[45] |
CHILLOTTI I, JOYE M, and PAILLIER P. Programmable bootstrapping enables efficient homomorphic inference of deep neural networks[C]. The 5th International Symposium on Cyber Security Cryptography and Machine Learning, Be’er Sheva, Israel, 2021: 1–19. doi: 10.1007/978-3-030-78086-9_1.
|
[46] |
CLET P E, ZUBER M, BOUDGUIGA A, et al. Putting up the swiss army knife of homomorphic calculations by means of TFHE functional bootstrapping[R]. Cryptology ePrint Archive 2022/149, 2022.
|
[47] |
KLUCZNIAK K and SCHILD L. FDFB: Full domain functional bootstrapping towards practical fully homomorphic encryption[J]. IACR Transactions on Cryptographic Hardware and Embedded Systems, 2022, 2023(1): 501–537. doi: 10.46586/tches.v2023.i1.501-537.
|
[48] |
YANG Zhaomin, XIE Xiang, SHEN Huajie, et al. TOTA: Fully homomorphic encryption with smaller parameters and stronger security[R]. Cryptology ePrint Archive, 2021/1347, 2021.
|
[49] |
CARPOV S, GAMA N, GEORGIEVA M, et al. Privacy-preserving semi-parallel logistic regression training with fully homomorphic encryption[J]. BMC Medical Genomics, 2020, 13(7): 88. doi: 10.1186/s12920-020-0723-0.
|
[50] |
GUIMARÃES A, BORIN E, and ARANHA D F. Revisiting the functional bootstrap in TFHE[J]. IACR Transactions on Cryptographic Hardware and Embedded Systems, 2021, 2021(2): 229–253. doi: 10.46586/tches.v2021.i2.229-253.
|
[51] |
CHILLOTTI I, LIGIER D, ORFILA J B, et al. Improved programmable bootstrapping with larger precision and efficient arithmetic circuits for TFHE[C]. The 27th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, 2021: 670–699. doi: 10.1007/978-3-030-92078-4_23.
|
[52] |
CHEN Hao, CHILLOTTI I, and SONG Y. Multi-key homomorphic encryption from TFHE[C]. The 25th International Conference on the Theory and Application of Cryptology and Information Security, Kobe, Japan, 2019: 446–472. doi: 10.1007/978-3-030-34621-8_16.
|
[53] |
BOURA C, GAMA N, GEORGIEVA M, et al. CHIMERA: Combining ring-LWE-based fully homomorphic encryption schemes[J]. Journal of Mathematical Cryptology, 2020, 14(1): 316–338. doi: 10.1515/jmc-2019-0026.
|
[54] |
CHEN Hao, DAI Wei, KIM M, et al. Efficient homomorphic conversion between (ring) LWE ciphertexts[C]. The 19th International Conference on Applied Cryptography and Network Security, Kamakura, Japan, 2021: 460–479. doi: 10.1007/978-3-030-78372-3_18.
|
[55] |
REN Xuanle, SU Le, GU Zhen, et al. HEDA: Multi-attribute unbounded aggregation over homomorphically encrypted database[J]. Proceedings of the VLDB Endowment, 2022, 16(4): 601–614. doi: 10.14778/3574245.3574248.
|
[56] |
GÖTTERT N, FELLER T, SCHNEIDER M, et al. On the design of hardware building blocks for modern lattice-based encryption schemes[C]. The 14th International Workshop on Cryptographic Hardware and Embedded Systems, Leuven, Belgium, 2012: 512–529. doi: 10.1007/978-3-642-33027-8_30.
|
[57] |
PÖPPELMANN T and GÜNEYSU T. Towards efficient arithmetic for lattice-based cryptography on reconfigurable hardware[C]. The 2nd International Conference on Cryptology and Information Security in Latin America, Santiago, Chile, 2012: 139–158. doi: 10.1007/978-3-642-33481-8_8.
|
[58] |
PÖPPELMANN T and GÜNEYSU T. Towards practical lattice-based public-key encryption on reconfigurable hardware[C]. The 20th International Conference on Selected Areas in Cryptography, Burnaby, Canada, 2014: 68–85. doi: 10.1007/978-3-662-43414-7_4.
|
[59] |
施佺, 韩赛飞, 黄新明, 等. 面向全同态加密的有限域FFT算法FPGA设计[J]. 电子与信息学报, 2018, 40(1): 57–62. doi: 10.11999/JEIT170312.
SHI Quan, HAN Saifei, HUANG Xinming, et al. Design of finite field FFT for fully homomorphic encryption based on FPGA[J]. Journal of Electronics & Information Technology, 2018, 40(1): 57–62. doi: 10.11999/JEIT170312.
|
[60] |
RIAZI M S, LAINE K, PELTON B, et al. HEAX: An architecture for computing on encrypted data[C]. The Twenty-Fifth International Conference on Architectural Support for Programming Languages and Operating Systems, Lausanne, Switzerland, 2020: 1295–1309. doi: 10.1145/3373376.3378523.
|
[61] |
REAGEN B, CHOI W S, KO Y, et al. Cheetah: Optimizing and accelerating homomorphic encryption for private inference[C]. The 2021 IEEE International Symposium on High-Performance Computer Architecture, Seoul, South Korea, 2021: 26–39. doi: 10.1109/HPCA51647.2021.00013.
|
[62] |
SAMARDZIC N, FELDMANN A, KRASTEV A, et al. F1: A fast and programmable accelerator for fully homomorphic encryption[C]. The 54th Annual IEEE/ACM International Symposium on Microarchitecture, Greece, 2021: 238–252. doi: 10.1145/3466752.3480070.
|
[63] |
SAMARDZIC N, FELDMANN A, KRASTEV A, et al. CraterLake: A hardware accelerator for efficient unbounded computation on encrypted data[C]. The 49th Annual International Symposium on Computer Architecture, New York, USA, 2022: 173–187. doi: 10.1145/3470496.3527393.
|
[64] |
KIM J, LEE G, KIM S, et al. ARK: Fully homomorphic encryption accelerator with runtime data generation and inter-operation key reuse[C]. The 2022 55th IEEE/ACM International Symposium on Microarchitecture, Chicago, USA, 2022: 1237–1254. doi: 10.1109/MICRO56248.2022.00086.
|
[65] |
JUNG W, KIM S, AHN J H, et al. Over 100x faster bootstrapping in fully homomorphic encryption through memory-centric optimization with GPUs[J]. IACR Transactions on Cryptographic Hardware and Embedded Systems, 2021, 2021(4): 114–148. doi: 10.46586/tches.v2021.i4.114-148.
|
[66] |
YANG Yinghao, ZHANG Huaizhi, FAN Shengyu, et al. Poseidon: Practical homomorphic encryption accelerator[C]. 2023 IEEE International Symposium on High-Performance Computer Architecture, Montreal, Canada, 2023: 870–881. doi: 10.1109/HPCA56546.2023.10070984.
|
[67] |
ZHU Yilan, WANG Xinyao, JU Lei, et al. FxHENN: FPGA-based acceleration framework for homomorphic encrypted CNN inference[C]. 2023 IEEE International Symposium on High-Performance Computer Architecture, Montreal, Canada, 2023: 896–907. doi: 10.1109/HPCA56546.2023.10071133.
|
[68] |
BRUTZKUS A, GILAD-BACHRACH R, and ELISHA O. Low latency privacy preserving inference[C]. The 36th International Conference on Machine Learning, Long Beach, USA, 2019: 812–821.
|
[69] |
FAN Shengyu, WANG Zhiwei, XU Weizhi, et al. TensorFHE: Achieving practical computation on encrypted data using GPGPU[C]. 2023 IEEE International Symposium on High-Performance Computer Architecture, Montreal, Canada, 2023: 922–934. doi: 10.1109/HPCA56546.2023.10071017.
|
[70] |
JIANG Lei, LOU Qian, and JOSHI N. MATCHA: A fast and energy-efficient accelerator for fully homomorphic encryption over the torus[C]. The 59th ACM/IEEE Design Automation Conference, San Francisco, USA, 2022: 235–240. doi: 3489517.3530435.
|
[71] |
DAI Wei. CUDA-accelerated fully homomorphic encryption library[EB/OL]. https://github.com/vernamlab/cuFHE, 2023.
|
[72] |
GENER Y S, NEWTON P, TAN D, et al. An FPGA-based programmable vector engine for fast fully homomorphic encryption over the torus[EB/OL]. https://people.ece.ubc.ca/lemieux/publications/gener-spsl2021.pdf, 2021.
|
[73] |
VAN BEIRENDONCK M, D'ANVERS J P, TURAN F, et al. FPT: A fixed-point accelerator for torus fully homomorphic encryption[C]. The 2023 ACM SIGSAC Conference on Computer and Communications Security, Copenhagen, Denmark, 2023: 741–755. doi: 10.1145/3576915.3623159.
|
[74] |
YE Tian, KANNAN R, and PRASANNA V K. FPGA acceleration of fully homomorphic encryption over the torus[C]. 2022 IEEE High Performance Extreme Computing Conference, Waltham, USA, 2022: 1–7. doi: 10.1109/HPEC55821.2022.9926381.
|
[75] |
AL BADAWI A, POLYAKOV Y, AUNG K M M, et al. Implementation and performance evaluation of RNS variants of the BFV homomorphic encryption scheme[J]. IEEE Transactions on Emerging Topics in Computing, 2021, 9(2): 941–956. doi: 10.1109/TETC.2019.2902799.
|
[76] |
AL BADAWI A, JIN Chao, LIN Jie, et al. Towards the AlexNet moment for homomorphic encryption: HCNN, the first homomorphic CNN on encrypted data with GPUs[J]. IEEE Transactions on Emerging Topics in Computing, 2021, 9(3): 1330–1343. doi: 10.1109/TETC.2020.3014636.
|
[77] |
DAI W and SUNAR B. cuHE: A homomorphic encryption accelerator library[C]. The 2nd International Conference on Cryptography and Information Security in the Balkans, Koper, Slovenia, 2016: 169–186. doi: 10.1007/978-3-319-29172-7_11.
|
[78] |
AL BADAWI A, VEERAVALLI B, MUN C F, et al. High-performance FV somewhat homomorphic encryption on GPUs: An implementation using CUDA[J]. IACR Transactions on Cryptographic Hardware and Embedded Systems, 2018, 2018(2): 70–95. doi: 10.13154/tches.v2018.i2.70-95.
|
[79] |
ÖZERK Ö, ELGEZEN C, MERT A C, et al. Efficient number theoretic transform implementation on GPU for homomorphic encryption[J]. The Journal of Supercomputing, 2022, 78(2): 2840–2872. doi: 10.1007/s11227-021-03980-5.
|
[80] |
MORSHED T, AL AZIZ M, and MOHAMMED N. CPU and GPU accelerated fully homomorphic encryption[C]. 2020 IEEE International Symposium on Hardware Oriented Security and Trust, San Jose, USA, 2020: 142–153. doi: 10.1109/HOST45689.2020.9300288.
|