Efficient hierarchical identity based encryption scheme in the standard model over lattices

Feng-he WANG; Chun-xiao WANG; Zhen-hua LIU

doi:10.1631/FITEE.1500219

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Efficient hierarchical identity based encryption scheme in the standard model over lattices

Regular Papers | Updated：2022-05-19

- Efficient hierarchical identity based encryption scheme in the standard model over lattices
- 标准模型下基于高效分级身份的格上加密方案
- Frontiers of Information Technology & Electronic Engineering Vol. 17, Issue 8, Pages: 781-791(2016)
- Affiliations：
  
  1Department of Mathematics and Physics, Shandong Jianzhu University, Jinan 250014, China
  2School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
- Author bio：
  
  E-mail:fenghe2166@163.com
  E-mail:xiao2166@126.com
- Funds：
- DOI：10.1631/FITEE.1500219
  CLC： TP309
- Received：13 July 2015，
  
  Accepted：21 January 2016，
  
  Published：2016-08
- Accepted：
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Feng-he WANG, Chun-xiao WANG, Zhen-hua LIU. Efficient hierarchical identity based encryption scheme in the standard model over lattices[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(8): 781-791.
DOI：

Feng-he WANG, Chun-xiao WANG, Zhen-hua LIU. Efficient hierarchical identity based encryption scheme in the standard model over lattices[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(8): 781-791. DOI： 10.1631/FITEE.1500219.

摘要

本文在标准模型下，利用固定维数的格基代理算法提出了一种高效的格基分级身份加密方案。其公钥尺寸仅为(

)log

比特，而消息-密文扩展因子仅为log

，其中

为最大分级深度，(

)为公开参数。本文构造了一种新的公钥赋值算法，将1个随机、公开的矩阵平均赋值为两个身份比特，从而仅仅需要

个公开矩阵来构造标准模型下的HIBE方案；与之相比，Crypto 2010所提出的HIBE方案中需要2

个同样尺寸的矩阵，公钥尺寸达到(2

)log

。为了将该方案的消息-密文扩展因子压缩到log

，本文基于Gentry的加密方案建立了一种基础加密算法，一次加密操作中能够加密

比特明文并得到

log

比特密文。因此，文中所提方案在公钥尺寸、消息-密文扩展因子等方面具有一定的优势。基于差错学习问题的困难性，我们证明该方案在选择身份、选择明文攻击下是安全的。

Abstract

Using lattice basis delegation in a fixed dimension

we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only (

)log

bits and whose message-ciphertext expansion factor is only log

where

is the maximum hierarchical depth and (

) are public parameters. In our construction

a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits

which implies that

random public matrices are enough to build the proposed HIBE scheme in the standard model

compared with the case in which 2

such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2

)log

. To reduce the message-ciphertext expansion factor of the proposed scheme to log

the encryption algorithm of this scheme is built based on Gentry's encryption scheme

by which

bits of plaintext are encrypted into

log

bits of ciphertext by a one time encryption operation. Hence

the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem

we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.

关键词

Keywords

references

S Agrawal , , , D Boneh , , , X Boyen . . Efficient lattice (H)IBE in the standard model . . 2010a . . Proc. 29th Annual Int. Conf. on the Theory and Applications of Cryptographic Techniques . . 553 - - 572 . . DOI: 10.1007/978-3-642-13190-5_28 http://doi.org/10.1007/978-3-642-13190-5_28 . .

S Agrawal , , , D Boneh , , , X Boyen . . Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE . . 2010b . . Proc. 30th Annual Cryptology Conf . . 98 - - 115 . . DOI: 10.1007/978-3-642-14623-7_6 http://doi.org/10.1007/978-3-642-14623-7_6 . .

S Agrawal , , , X Boyen , , , V Vaikuntanathan , , , 等 . . Functional encryption for threshold functions (or fuzzy IBE) from lattices . . 2012 . . Proc. 15th Int. Conf. on Practice and Theory in Public Key Cryptography . . 280 - - 297 . . DOI: 10.1007/978-3-642-30057-8_17 http://doi.org/10.1007/978-3-642-30057-8_17 . .

J Alwen , , , C Peikert . . Generating shorter bases for hard random lattices . . 2009 . . Proc. 26th Int. Symp. on Theoretical Aspects of Computer Science . . 75 - - 86 . . DOI: 10.4230/LIPIcs.STACS.2009.1832 http://doi.org/10.4230/LIPIcs.STACS.2009.1832 . .

D Boneh , , , M Franklin . . Identity-based encryption from the Weil pairing . . 2001 . . Proc. 21st Annual Int. Cryptology Conf . . 213 - - 229 . . DOI: 10.1007/3-540-44647-8_13 http://doi.org/10.1007/3-540-44647-8_13 . .

D Boneh , , , X Boyen , , , EJ Goh . . Hierarchical identity based encryption with constant size ciphertext . . 2005 . . Proc. 24th Annual Int. Conf. on the Theory and Applications of Cryptographic Techniques . . 440 - - 456 . . DOI: 10.1007/11426639_26 http://doi.org/10.1007/11426639_26 . .

X Boyen , , , B Waters . . Anonymous hierarchical identity-based encryption (without random oracles) . . 2006 . . Proc. 26th Annual Int. Cryptology Conf . . 290 - - 307 . . DOI: 10.1007/11818175_17 http://doi.org/10.1007/11818175_17 . .

R Canetti , , , S Halevi , , , J Katz . . A forward-secure public-key encryption scheme . . 2003 . . Proc. Int. Conf. on the Theory and Applications of Cryptographic Techniques . . 255 - - 271 . . DOI: 10.1007/3-540-39200-9_16 http://doi.org/10.1007/3-540-39200-9_16 . .

D Cash , , , D Hofheinz , , , E Kiltz , , , 等 . . Bonsai trees, or how to delegate a lattice basis . . 2010 . . Proc. 29th Annual Int. Conf. on the Theory and Applications of Cryptographic Techniques . . 523 - - 552 . . DOI: 10.1007/978-3-642-13190-5_27 http://doi.org/10.1007/978-3-642-13190-5_27 . .

Y Cheng , , , ZY Wang , , , J Ma , , , 等 . . Efficient revocation in ciphertext-policy attribute-based encryption based cryptographic cloud storage . . J. Zhejiang Univ.-Sci. C (Comput. & Electron.) , , 2013 . . 14 ( ( 2 ): ): 85 - - 97 . . DOI: 10.1631/jzus.C1200240 http://doi.org/10.1631/jzus.C1200240 . .

C Gentry , , , S Halevi . . Hierarchical identity based encryption with polynomially many levels . . 2009 . . Proc. 6th Theory of Cryptography Conf . . 437 - - 456 . . DOI: 10.1007/978-3-642-00457-5_26 http://doi.org/10.1007/978-3-642-00457-5_26 . .

C Gentry , , , A Silverberg . . Hierarchical ID-based cryptography . . 2002 . . Proc. 8th Int. Conf. on the Theory and Application of Cryptology and Information Security . . 548 - - 566 . . DOI: 10.1007/3-540-36178-2_34 http://doi.org/10.1007/3-540-36178-2_34 . .

C Gentry , , , C Peikert , , , V Vaikuntanathan . . Trapdoors for hard lattices and new cryptographic constructions . . 2008 . . Proc. 40th Annual ACM Symp. on Theory of Computing . . 197 - - 206 . . DOI: 10.1145/1374376.1374407 http://doi.org/10.1145/1374376.1374407 . .

C Gentry , , , S Halevi , , , V Vaikuntanathan . . A simple BGN-type cryptosystem from LWE . . 2010 . . Proc. 29th Annual Int. Conf. on the Theory and Applications of Cryptographic Techniques . . 506 - - 522 . . DOI: 10.1007/978-3-642-13190-5_26 http://doi.org/10.1007/978-3-642-13190-5_26 . .

J Horwitz , , , B Lynn . . Toward hierarchical identitybased encryption . . 2014 . . Proc. Int. Conf. on the Theory and Applications of Cryptographic Techniques . . 466 - - 481 . . DOI: 10.1007/3-540-46035-7_31 http://doi.org/10.1007/3-540-46035-7_31 . .

YP Hu , , , H Lei , , , FH Wang , , , 等 . . Gaussian sampling of lattices for cryptographic applications . . Sci. China Inform. Sci. , , 2014 . . 57 ( ( 7 ): ): 072112.1 - - 072112.8 . . DOI: 10.1007/s11432-013-4843-4 http://doi.org/10.1007/s11432-013-4843-4 . .

D Micciancio , , , O Regev . . Worst-case to averagecase reductions based on Gaussian measures . . 2004 . . Proc. 45th Annual IEEE Symp. on Foundations of Computer Science . . 372 - - 381 . . DOI: 10.1109/FOCS.2004.72 http://doi.org/10.1109/FOCS.2004.72 . .

O Regev . . On lattices, learning with errors, random linear codes, and cryptography . . 2005 . . Proc. 37th Annual ACM Symp. on Theory of Computing . . 84 - - 93 . . DOI: 10.1145/1060590.1060603 http://doi.org/10.1145/1060590.1060603 . .

K Singh , , , C Pandurangan , , , AK Banerjee . . Adaptively secure efficient lattice (H)IBE in standard model with short public parameters . . 2012 . . Proc. 2nd Int. Conf. on Security, Privacy, and Applied Cryptography Engineering . . 153 - - 172 . . DOI: 10.1007/978-3-642-34416-9_11 http://doi.org/10.1007/978-3-642-34416-9_11 . .

K Singh , , , C Pandu Rangan , , , AK Banerjee . . Efficient lattice HIBE in the standard model with shorter public parameters . . 2014 . . Proc. 2nd IFIP TC5/8 Int. Conf. on Information and Communication Technology . . 542 - - 553 . . DOI: 10.1007/978-3-642-55032-4_56 http://doi.org/10.1007/978-3-642-55032-4_56 . .

FH Wang , , , YP Hu , , , BC Wang . . Lattice-based linearly homomorphic signature scheme over binary field . . Sci. China Inform. Sci. , , 2013 . . 56 ( ( 11 ): ): 112108.1 - - 112108.9 . . DOI: 10.1007/s11432-012-4681-9 http://doi.org/10.1007/s11432-012-4681-9 . .

FH Wang , , , ZH Liu , , , CX Wang . . Full secure identity-based encryption scheme with short public key size over lattices in the standard model . . Int. J. Comput. Math. , , 2016 . . 93 ( ( 6 ): ): 854 - - 863 . . DOI: 10.1080/00207160.2015.1029464 http://doi.org/10.1080/00207160.2015.1029464 . .

B Waters . . Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions . . 2009 . . Proc. 29th Annual Int. Cryptology Conf. . . 619 - - 636 . . DOI: 10.1007/978-3-642-03356-8_36 http://doi.org/10.1007/978-3-642-03356-8_36 . .

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