基于Rotation-XOR的MDS线性变换的研究

在分组密码的扩散层中构造MDS线性变换可实现良好的扩散性. 构造MDS线性变换的方法有很多种, 其中基于Rotational-XOR的MDS线性变换软硬件实现效率高, 能够增强密码算法抵抗各种密码分析的能力, 适用于对称密码算法设计, 例如SMS4算法、ZUC算法等. 本文研究构造MDS线性变换的必要条件, 探寻分组规模为64、分块规模为8时基于Rotational-XOR的MDS线性变换. 首先通过分析首行矩阵的性质, 给出MDS矩阵的一个必要条件为矩阵中不可能有连续三个矩阵块相同, 根据该条件证明此规模下异或项数取最小值9项时不存在MDS线性变换, 并利用Magma软件验证该结论. 进而研...

Full description

Saved in:
Bibliographic Details
Published inJournal of Cryptologic Research Vol. 7; no. 5; p. 668
Main Authors ZHANG, Jing, WANG, Xin, Li-Na, ZHANG, YANG, Bo, Bing-Jie, HU, 张晶, 王鑫, 张丽娜, 杨波, 胡冰洁
Format Journal Article
LanguageChinese
Published Beijing Chinese Association for Cryptologic Research, Journal of Cryptologic Research 01.01.2020
Subjects
Algorithms
Cryptography
Diffusion barriers
Diffusion layers
Encryption
Linear transformations
Magma
Mathematical analysis
Matrices (mathematics)
Rotation
Online AccessGet full text
ISSN2097-4116
DOI10.13868/j.cnki.jcr.000398

Cover

Abstract 在分组密码的扩散层中构造MDS线性变换可实现良好的扩散性. 构造MDS线性变换的方法有很多种, 其中基于Rotational-XOR的MDS线性变换软硬件实现效率高, 能够增强密码算法抵抗各种密码分析的能力, 适用于对称密码算法设计, 例如SMS4算法、ZUC算法等. 本文研究构造MDS线性变换的必要条件, 探寻分组规模为64、分块规模为8时基于Rotational-XOR的MDS线性变换. 首先通过分析首行矩阵的性质, 给出MDS矩阵的一个必要条件为矩阵中不可能有连续三个矩阵块相同, 根据该条件证明此规模下异或项数取最小值9项时不存在MDS线性变换, 并利用Magma软件验证该结论. 进而研究异或项数为11项时的MDS线性变换, 将此情况下的所有线性变换分为三种情况, 分别是一个矩阵中至多有一个自由项、存在两个自由项落在同一矩阵中和三个自由项恰好落在同一矩阵中. 这三种情况将该规模下的8^8 * 56 * 55 * 54个线性变换等价划分为15种形式, 设计15个算法分别搜索后得到此规模下异或项数取11项时也不存在MDS线性变换. 本文的结论和搜索方法对研究分块规模为8的MDS扩散层具有启示作用.
AbstractList 在分组密码的扩散层中构造MDS线性变换可实现良好的扩散性. 构造MDS线性变换的方法有很多种, 其中基于Rotational-XOR的MDS线性变换软硬件实现效率高, 能够增强密码算法抵抗各种密码分析的能力, 适用于对称密码算法设计, 例如SMS4算法、ZUC算法等. 本文研究构造MDS线性变换的必要条件, 探寻分组规模为64、分块规模为8时基于Rotational-XOR的MDS线性变换. 首先通过分析首行矩阵的性质, 给出MDS矩阵的一个必要条件为矩阵中不可能有连续三个矩阵块相同, 根据该条件证明此规模下异或项数取最小值9项时不存在MDS线性变换, 并利用Magma软件验证该结论. 进而研究异或项数为11项时的MDS线性变换, 将此情况下的所有线性变换分为三种情况, 分别是一个矩阵中至多有一个自由项、存在两个自由项落在同一矩阵中和三个自由项恰好落在同一矩阵中. 这三种情况将该规模下的8^8 * 56 * 55 * 54个线性变换等价划分为15种形式, 设计15个算法分别搜索后得到此规模下异或项数取11项时也不存在MDS线性变换. 本文的结论和搜索方法对研究分块规模为8的MDS扩散层具有启示作用.
Author 张丽娜
YANG, Bo
杨波
Li-Na, ZHANG
ZHANG, Jing
Bing-Jie, HU
胡冰洁
张晶
WANG, Xin
王鑫
Author_xml – sequence: 1
  givenname: Jing
  surname: ZHANG
  fullname: ZHANG, Jing
– sequence: 2
  givenname: Xin
  surname: WANG
  fullname: WANG, Xin
– sequence: 3
  givenname: ZHANG
  surname: Li-Na
  fullname: Li-Na, ZHANG
– sequence: 4
  givenname: Bo
  surname: YANG
  fullname: YANG, Bo
– sequence: 5
  givenname: HU
  surname: Bing-Jie
  fullname: Bing-Jie, HU
– sequence: 6
  fullname: 张晶
– sequence: 7
  fullname: 王鑫
– sequence: 8
  fullname: 张丽娜
– sequence: 9
  fullname: 杨波
– sequence: 10
  fullname: 胡冰洁
BookMark eNotjztOw0AURacIEiFkA7TUY978PG9KFL5SUKSQgi7yjMeSDbKD7fQUtECTAtGAaBAboHDDZki8DSxBdaVTnKO7Q3p5kXtC9hgETGCIB1ng8us0yFwZAIAw2CN9DkZTyVi4TYZVlVpQKhTIJesTun5tfprHaVFHdVrk9GoybV_uL44u2-Z7c_exfnrePLx3pH1btZ9fu2QriW4qP_zfAZmdHM9GZ3Q8OT0fHY7pQqGhKraxZZFlCAl3IZfokYHUHpTngoWxAC0dT5QElFpHTGtrnPQ2sYjKOjEg-3_aRVncLn1Vz7NiWeZdcc7RKIZadgd-AbH6T-c
ContentType Journal Article
Copyright 2020. This work is published under http://www.jcr.cacrnet.org.cn/EN/column/column4.shtml Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2020. This work is published under http://www.jcr.cacrnet.org.cn/EN/column/column4.shtml Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID JQ2
DOI 10.13868/j.cnki.jcr.000398
DatabaseName ProQuest Computer Science Collection
DatabaseTitle ProQuest Computer Science Collection
DatabaseTitleList ProQuest Computer Science Collection
DeliveryMethod fulltext_linktorsrc
GroupedDBID -SI
-S~
ALMA_UNASSIGNED_HOLDINGS
CAJEI
JQ2
PB1
PB9
Q--
ID FETCH-LOGICAL-p589-5dbdb1ab180f2c6248e81047e05e2316d3074c2f5408477a177b9c4ebfb885bc3
ISSN 2097-4116
IngestDate Mon Jun 30 15:01:27 EDT 2025
IsPeerReviewed false
IsScholarly true
Issue 5
Language Chinese
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-p589-5dbdb1ab180f2c6248e81047e05e2316d3074c2f5408477a177b9c4ebfb885bc3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
PQID 2895187456
PQPubID 6503834
ParticipantIDs proquest_journals_2895187456
PublicationCentury 2000
PublicationDate 20200101
PublicationDateYYYYMMDD 2020-01-01
PublicationDate_xml – month: 01
  year: 2020
  text: 20200101
  day: 01
PublicationDecade 2020
PublicationPlace Beijing
PublicationPlace_xml – name: Beijing
PublicationTitle Journal of Cryptologic Research
PublicationYear 2020
Publisher Chinese Association for Cryptologic Research, Journal of Cryptologic Research
Publisher_xml – name: Chinese Association for Cryptologic Research, Journal of Cryptologic Research
SSID ssib055638241
ssib058688234
Score 2.1824296
Snippet 在分组密码的扩散层中构造MDS线性变换可实现良好的扩散性. 构造MDS线性变换的方法有很多种, 其中基于Rotational-XOR的MDS线性变换软硬件实现效率高, 能够增强密码算法抵抗各种密码分析的能力, 适用于对称密码算法设计, 例如SMS4算法、ZUC算法等. 本文研究构造MDS线性变换的必要条件,...
SourceID proquest
SourceType Aggregation Database
StartPage 668
SubjectTerms Algorithms
Cryptography
Diffusion barriers
Diffusion layers
Encryption
Linear transformations
Magma
Mathematical analysis
Matrices (mathematics)
Rotation
Title 基于Rotation-XOR的MDS线性变换的研究
URI https://www.proquest.com/docview/2895187456
Volume 7
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07b9RAEF4dSUODQIB4BJSCLX34ta_STmydouSCDkdyd_L61uJAuouOS0EqClqgoUA0iRAS4g9QXMOfIbm_wazf4sKzWa3G-7JnPPPt7swuQg-onTiKU5iWAJ4wXIuPDOk4I8NyGZemldEkX-_Y69PegbsTk7jT-dTyWjqay256fGFcyf9wFWjAVx0l-w-crRsFAuSBv5AChyH9Kx7jgGARYt_DgatTHgymxda6Ee8PcMCwAKK7t_1Y56GAH-KAaucGj-m6PMSC55Rt7Nl1eZ3xTCyKjMA-_QWE3Zq9OJwX2rN24atXonteEQ61UxlHrfpLWjxuPIHGRj8HsHmFWgmVBf1pe1nCNn9altC3fyt9tEojZLnf5EUDK_YK_jz2XCvapmAgU0WAZqXCWUtSSUsd0-LKnhUz4XDKczuRTp6Nu0_TWTcPUuaNUawcAfr7w_Bgd3cYBXF0Ca3bjGlngHU_6D8aVHpLn7HG7QZWEmid27lDQz3aMl5Ld_xwpdsVHJCDm-gqulJ-lk2vELFrqHP85Doyzk4W3xdv2iK1_PAKhGm5-Hb-8vPZ2_fnrz8CZXn6bvnl6w0UhUG01TPK2zWMQ8KFQUZyJK1EWtzM7JTaLldcH9uhTKIA89MRKH83tTNA9ABgWGIxJkXqKplJzolMnZtobTKdqFtok0iuRMYz4VDlAv5OWGJySURKLGYqYt1GG9XrDcu_5_kQJvpE3wdJ6J3fP76LLjfytYHW5rMjdQ-A4FzeL_nwAwt1Wug
linkProvider ProQuest
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%E5%9F%BA%E4%BA%8ERotation-XOR%E7%9A%84MDS%E7%BA%BF%E6%80%A7%E5%8F%98%E6%8D%A2%E7%9A%84%E7%A0%94%E7%A9%B6&rft.jtitle=Journal+of+Cryptologic+Research&rft.au=ZHANG%2C+Jing&rft.au=WANG%2C+Xin&rft.au=Li-Na%2C+ZHANG&rft.au=YANG%2C+Bo&rft.date=2020-01-01&rft.pub=Chinese+Association+for+Cryptologic+Research%2C+Journal+of+Cryptologic+Research&rft.issn=2097-4116&rft.volume=7&rft.issue=5&rft.spage=668&rft_id=info:doi/10.13868%2Fj.cnki.jcr.000398&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2097-4116&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2097-4116&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2097-4116&client=summon