基于LPN困难问题的后量子安全公钥加密  

Post-quantum public key encryption based on LPN

作　　者：徐胜峰 李祥学[1,2] XU Shengfeng;LI Xiangxue(School of Computer Science and Technology,East China Normal University,Shanghai 200062,China;School of Software Engineering,East China Normal University,Shanghai 200062,China)

机构地区：[1]华东师范大学计算机科学与技术学院,上海200062 [2]华东师范大学软件工程学院,上海200062

出　　处：《西安邮电大学学报》2021年第5期47-61,共15页Journal of Xi’an University of Posts and Telecommunications

基　　金：国家自然科学基金项目(61971192);国家密码发展基金项目(MMJJ20180106)。

摘　　要：对基于LPN问题的公钥加密方案进行研究,提出一个低噪紧凑LPN(Exact LPN,xLPN)问题的变体VxLPN(Variant of the Exact LPN,VxLPN)问题,并证明了VxLPN问题和标准LPN问题一样困难。利用双陷门技术,分别构造基于VxLPN的选择明文攻击下的不可区分(Indistinguishability against Chosen Plaintext Attack,IND-CPA)安全的公钥加密方案和基于VxLPN的选择密文攻击下的不可区分(Indistinguishability against Chosen Ciphertext Attack,IND-CCA)安全的公钥加密方案。性能分析表明,在相同安全参数情况下,基于VxLPN的IND-CCA安全的公钥加密方案解码错误率更低。Public key encryption scheme based on LPN is studied.A variant problem of the low-noise compact LPN(xLPN)problem,Variant of the Exact LPN(VxLPN),is proposed.It is proved that the VxLPN problem is as hard as the standard LPN problem.Double trapdoor technology is used to construct the indistinguishability against Chosen Plaintext Attack(IND-CPA)and the indistinguishability against Chosen Ciphertext Attack(IND-CCA)secure public key encryption(PKE)schemes from VxLPN.For the same security parameters,our IND-CCA secure PKE has a lower decoding failure rate.

关 键 词：后量子密码学 LPN问题 公钥加密 低噪 解码错误率 

分 类 号：TN918.4[电子电信—通信与信息系统]