Identity-based Matrix Encryption Scheme Based on Lattices

doi:10.3969/j.issn.1671-1122.2019.01.005

Abstract

Abstract:

The lattice-based cryptosystem is a public key cryptosystem that resists quantum computing attacks. Once the quantum computer is available, it will impact on the widely used public key cryptosystems, such as integer factorization-based cryptosystems and discrete logarithm-based cryptosystems. Hence, the lattice-based cryptosystem has become a research focus in the network security field in the recent years. Identity-based encryption scheme simplifies the management of the user’s public key, and can be applied to the resource-constrained situations. At present, many identity-based encryption schemes based on lattices have been proposed. But these schemes are all single-bit encryption schemes. Consequently, this paper designs a lattice-based matrix public key encryption scheme by using Peikert, Vaikuntanathan and Waters’ ciphertext packing technique. This paper proves that the proposed public key encryption scheme is IND-CPA secure based on the LWE hardness assumption. And then, based on the proposed public key encryption scheme, this paper constructs an identity-based matrix encryption scheme based on lattices in the light of the dual cryptosystem defined by Gentry, Peikert and Vaikuntanathan. This paper proves that the proposed identity-based encryption scheme satisfies the IND-sID-CPA security based on the LWE hardness assumption.

Key words: identity-based encryption, lattice, LWE problem, packing

CLC Number:

TP309

Mingxiang LI, Hongtao WANG. Identity-based Matrix Encryption Scheme Based on Lattices[J]. Netinfo Security, 2019, 19(1): 34-41.

References 23

[1]	PEIKERT C.A Decade of Lattice Cryptography[J]. Foundations and Trends in Theoretical Computer Science, 2016, 10(4): 283-424.
[2]	ZHANG Pingyuan, JIANG Han, CAI Jie, et al.Recent Advances in Lattice-based Cryptography[J]. Journal of Computer Research and Development, 2017, 54(10): 2121-2129.
	张平原, 蒋瀚, 蔡杰, 等. 格密码技术近期研究进展[J]. 计算机研究与发展. 2017, 54(10): 2121-2129.
[3]	REGEV O. On Lattices, Learning with Errors, Random Linear Codes, and Cryptography[C]//ACM. The 37th Annual ACM Symposium on Theory of Computing-STOC 2005, May 21-24, 2005, Baltimore, Maryland, USA. New York: ACM, 2005: 94-103.
[4]	GENTRY C, PEIKERT C, VAIKUNTANATHAN V.Trapdoors for Hard Lattices and New Cryptographic Constructions[C]//ACM. The 40th Annual ACM Symposium on Theory of Computing-STOC 2008, May 17-20, 2008, Victoria, British Columbia, Canada. New York: ACM, 2008: 197-206.
[5]	AGRAWAL S, BONEH D, BOYEN X. Efficient Lattice (H)IBE in the Standard Model[C]//IACR. The 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques-Eurocrypt 2010, May 30-June 3, 2010, Nice, French Riviera, France. Heidelberg: Springer, 2010: 553-572.
[6]	YAMADA S.Adaptively Secure Identity-based Encryption from Lattices with Asymptotically Shorter Public Parameters[C]//IACR. The 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques-Eurocrypt 2016, May 8-12, 2016, Vienna, Austria. Heidelberg: Springer, 2016: 32-62.
[7]	YE Qing, HU Mingxing, TANG Yongli, et al.Novel Hierarchical Identity-based Encryption Scheme from Lattice[J]. Journal on Communications, 2017, 38(11): 54-64.
	叶青, 胡明星, 汤永利, 等. 新的格上基于身份的分级加密方案[J]. 通信学报. 2017, 38(11): 54-64.
[8]	KAWACHI A, TANAKA K, XAGAWA K.Multi-bit Cryptosystems Based on Lattice Problems[C]//IACR. The 10th International Conference on Practice and Theory in Public-key Cryptography-PKC 2007, April 16-20, 2007, Beijing, China. Heidelberg: Springer, 2007: 315-329.
[9]	PEIKERT C, VAIKUNTANATHAN V, WATERS B.A Framework for Efficient and Composable Oblivious Transfer[C]//IACR. The 28th Annual International Cryptology Conference-Crypto 2008, August 17-21, 2008, Santa Barbara, California, USA. Heidelberg: Springer, 2008: 554-571.
[10]	LI Zengpeng, MA Chunguang, ZHANG Lei,et al.Two Types LWE-based Multi-bit Lattice-based Encryption Schemes[J].Netinfo Security, 2017, 17(10): 1-7.
	李增鹏, 马春光, 张磊, 等. 两类基于容错学习的多比特格公钥加密方案[J]. 信息网络安全, 2017, 17(10): 1-7.
[11]	MARTINS P, SOUSA L, MARIANO A. A Survey on Fully Homomorphic Encryption: an Engineering Perspective[EB/OL]. ,2018-7-23.
[12]	ACAR A, AKSU H, ULUAGAC A S, et al.A Survey on Homomorphic Encryption Schemes: Theory and Implementation[J]. ACM Computing Surveys. 2018, 51(4):1-35.
[13]	LIU Mingjie, WANG An.Fully Homomorphic Encryption and Its Applications[J]. Journal of Computer Research and Development, 2014, 51(12): 2593-2603.
	刘明洁, 王安. 全同态加密研究动态及其应用概述[J]. 计算机研究与发展. 2014, 51(12): 2593-2603.
[14]	LV Haifeng, DING Yong, DAI Hongyan, et al.Survey on LWE-based Fully Homomorphic Encryption Scheme[J]. Netinfo Security, 2015, 15(1): 32-38.
	吕海峰, 丁勇, 代洪艳, 等. LWE上的全同态加密研究[J]. 信息网络安全, 2015, 15(1): 32-38.
[15]	BRAKERSKI Z, GENTRY C, HALEVI S.Packed Ciphertexts in LWE-based Homomorphic Encryption[C]//IACR. The 16th International Conference on Practice and Theory in Public-key Cryptography-PKC 2013, February 26-March 1, 2013, Nara, Japan. Heidelberg: Springer, 2013: 1-13.
[16]	HIROMASA R, ABE M, OKAMOTO T.Packing Messages and Optimizing Bootstrapping in GSW-FHE[C]//IACR. The 18th International Conference on Practice and Theory in Public-key Cryptography-PKC 2015, March 30-April 1, 2015, Maryland, USA. Heidelberg: Springer, 2015: 699-715.
[17]	WANG Biao, WANG Xueqing, XUE Rui, et al.Matrix FHE and Its Application in Optimizing Bootstrapping[J]. The Computer Journal, 2018, 61(12): 1845-1861.
[18]	ALWEN J, PEIKERT C.Generating Shorter Bases for Hard Random Lattices[J]. Theory of Computing Systems. 2011, 48(3): 535-553.
[19]	MICCIANCIO D, REGEV O.Worst-case to Average-case Reductions Based on Gaussian Measures[J]. SIAM Journal on Computing, 2007, 37(1): 267-302.
[20]	PERIKERT C.Public-key Cryptosystems from the Worst-case Shortest Vector Problem[C]//ACM. The 41st Annual ACM Symposium on Theory of Computing-STOC 2009, May 31-June 2, 2009, Bethesda, Maryland, USA. New York: ACM, 2009: 333-342.
[21]	MICCIANCIO D, MOL P.Pseudorandom Knapsacks and the Sample Complexity of LWE Search-to-decision Reductions[C]//IACR. The 31st Annual International Cryptology Conference-Crypto 2011, August 14-18, 2011, Santa Barbara, California, USA. Heidelberg: Springer, 2011: 465-484.
[22]	MICCIANCIO D, PEIKERT C.Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller[C]//IACR. The 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques-Eurocrypt 2012, April 15-19, 2012, Cambridge, UK. Heidelberg: Springer, 2012: 700-718.
[23]	DODIS Y, REYZIN L, SMITH A.Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data[C]//IACR. The 23rd Annual International Conference on the Theory and Applications of Cryptographic Techniques-Eurocrypt 2004, May 2-6, 2004, Interlaken, Switzerland. Heidelberg: Springer, 2004: 523-540.