Niederreiter public-key cryptosystem based on QC-LDPC

doi:10.3724/SP.J.1087.2011.01906

Journal of Computer Applications ›› 2011, Vol. 31 ›› Issue (07): 1906-1908.DOI: 10.3724/SP.J.1087.2011.01906

• Information security • Previous Articles Next Articles

Niederreiter public-key cryptosystem based on QC-LDPC

Lei-Xin YANG,Wei-zhang DU

College of Computer and Communication Engineering, Changsha University of Science and Technology,Changsha Hunan 410114, China

Received:2011-01-10 Revised:2011-02-27 Online:2011-07-01 Published:2011-07-01
Contact: Lei-Xin YANG

基于QC-LDPC码的Niederreiter公钥密码体制

杨磊鑫,杜伟章

长沙理工大学计算机与通信工程学院，长沙 410114

通讯作者: 杨磊鑫
作者简介:杨磊鑫(1984-),男,安徽阜阳人,硕士研究生,主要研究方向:信息安全;杜伟章(1965-),女,湖南长沙人,教授,博士,主要研究方向:密码学、信息安全、信道编码。

Abstract

Abstract: A Niederreiter public-key cryptosystem based on QC-LDPC codes was proposed. As the check matrix of QC-LDPC codes is spare，who has the structure of circulative blocks and high error correction capability, compared with other public-key cryptosystem，the key sizes of the new cryptosystem is reduced and transmission rate is improved. A new parity-check matrix was mapped by invertible transformation matrix Q with diagonal form. The sparse characteristic of is countervailed. Through analyzing existing attacking methods，the security of the cryptosystem is confirmed to be improved.

Key words: Low-Density Parity-Check (LDPC) codes, QC-LDPC codes, cyclic matrices, Niederreiter public-key cryptosystem, security analysis

摘要： 提出基于QC-LDPC码构造的Niederreiter公钥密码体制。由于QC-LPDC码的校验矩阵具有稀疏和分块循环的特性，且QC-LPDC码的纠错能力大，与以往基于纠错码构造的公钥密码体制相比，该体制密钥量大大减少，提高了传信率。同时引入对角形式的可逆变换矩阵Q，通过线性变换产生新的校验矩阵，隐藏了码字的校验矩阵，可以抵消矩阵稀疏易攻击的弱点，增加了体制的安全性。并且通过对现有的攻击方法分析，证明了体制的安全性。

关键词: 低密度奇偶校验码, 准循环低密度奇偶校验码, 循环矩阵, Niederreiter公钥密码体制, 安全分析

Lei-Xin YANG Wei-zhang DU. Niederreiter public-key cryptosystem based on QC-LDPC[J]. Journal of Computer Applications, 2011, 31(07): 1906-1908.

杨磊鑫杜伟章. 基于QC-LDPC码的Niederreiter公钥密码体制[J]. 计算机应用, 2011, 31(07): 1906-1908.

References

［1］BERLEKAMP E R，McELIECE R J，van TILBORG H C A. On the inherent intractability of certain coding problems［J］. IEEE Transactions on Information Theory，1978，24(3)：384-386.

［2］McELIECE R J. A public-key cryptosystem based on algebraic coding theory［EB/OL］.［2010-10-20］.http://www.cs.colorado.edu/~jrblack/class/csci7000/f03/.../mceliece.pdf.

［3］NIEDERREITER H. Knapsack-type crypto-systems and algebraic coding theory［J］. Problems of Control and Information Theory,1986,15(2):159-166.

［4］GALLAGER R G. Low-density parity-check codes［J］. IRE Transactions on Information Theory,1962,8(1):21-28.

［5］MONICO C, ROSENTHAL J, SHOKROLLAHI A. Using low density parity check codes in the McEliece cryptosystem［C］// IEEE International Symposium on Information Theory. New York: IEEE, 2000：215.

［6］RICHARDSON T J， URBANKE R L. The capacity of low-density parity-check codes under message-passing decoding［EB/OL］.［2010-09-25］.http://www.ldpc-codes.com/papers/capacity.pdf.

［7］BALDI M,CHIARALUCE F. Cryptanalysis of a new instance of McEliece cryptosystem based on QC-LDPC codes［C］// IEEE International Symposium on Information Theory. New York: IEEE, 2007：2591-2595.

［8］LI YUANXING, DEN R H, WANG XINMEI. On the equivalence of McElieces and Niederreiters public-key cryptosystems［J］. IEEE Transactions on Information Theory, 1994，40(1)：271-273.

［9］TANNER R M．A recursive approach to low complexity codes［J］. IEEE Transactions on Information Theory, 1981,27(5)：533-547.

［10］STERN J. A method for finding codewords of small weight［C］// Proceedings of the 3rd International Colloquium on Coding Theory and Applications. London: Springer-Verlag, 1989：106-113.

［11］HIROTOMO M, MOHRI M, MORII M. A probabilistic computation method for the weight distributionof low-density parity-check codes［C］// IEEE International Symposium on Information Theory. New York:IEEE, 2005: 2166-2170.

[1]	SHEN Ziyi, WANG Weiya, JIANG Donghua, RONG Xianwei. Visual image encryption algorithm based on Hopfield chaotic neural network and compressive sensing [J]. Journal of Computer Applications, 2021, 41(10): 2893-2899.
[2]	WANG Zhong, HAN Yiliang. Dual public-key cryptographic scheme based on improved Niederreiter cryptosystem [J]. Journal of Computer Applications, 2019, 39(7): 1997-2000.
[3]	MA Lan, CUI Bohua, LIU Xuan, YUE Meng, WU Zhijun. Hidden semi-Markov model-based approach to detect DDoS attacks in application layer of SWIM system [J]. Journal of Computer Applications, 2019, 39(7): 1973-1978.
[4]	QIAO Ying, HE Yucheng, ZHOU Lin. Novel channel-adaptive coded cooperation scheme [J]. Journal of Computer Applications, 2015, 35(5): 1218-1223.
[5]	WANG Chang-da GONG Ting-ting ZHOU Cong-hua. Security analysis of digital rights management system based on usage control [J]. Journal of Computer Applications, 2012, 32(10): 2771-2775.
[6]	ZHANG Long-xiang. Security analysis of a RFID authentication protocol based on physically unclonable function [J]. Journal of Computer Applications, 2012, 32(08): 2280-2282.
[7]	. Analysis and improvement of proxy signature schemes over braid group [J]. Journal of Computer Applications, 2010, 30(4): 1030-1032.
[8]	. New image encryption algorithm based on composite chaotic system [J]. Journal of Computer Applications, 2010, 30(05): 1209-1211.
[9]	Xin ZHANG Fang-wei LI Chun-lan PAN. Improved remote authentication scheme with smart card [J]. Journal of Computer Applications, 2009, 29(4): 950-951.
[10]	. Improvement of ID-based proxy signature scheme without trusted PKG [J]. Journal of Computer Applications, 2008, 28(12): 3208-3210.
[11]	. Cryptanalysis of Ku-Chien’s Remote Authentication Scheme [J]. Journal of Computer Applications, 2006, 26(5): 1055-1057.

Niederreiter public-key cryptosystem based on QC-LDPC

基于QC-LDPC码的Niederreiter公钥密码体制

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 11

Recommended Articles

Metrics