理想格上基于身份的加密算法研究  

Research on identity-based encryption algorithms on the ideal lattice

作　　者：黄文晋 唐春明[2,3] 贾惠文 HUANG Wen-jin;TANG Chun-ming;JIA Hui-wen(School of Mathematics and Information Science,Guangzhou 510006,China;Guangzhou Center for Applied Mathematics,Guangzhou 510006,China;The Key Laboratory of Information Security Technology,Guangzhou 510006,China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006 [2]广州大学广州数学中心,广东广州510006 [3]广州大学广东省广州市共建信息安全技术重点实验室,广东广州510006

出　　处：《广州大学学报（自然科学版）》2022年第4期37-45,共9页Journal of Guangzhou University:Natural Science Edition

摘　　要：格上基于身份的加密算法(Identity-Based Encryption, IBE)可以抵抗量子攻击,能有效解决公钥密码管理系统效率低的问题,因此,国内外学者提出了一系列基于格的身份加密方案。文章运用Jia等提出的基于非球形高斯的原像采样算法,对IBE方案中用户私钥的提取进行了改进。实验结果表明,在保证IBE加密与解密正确性的情况下,可以有效降低用户私钥的尺寸,提升IBE方案的空间效率。文章运用的基于非球形高斯的用户私钥提取算法有2个模式:(1)采用模式1后,在42.6-bit的安全性下,用户私钥的尺寸由21.75 kB减小至13.31 kB;在109.8-bit的安全性下,用户私钥的尺寸由50.36 kB减小至32.25 kB;(2)采用模式2后,在42.6-bit的安全性下,用户私钥的尺寸由21.75 kB减小至10.18 kB;在109.8-bit的安全性下,用户私钥的尺寸由50.36 kB减小至21.86 kB,相比于模式1,模式2能更有效地节省用户私钥的内存开销。Identity-Based Encryption(IBE) on lattices resists quantum attacks and effectively solves the problem of low efficiency of public key cryptography management systems, so scholars at home and abroad have proposed a series of lattice-based identity encryption schemes. In this paper, the extraction of user private keys in the IBE scheme is improved by using the prototype sampling algorithm based on non-spherical Gaussian proposed by Jia, et al. Experimental results show that under the condition of ensuring the correctness of IBE encryption and decryption, the size of the user’s private key can be effectively reduced and the space efficiency of the IBE scheme can be improved. The non-spherical Gaussian-based user private key extraction algorithm used in this article has two modes:(1) After adopting mode 1, the size of the user’s private key is reduced from 21.75 kB to 13.31 kB under the security of 42.6-bit;under the security of 109.8-bit, the size of the user’s private key is reduced from 50.36 kB to 32.25 kB;(2) After adopting mode 2, under the security of 42.6-bit, the size of the user’s private key is reduced from 21.75 kB to 10.18 kB;under the security of 109.8-bit, the size of the user’s private key is reduced from 50.36 kB to 21.86 kB, which can more effectively save the memory overhead of the user’s private key than mode 1.

关 键 词：格密码 IBE 非球形高斯采样 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]