基于多变量和LRPC码的抗量子密码方案研究

doi:10.3969/j.issn.1671-1122.2019.08.006

信息网络安全 ›› 2019, Vol. 19 ›› Issue (8): 36-43.doi: 10.3969/j.issn.1671-1122.2019.08.006

基于多变量和LRPC码的抗量子密码方案研究

韩益亮(), 王众

武警工程大学密码工程学院,陕西西安710086

收稿日期:2019-01-15 出版日期:2019-08-10 发布日期:2020-05-11
作者简介:
作者简介：韩益亮（1977—）,男,甘肃,教授,博士,主要研究方向为抗量子密码;王众（1995—）,男,山东,硕士研究生,主要研究方向为抗量子密码。
基金资助:
国家自然科学基金[61572521]

Anti-quantum Cryptography Scheme Based on Multivariate and LRPC Codes

YiLiang HAN(), Zhong WANG

Engineering University of PAP, College of Cryptographic Engineering, Xi’an Shaanxi 710086, China

Received:2019-01-15 Online:2019-08-10 Published:2020-05-11

摘要/Abstract

摘要：

多变量公钥密码与编码密码,具有抵御量子计算攻击的能力以及较高的效率,二者因而作为抗量子密码的优良候选者。编码密码在构造核心映射时与多变量公钥密码有一定的相似性,数据压缩的能力也是编码密码的优势之一。因此将编码密码与多变量公钥密码的核心映射相结合来增强多变量公钥密码的安全性成为一种可行的选择。文章将LRPC码与多变量密码中的Simple Matrix改进版相结合,构造出新的方案,该方案相比于Cubic Simple Matrix方案,密文扩展率下降了50％,并结合了编码密码的优势。该方案由于是在Simple Matrix改进版基础上构造的,因此相比于之前提出的基于LRPC码和多变量的签密方案在选择LRPC码时更加灵活,经实验验证,该方案满足IND-CPA安全。

关键词: 多变量公钥密码, LRPC码, 核心映射, 安全性分析

Abstract:

Multivariable publickey cryptography and coding cryptography have the ability to resist quantum computation attacks and high efficiency of use, both of which are therefore reliable candidates for anti-quantum cryptography. In the multivariable public key cryptography, the construction of the central mapping is very important. Because the coding cryptography has similar matrix operations with multivariate cryptography and the ability of data compression, it is a hot direction to combine coding cryptography with multivariate cryptography. This paper combines the LRPC code in the coding with the Simple Matrix improvement scheme in multivariate cryptography to construct a new scheme. Compared to the Cubic Simple Matrix scheme, the ciphertext expansion rate is reduced by 50%, and the advantages of the coded password are combined. Since the new scheme is constructed on the basis of the improved version of Simple Matrix, it is more flexible when selecting LRPC codes than the previous signcryption schemes based on LRPC and multivariate cryptosystem. In addition, under the random oracle model, the new scheme was proved to satisfy IND-CPA security.

Key words: multivariable public key cryptography, LRPC, central mapping, security analysis

中图分类号:

TP309

韩益亮, 王众. 基于多变量和LRPC码的抗量子密码方案研究[J]. 信息网络安全, 2019, 19(8): 36-43.

YiLiang HAN, Zhong WANG. Anti-quantum Cryptography Scheme Based on Multivariate and LRPC Codes[J]. Netinfo Security, 2019, 19(8): 36-43.

图/表 1

参考文献 21

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方案	参数(F=GF(q),s,n,m,d,r)	公钥/KB	私钥/KB	明文/bit	密文/bit
Cubic Simple Matrix	(GF(2⁸),6,36,72,0,0)	1120	50	201	402
Cubic Simple Matrix	(GF(2⁸),8,64,128,0,0)	5986	153	512	1024
本文方案	(GF(2⁸),6,36,72,5,4)	1202	53	201	201
本文方案	(GF(2⁸),8,64,128,5,4)	6058	154	512	512

基于多变量和LRPC码的抗量子密码方案研究

Anti-quantum Cryptography Scheme Based on Multivariate and LRPC Codes

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