标准模型下基于高效分级身份的格上加密方案

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

doi:10.1631/FITEE.1500219

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标准模型下基于高效分级身份的格上加密方案

常规文章 | Updated：2022-05-19

- 标准模型下基于高效分级身份的格上加密方案
- Efficient hierarchical identity based encryption scheme in the standard model over lattices
- 信息与电子工程前沿（英文） 2016年17卷第8期页码：781-791
- 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：
  
  Project supported by the National Natural Science Foundation of China (Nos. 61303198, 61471409, 61472470, and 61402112) and the Natural Science Foundation of Shandong Province, China (No. ZR2013FQ031)
- DOI：10.1631/FITEE.1500219
  中图分类号： TP309
- 收稿：2015-07-13，
  
  录用：2016-1-21，
  
  纸质出版：2016-08
- Accepted：
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标准模型下基于高效分级身份的格上加密方案[J]. 信息与电子工程前沿（英文）, 2016,17(8):781-791.

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.
标准模型下基于高效分级身份的格上加密方案[J]. 信息与电子工程前沿（英文）, 2016,17(8):781-791. DOI： 10.1631/FITEE.1500219.

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

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