MDS矩阵构造方法

李鹏飞; 李永强

doi:10.11959/j.issn.2096-109x.2016.00063

您当前的位置：

首页 >

文章列表页 >

MDS矩阵构造方法

学术论文 | 更新时间：2024-06-03

- MDS矩阵构造方法
- Construction of MDS matrices
- 网络与信息安全学报 2016年2卷第6期页码：44-53
- 作者机构：
  
  1. 中国科学院信息工程研究所信息安全国家重点实验室，北京 100093
  2. 中国科学院大学，北京 100049
- 作者简介：
  
  [ "李鹏飞（1991-），男，陕西渭南人，中国科学院信息工程研究所硕士生，主要研究方向为密码学。" ]
  [ "李永强（1982-），男，吉林集安人，博士，中国科学院信息工程研究所副研究员，主要研究方向为对称密码算法关键部件的构造、对称密码算法分析。" ]
- 基金信息：
  
  国家自然科学基金资助项目;The National Natural Science Foundation of China(61379142);国家自然科学基金资助项目;The National Natural Science Foundation of China(61303255)
- DOI：10.11959/j.issn.2096-109x.2016.00063
  中图分类号： TP393
- 网络首发：2016-06，
  
  纸质出版：2016-06-15
- 稿件说明：
移动端阅览
李鹏飞, 李永强. MDS矩阵构造方法[J]. 网络与信息安全学报, 2016,2(6):44-53.

Peng-fei LI, Yong-qiang LI. Construction of MDS matrices[J]. Chinese Journal of Network and Information Security, 2016, 2(6): 44-53.
李鹏飞, 李永强. MDS矩阵构造方法[J]. 网络与信息安全学报, 2016,2(6):44-53. DOI： 10.11959/j.issn.2096-109x.2016.00063.

Peng-fei LI, Yong-qiang LI. Construction of MDS matrices[J]. Chinese Journal of Network and Information Security, 2016, 2(6): 44-53. DOI： 10.11959/j.issn.2096-109x.2016.00063.

摘要

针对MDS矩阵的设计策略做了综述。阐述了MDS矩阵构造中的关键问题，并对当前典型和常见MDS矩阵的构造方法从原理、实现机制等方面进行了分析和讨论。另外，调研了最近几年关于轻量级MDS矩阵的研究成果。

Abstract

A survey for MDS matrices design strategy was made.Design strategies and the key issues during the de-sign were elaborated

and many aspects such as principle and implementation mechanisms of some typical and common construction of MDS matrices were analyzed and discussed.In addition

the research results on lightweight MDS matrices in recent years were investigated.

关键词

Keywords

references

SHANNON C E . Communication theory of secrecy systems [J ] . Bell System Technical Journal , 2015 , 28 ( 4 ): 656 - 715 .

BIHAM E , SHAMIR A . Differential cryptanalysis of DES-like cryptosystems [J ] . Journal of Cryptology , 1991 , 4 ( 1 ): 3 - 72 .

MATSUI M . Linear cryptanalysis method for DES cipher [M ] // Advances in Cryptology — EUROCRYPT . Berlin Heidelberg : Springer , 1993 : 386 - 397 .

DAEMEN J , RIJMEN V . The design of rijndael,AES—the ad-vanced encryption standard [M ] Advances in Cryptology — EUROCRYPT . Berlin Heidelberg : Springer , 2002 .

RIJMEN V , DAEMEN J . The cipher SHARK [C ] // Fast Software Encryption .c 1996 : 99 - 112 .

SCHNEIER B , KELSEY J , WHITING D , et al . Twofish:a 128 bit block cipher [C ] // The 1st AES Candidate Conference on National Institute for Standards and Technology .c 1998 .

SCHNEIER B , KELSEY J , WHITING D , et al . The twofish en-cryption algorithm [M ] . 1999 .

DAEMEN J , KNUDSEN L R , RIJMEN V . The block cipher square [C ] // The 4th fast software encryption workshop .c 1997 : 149 - 165 .

BARRETO P , RIJMEN V . The anubis block cipher [EB/OL ] . http://www.larc.usp.br/～pbarreto/AnubisPage.html http://www.larc.usp.br/～pbarreto/AnubisPage.html .

BARRETO P , RIJMEN V . The khazad legacy-level block cipher [J ] . Primitive Submitted to NESSIE , 2000 .

JUNOD P , VAUDENAY S . FOX:a new family of block ci-phers [C ] // Selected Areas in Cryptography .c 2004 : 114 - 119 .

SHIRAI T , SHIBUTANI K , AKISHITA T , et al . The 128 bit block cipher CLEFIA [C ] // International Workshop on Fast Software En-cryption .c 2007 : 181 - 195 .

GUO J , PEYRIN T , POSCHMANN A , et al . The LED block ci-pher [C ] // International Workshop on Cryptographic Hardware and Embedded Systems .c 2011 : 326 - 341 .

WATANABE D , FURUYA S , YOSHIDA H , et al . A new key-stream generator MUGI [C ] // FSE 2002 .c 2002 : 179 - 194 .

FILHO G D , BARRETO P , RIJMEN V . The maelstrom-0 Hash function [C ] // The 6th Brazilian Symposium on Information and Computer Systems Security .c 2006 .

GAURAVARAM P , KNUDSEN L R , MATUSIEWICZ K , et al . Grøstl a SHA-3 candidate [EB/OL ] . http://www.groestl.info http://www.groestl.info .

BARRETO P S L M , RIJMEN V . Encyclopedia of cryptography and security [C ] // 2nd Edn .c 2011 : 1384 - 1385 .

GUO J , PEYRIN T , POSCHMANN A . The PHOTON family of lightweight hash functions [C ] // Rogaway-CRYPTO 2011 .c 2011 : 222 - 239 .

DAMGÅRD I B . A design principle for hash functions [C ] // Ad-vances in Cryptology-CRYPTO'89 .c 1990 : 416 - 427 .

RAO A R , BHIMASANKARAM P . Linear algebra [M ] . Hindu-stan Book Agency .

KISHAN C G , INDRANIL G R . On constructions of circulant MDS matrices for lightweight cryptography [C ] // ISPEC .c 2014 : 564 - 576 .

YOUSSEF A M , MISTER S , TAVARES S E . On the design of linear transformations for substitution permutation encryption net-works [C ] // Workshop On Selected Areas in Cryptography(SAC) .c 1997 : 40 - 48 .

WILLIAMS F J M , SLOANE N J A . The theory of error correcting codes [M ] Elsevier , 1977 .

SAJADIEH M , DAKHILALIAN M , MAL H , et al . On construc-tion of involutory MDS matrices from vandermonde matrices in [C ] // Design,Codes Cryptography .c 2012 : 1 - 22 .

LINT J H V . Algebraic geometric codes [M ] // Coding theory and design theory . New York : Springer , 1990 : 137 - 162 .

AUGOT D , FINIASZ M . Direct construction of recursive MDS diffusion layers using shortened BCH codes [C ] // International Workshop on Fast Software Encryption .c 2014 : 3 - 17 .

GOPPA V D . A new class of linear correcting codes [J ] . Problemy Peredachi Informatsii , 1970 , 6 ( 3 ): 24 - 30 .

BERGER T P , OURIVSKI A . Construction of new MDS codes from gabidulin codes [C ] // ACCT .c 2009 : 40 - 47 .

杨谱 . 分组迭代密码函数的扩散层分析及应用 [D ] . 西安 : 西安电子科技大学 , 2013 .

YANG P . Cryptanalysis and applications for diffusion layer of iterated block function [D ] . Xi’an : Xidian University , 2013 .

JUNOD P , VAUDENAY S . Perfect diffusion primitives for block ciphers [C ] // International Workshop on Selected Areas in Cryptog-raphy .c 2004 : 84 - 99 .

何凌云 . 分组密码扩散层的改进研究 [D ] . 杭州 : 杭州电子科技大学 , 2011 .

HE L Y . Research on the improvement of block cipher diffusion layer [D ] . Hangzhou : Hangzhou Dianzi University , 2011 .

郭艳珍，韩文报，赵龙，等． AES 列混合变换 [J ] . 解放军理工大学学报(自然科学版) , 2009 ( 3 ): 232 - 236 .

GUO Y Z , HAN W B , ZHAO L , et al . AES mixColumns transformation [J ] . Journal of PLA University of Science and Technol-ogy( Natural Science Edition) , 2009 ( 3 ): 232 - 236 .

刘丽辉，徐林杰，张祖平，等．有限域上Hadamard型MDS矩阵研究 [J ] . 舰船电子工程 , 2014 ( 5 ): 41 - 45 .

LIU L H , XU L J , ZHANG Z P , et al . Investigate for MDS matrix of hadamard type on finite fields [J ] . Ship Electronic Engineering , 2014 ( 5 ): 41 - 45 .

崔霆，金晨辉 . 对合 Cauchy-Hadamard 型 MDS 矩阵的构造 [J ] . 电子与信息学报 , 2010 , 32 ( 2 ): 500 - 503 .

CUI T , JIN C H . Construction of involution cauchy-hadamard type MDS matrices [J ] . Journal of Electronics ＆ Information Technology , 2010 , 32 ( 2 ): 500 - 503 .

GUPTA K C , RAY I G . On constructions of involutory MDS ma-trices [C ] // International Conference on Cryptology in Africa .c 2013 : 43 - 60 .

NAKAHARA J R , ÉLcio A . A new involutory mds matrix for the AES [J ] . Network Security , 2009 , 9 ( 2 ): 109 - 116 .

DEHNAVI S M , SHAMSABAD M R M , RISHAKANI A M , et al . Efficient MDS diffusion layers through decomposition of matri-ces [M ] // IACR Cryptology . ePrint Archive , 2015 .

SIM S M , KHOO K , OGGIER F , et al . Lightweight MDS Involu-tion Matrices [C ] // FSE 2015 .c 2015 .

LIU M , SIM S M . Lightweight MDS generalized circulant matri-ces [C ] // Fast Software Encryption .c 2016 .

LI Y , WANG M . On the construction of lightweight circulant involutory MDS matrices [C ] // Fast Software Encryption .c 2016 .

崔霆，金晨辉 . 分组密码 Cauchy 型 MDS 扩散结构的几点注记 [J ] . 电子学报 , 2011 , 39 ( 7 ): 1603 - 1607 .

CUI T , JIN C H . Several remarks of Cauchy type MDS diffusion layer for block cipher [J ] . Acta Electronica Sinica , 2011 , 39 ( 7 ): 1603 - 1607 .

CUI T , JIN C , KONG Z . On compact cauchy matrices for substitu-tion-permutation networks [J ] . IEEE Transactions on Computers , 2015 , 64 ( 7 ): 2098 - 2102 .

马庆禄，魏悦川，潘晓中 . 基于 Cauchy 矩阵的线性变换的研究 [J ] . 计算机应用研究 , 2015 , 32 ( 7 ): 2144 - 2146 .

MA Q L , WEI Y C , PAN X Z . Research on linear transformations based on Cauchy matrix [J ] . Application Research of Computers , 2015 , 32 ( 7 ): 2144 - 2146 .

LACAN J , FIMES J . Systematic MDS erasure codes based on vandermonde matrices [J ] . IEEE Communications Letters , 2004 , 8 ( 9 ): 570 - 572 .

无线局域网产品中使用的SMS4算法 [EB/OL ] . http://www.oscca.gov.cn/UpFile/200621016423197990.pdf http://www.oscca.gov.cn/UpFile/200621016423197990.pdf .

SMS4 algorithm used in wireless LAN products [EB/OL ] . http://www.oscca.gov.cn/UpFile/200621016423197990.pdf http://www.oscca.gov.cn/UpFile/200621016423197990.pdf .

ETSI/SAGE TS 35.222-2011,specification of the 3GPP confiden-tiality and integrity algorithms 128-EEA3 ＆ 128-EIA3;document 2:ZUC Specification[ [S ] .

HONG D , SUNG J , HONG S , et al . HIGHT:a new block cipher suitable for low-resource device [M ] // Cryptographic Hardware and Embedded Systems-CHES 2006 . Berlin Heidelberg : Springer , 2006 : 46 - 59 .

National institute of standards and technology [S ] . The Secure Hash Standard , 2002 .

RIVEST R L , AGRE B , BAILEY D V , et al . The MD6 hash func-tion [J ] . Invited Talk at CRYPTO , 2008 .

ZHANG W , WU W , FENG D , et al . Some new observations on the SMS4 block cipher in the Chinese WAPI standard [M ] // Information Security Practice and Experience . Berlin Heidelberg : Springer , 2009 : 324 - 335 .

王金波 . 基于循环移位构造最优线性变换 [C ] . 中国密码学会2007年会，成都．c 2007 : 306 - 307 .

WANG J B . The optimal permutation in cryptography based on cyclic-shift linear transform [C ] // China Crypt'2007,Chengdu .c 2007 : 306 - 307 .

李瑞林，熊海，李超 . 基于循环移位和异或运算的对合线性变换研究 [J ] . 国防科技大学学报 , 2012 , 34 ( 2 ): 46 - 50 .

LI R , XIONG H , LI C . Research on involutional linear transforma-tions based on rotation and XOR [J ] . Journal of National University of Defense Technology , 2012 , 34 ( 2 ): 46 - 50 .

ANDREEVA E , BILGIN B , BOGDANOV A , et al . PRIMATEs v1.02 submission to the CAESAR competition [EB/OL ] . http://competitions.cr.yp.to/round2/primatesv102.pdf http://competitions.cr.yp.to/round2/primatesv102.pdf .

SAJADIEH M , DAKHILALIAN M , MALA H , et al . Recursive diffusion layers for block ciphers and Hash functions [C ] // FSE 2012 .c 2012 : 385 - 401 .

WU S , WANG M , WU W , et al . Recursive diffusion layers for (lightweight) block ciphers and Hash functions [C ] // SAC 2012 .c 2012 : 355 - 371 .

AUGOT D , FINIASZ M . Exhaustive search for small dimension recursive MDS diffusion layers for block ciphers and hash func-tions [C ] // 2013 IEEE International Symposium on Information Theory (ISIT) .c 2013 : 1551 - 1555 .

BERGER T P . Construction of recursive MDS diffusion layers from gabidulin codes [C ] // Indocrypt .c 2013 : 274 - 285 .

KHOO K , PEYRIN T , POSCHMANN A , et al . FOAM:searching for hardware optimal spn structures and components with a fair comparison [C ] // Cryptographic Hardware and Embedded Systems (CHES) .c 2014 : 433 - 450 .

刘鸿博，金晓刚，段俊红 . 分组密码中 MDS 矩阵的实现方法效能分析 [J ] . 信息安全与通信保密 , 2013 ( 10 ): 77 - 78 .

LIU H B , JIN X G , DUAN J H . Efficiency analysis of MDS matrix applied in block cipher [J ] . Information Security and Communica-tions Privacy , 2013 ( 10 ): 77 - 78 .

浏览量

1160

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

改进的Joltik-BC-128算法的中间相遇攻击

LowMC实例的差分枚举攻击效果分析

基于密码结构的扩散层构造

自动化搜索ARX密码差分特征的方法