Computer Science ›› 2022, Vol. 49 ›› Issue (5): 341-346.doi: 10.11896/jsjkx.210300089

• Information Security • Previous Articles     Next Articles

NTRU Type Fully Homomorphic Encryption Scheme over Prime Power Cyclotomic Rings

QIN Xiao-yue, HUANG Ru-wei, YANG Bo   

  1. School of Computer and Electronic Information,Guangxi University,Nanning 530004,China
  • Received:2021-03-08 Revised:2021-07-22 Online:2022-05-15 Published:2022-05-06
  • About author:QIN Xiao-yue,born in 1997,postgra-duate,is a member of China Computer Federation.Her main research interests include holomorphic encryption of NTRU system and so on.
    HUANG Ru-wei,born in 1978,Ph.D,professor,is a member of China Computer Federation.Her main research interests include cloud computing and homomorphic encryption.
  • Supported by:
    National Natural Science Foundation of China(62062009).

Abstract: Full homomorphic encryption (FHE) supports arbitrary computation on the ciphertext without the requirement of decryption,which provides protection for privacy security in cloud computing.However,the current FHE scheme constructed using the approximate eigenvector method requires complex matrix multiplications,which is computationally complicated and cannot resist subfield attacks.In this paper,a new FHE scheme was proposed by using the power-of-prime cyclotomic ring instead of a power-of-two cyclotomic ring,and the complex matrix multiplications in homomorphic multiplications were effectively avoided by modifying the ciphertext form and decryption structure.Compared with similar schemes,the proposed scheme improves the efficiency at least by a factor of lφ(x)/2d and is secure against IND-CPA attacks.

Key words: Prime power cyclotomic rings, Fully homomorphic encryption, IND-CPA security

CLC Number: 

  • TP309
[1]LI R Q,JIA C F.A multi key homomorphic encryption scheme based on NTRU[J].Acta Cryptologica Sinica,2020,7 (5):683-697.
[2]GENTRY C.Fully Homomorphic Encryption Using Ideal Lattices[J].Proceedings of the Annual Acm Symposium on Theory of Computing,2009,9(4):169-178.
[3]BRAKERSKI Z.Fully homomorphic encryption without modulus switching from classical GapSVP[C]//Advances in Crypto-logy-CRYPTO,2012.Springer Berlin Heidelberg,2012:868-886.
[4]GENTRY C,SAHAI A,WATERS B.Homomorphic encryption from learning with errors:Concept ually-simpler,Asymptotically faster,attribute based[C]//Advances in Cryptology(CRYPTO 2013).Berlin,Heidelberg:Springer,2013:75-92.
[5]DORÖZ Y,SUNAR B.Flattening NTRU for Evaluation KeyFree Homomorphic Encryption[J].Journal of Mathematical Cryptology,2020,14(1):66-83.
[6]LI Z C,ZHANG J M,YANG Y T,et al.A Fully homomorphic Encryption Scheme Based on NTRU[J].ACTA Electronica Si-nica,2018,46(4):938-944.
[7]KHEDR A,GULAK G.SecureMed:Secure Medical Computa-tion Using GPU-Accelerated Homomorphic Encryption Scheme[J].IEEE J Biomed Health Inform,2018,22(2):597-606.
[8]ALBRECHT M,BAI S,DUCAS L.A subfifield lattice attack on overstretched NTRU assumptions[C]//Proceedings of Annual Cryptology Conference.Cham:Springer,2016:153-178.
[9]CHEONJ H,JEONG J,LEE C.An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without an encoding of zero[J].LMS Journal of Computation and Mathematics,2016,19(A):255-266.
[10]SMART N P,VERCAUTEREN F.Fully homomorphic SIMD operations[J].Designs,Codes& Cryptography,2014,71:57-81.
[11]MIGLIORE V,BONNORON G,FONTAINE C.Practical Pa-rameters for Somewhat Homomorphic Encryption (SHE) Schemes on Binary Circuits[J].IEEE Transactions on Computers,2018,67:1550-1560.
[12]DORÖZ Y,HU Y,SUANR B.Homomorphic AES evaluationusing the modified LTV scheme[J].Designs,Codes and Cryptography,2016,80(2):333-358.
[13]LŎPEZ-ALT A,TROMER E,VAIKUNTANATHAN V.On-the fly rnultiparty computation on the cloud via multikey fully homornorphic encryption[C]//Proceedings of the 44th Annual ACM Symposium on Theory of Comnputing.ACM,2012:1219-1234.
[14]YU Y,XU G,WANG X.Provably Secure NTRU Instances over Prime Cyclotomic Rings[C]//IACR International Workshop on Public Key Cryptography.2017.
[15]STEHLÉ D,STEINFELD R.Making NTRU as secure asworst-case problems over ideal lattices[C]//Springer-Verlag.2011.
[16]QIN X Y,HUANG R W.Research on the homomorphic encryption of NTRU system[J/OL].Computer Application Research:1-8.[2021-02-22].
[17]RUDOLF L,HARALD N,COHN F M.Finite fields[M].Cambridge University Press,1997.
[18]CHEN Y L.Cyclotomic polynomials over finite fields[J].Journal of Hubei Normal University (Natural Science Edition),2012,32 (2):1-5.
[19]LYUBASHEVSKY V,PEIKERT C,REGEV O.On ideal lat-tices and learning with errors over rings[C]//Advances in Cryptology-EUROCRYPT 2010,29th Annual International Confe-rence on the Theory and Applications of Cryptographic Techniques.French Riviera:ACM,2010.
[20]CHE X L,ZHOU H N,ZHOU T P,et al.Decryption structure of multi key homomorphic encryption scheme based on public key cryptosystem[J/OL].Computer Application:1-7.[2021-04-28].
[21]ZHOU H N,LI N B,CHE X L,et al.Multi key holomorphic scheme based on prime power order cyclotomic polynomial ring[J].Information Network Security,2020,20 (5):83-87.
[22]CHEON J H,KIM J,LEE M S,et al.CRT-based fully homomorphic encryption over the integers[J].Information Sciences,2015,310:149-162.
[23]ADRIANA L A,ERAN T,VINOD V.On-the-fly multipartycomputation on the cloud via multikey fully homomorphic encryption[C]//Proceedings of the 44th symposium on Theory of Computing.ACM,2012:1219-1234.
[24]HOFFSTEIN J, SILVERMAN J.Optimizations for NTRU[J].Proceedings Public Key Cryptography & Computational Number Theory,2000.
[25]LYUBASHEVSKY V,PEIKERT C,REGEV O.A toolkit for ring-LWE cryptography[C]//Annual International Conference on the Theory and Applications of Cryptographic Techniques.Berlin,Heidelberg:Springer,2013:35-54.
[1] LI Meng-tian, HU Bin. RLWE-based Fully Homomorphic Encryption Scheme with Batch Technique [J]. Computer Science, 2019, 46(3): 209-216.
[2] SHI Jing-qi, YANG Geng, SUN Yan-jun, BAI Shuang-jie and MIN Zhao-e. Efficient Parallel Algorithm of Fully Homomorphic Encryption Supporting Operation of Floating-point Number [J]. Computer Science, 2018, 45(5): 116-122.
[3] MAO He-feng, HU Bin. Homomorphic Evaluation of Lightweight Block Cipher over Integers [J]. Computer Science, 2018, 45(11): 169-175.
Full text



[1] WANG Zhen-chao, HOU Huan-huan and LIAN Rui. Path Optimization Scheme for Restraining Degree of Disorder in CMT[J]. Computer Science, 2018, 45(4): 122 -125 .
[2] XU Tao,DU Yu-xuan,LV Zong-lei. Sensor Node Deployment Model Based on Linear Programming[J]. Computer Science, 2018, 45(7): 110 -115 .
[3] NIU Wei-na, ZHANG Xiao-song, YANG Guo-wu, ZHUO Zhong-liu, LU Jia-zhong. Modeling and Analysis of Botnet with Heterogeneous Infection Rate[J]. Computer Science, 2018, 45(7): 135 -138 .
[4] LIU Yan, ZHU Chun-jie and WANG Fang. Analysis and Optimization of DiskSeen Prefetching Algorithm[J]. Computer Science, 2017, 44(6): 23 -30 .
[5] LI Chao, LIU Hong-zhe, YUAN Jia-zheng and ZHENG Yong-rong. Real-time Lane Detection Algorithm Based on Inter-frame Correlation[J]. Computer Science, 2017, 44(2): 317 -323 .
[6] PENG Jian-shan, ZHOU Chuan-tao, WANG Qing-xian and DING Da-zhao. Construction Method of ROP Frame Based on Multipath Dispatcher[J]. Computer Science, 2018, 45(1): 240 -244 .
[7] HAN Jin, SHI Jin and REN Yong-jun. DTN Routing Algorithm Based on Region Segmentation[J]. Computer Science, 2015, 42(10): 113 -116 .
[8] XU Feng-sheng, YAN Li-mei and SHI Kai-quan. Dynamic Data Intelligent Mining with Attributes Disjunctive Reduction and Expansion Characteristics[J]. Computer Science, 2015, 42(5): 215 -220 .
[9] LI Ai-jing, DONG Chao, TAO Bing-yang, TIAN Chang, WANG Hai and GAO Wei. Low-cost Access Point Detection Algorithm Based on Periodicity Identification[J]. Computer Science, 2015, 42(3): 31 -34 .
[10] WANG Zhen-zhen,HE Ming and DU Yong-ping. Text Similarity Computing Based on Topic Model LDA[J]. Computer Science, 2013, 40(12): 229 -232 .