基于Polar码改进的RLCE公钥加密方案

doi:10.11959/j.issn.2096-109x.2020068

网络与信息安全学报 ›› 2020, Vol. 6 ›› Issue (5): 110-118.doi: 10.11959/j.issn.2096-109x.2020068

基于Polar码改进的RLCE公钥加密方案

李喆¹,韩益亮^1,²(),李鱼¹

¹ 武警工程大学密码工程学院，陕西西安 710086
² 武警部队密码与信息安全保密重点实验室，陕西西安 710086

修回日期:2020-03-21 出版日期:2020-10-15 发布日期:2020-10-19
作者简介:李喆（1994- ），男，安徽宿州人，武警工程大学硕士生，主要研究方向为抗量子密码|韩益亮（1977- ），男，甘肃会宁人，武警工程大学教授、博士生导师，主要研究方向为信息安全、舆情分析|李鱼（1995- ），男，重庆丰都人，武警工程大学硕士生，主要研究方向为格密码
基金资助:
国家自然科学基金(61572521);武警工程大学科研创新团队科学基金(KYTD201805)

Improved RLCE public key encryption scheme based on Polar codes

Zhe LI¹,Yiliang HAN^1,²(),Yu LI¹

¹ College of Cryptographic Engineering,Engineering University of PAP,Xi’an 710086,China
² Key Laboratory of PAP for Cryptology and Information Security,Xi’an 710086,China

Revised:2020-03-21 Online:2020-10-15 Published:2020-10-19
Supported by:
The National Natural Science Foundation of China(61572521);The Scientific Foundation of the Scientific Research and Innovation Team of Engineering University of PAP(KYTD201805)

摘要/Abstract

摘要：

针对PolarRLCE方案不具有语义安全，易受到自适应选择密文攻击（IND-CCA2，adaptively chosen ciphertext attacks）的缺点。在RLCE（random linear code encryption）方案的基础上，利用RLCE方案的结构和Polar码的极化性质，将Polar码作为方案的底层编码，通过RLCEspad消息填充的方法，采用普通编码对密文进行编码，提出一种具有语义安全、可以达到IND-CCA2安全的改进的RLCE公钥加密方案。改进后的方案将公钥矩阵转为系统矩阵，减小了公钥存储空间；对部分私钥进行预计算，减小了私钥存储空间。通过分析，所提方案未改变PolarRLCE方案的结构，可以抵抗针对汉明循环码的结构化等攻击。在128 bit安全级别，相较于HermitianRLCE方案、GRSRLCE方案和GoppaMcEliece方案，所提方案的公钥尺寸分别减少了4%、46.5%、47.9%。

关键词: Polar码, 随机线性码加密, 消息填充, 自适应选择密文攻击, 结构化攻击

Abstract:

For PolarRLCE has no semantic security and be vulnerable to adaptively chosen ciphertext attacks.Based onrandom linear code encryptionscheme,the structure of the RLCE scheme and Polar code polarization propertieswere used to make the Polar code as underlying encoding scheme,and through the method of RLCEspad message padding,a kind of improved public key encryption scheme which considers semantic security and can resistant toadaptively chosen ciphertext attacks was proposed.The improved scheme transformed the public key matrix into a system matrix and reduces the storage space of the public key.Some pre-computation for private key are estimated to reduce the storage space of private key.Through analysis,this scheme does not change the structure of PolarRLCE scheme,which can resist structural attacks against hamming quasi-cyclic codes.At the 128 bit security level,compared with HermitianRLCE scheme,GRSRLCE scheme and GoppaMcEliece scheme,the public key size of this scheme decreased by 4%,46.5% and 47.9% respectively.

Key words: Polar code, random linear code encryption, message padding, adaptively chosen ciphertext attacks, structural attacks

中图分类号:

TP309.7

李喆,韩益亮,李鱼. 基于Polar码改进的RLCE公钥加密方案[J]. 网络与信息安全学报, 2020, 6(5): 110-118.

Zhe LI,Yiliang HAN,Yu LI. Improved RLCE public key encryption scheme based on Polar codes[J]. Chinese Journal of Network and Information Security, 2020, 6(5): 110-118.

图/表 2

参考文献 26

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信息集译码	公钥尺寸/kB
信息集译码	本文	Polar RLCE^[14]	Hermitian RLCE^[13]	GRS RLCE^[11]	Goppa McEliece^[8]
128 bit安全级别	98	98	103	183	188
192 bit安全级别	256	256	198	440	490
256 bit安全级别	380	380	313	1203	900

基于Polar码改进的RLCE公钥加密方案

Improved RLCE public key encryption scheme based on Polar codes

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