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| Efficient hierarchical identity based encryption scheme in the standard model over lattices |
| Feng-he Wang, Chun-xiao Wang, Zhen-hua Liu |
| Department of Mathematics and Physics, Shandong Jianzhu University, Jinan 250014, China; School of Mathematics and Statistics, Xidian University, Xi'an 710071, China |
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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 (dm2+mn)logq bits and whose message-ciphertext expansion factor is only logq, where d is the maximum hierarchical depth and (n,m,q) 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 d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2dm2+mn+m)logq. To reduce the message-ciphertext expansion factor of the proposed scheme to logq, the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m2 bits of plaintext are encrypted into m2logq 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.
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Received: 13 July 2015
Published: 05 August 2016
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标准模型下基于高效分级身份的格上加密方案
概要：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(dm2+mn)logq比特，而消息-密文扩展因子仅为logq，其中d为最大分级深度，(n,m,q)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d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2d个同样尺寸的矩阵，公钥尺寸达到(2dm2+mn+m)logq。为了将该方案的消息-密文扩展因子压缩到logq，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m2比特明文并得到m2logq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。
关键词：
分级身份加密,
格密码,
标准模型,
差错学习问题,
高斯
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