Impossible differential cryptanalysis of reduced-round <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><msup><mrow><mi mathvariant="bold-italic">μ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/22C9D519-EA4F-4e54-A8CF-1ACB826F2179-M002.jpg"><?fx-imagestate width="5.50333309" height="5.58799982"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/22C9D519-EA4F-4e54-A8CF-1ACB826F2179-M002c.jpg"><?fx-imagestate width="5.50333309" height="5.58799982"?></graphic></alternatives></inline-formula> algorithm based on matrix method

DU Xiaoni; YU Tian; JIA Meichun; LIANG Lifang

doi:10.11959/j.issn.1000-436x.2024196

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Impossible differential cryptanalysis of reduced-round

μ^{2}

algorithm based on matrix method

Papers | 更新时间：2024-12-24

- Impossible differential cryptanalysis of reduced-round $μ^{2}$ algorithm based on matrix method
- Journal on Communications Vol. 45, Issue 11, Pages: 106-113(2024)
- 作者机构：
  
  1.西北师范大学数学与统计学院，甘肃兰州 730070
  2.西北师范大学密码技术与数据分析重点实验室，甘肃兰州 730070
- 作者简介：
- 基金信息：
  
  The Funds for Innovative Fundamental Research Group Project of Gansu Province(23JRRA684)
- DOI：10.11959/j.issn.1000-436x.2024196
  CLC： TP309.7
- Received：02 July 2024，
  
  Revised：2024-10-22，
  
  Published：25 November 2024
- 稿件说明：
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杜小妮,余恬,贾美纯等.基于矩阵方法的减轮μ2算法不可能差分分析[J].通信学报,2024,45(11):106-113.

DU Xiaoni,YU Tian,JIA Meichun,et al.Impossible differential cryptanalysis of reduced-round μ2 algorithm based on matrix method[J].Journal on Communications,2024,45(11):106-113.
杜小妮,余恬,贾美纯等.基于矩阵方法的减轮μ2算法不可能差分分析[J].通信学报,2024,45(11):106-113. DOI： 10.11959/j.issn.1000-436x.2024196.

DU Xiaoni,YU Tian,JIA Meichun,et al.Impossible differential cryptanalysis of reduced-round μ2 algorithm based on matrix method[J].Journal on Communications,2024,45(11):106-113. DOI： 10.11959/j.issn.1000-436x.2024196.

Impossible differential cryptanalysis of reduced-round

μ^{2}

algorithm based on matrix method

PDF Download

摘要

为了评估

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算法在不可能差分分析方面的安全性，首先基于矩阵方法，结合中间相错技术构造了

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算法的9轮不可能差分区分器。其次在该区分器的基础上分别向前和向后扩展2轮，利用密钥桥技术，对

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算法进行了13轮密钥恢复攻击。研究结果表明，该攻击可恢复45 bit主密钥，数据复杂度为

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个选择明文，时间复杂度为

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2.45533323

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=71157572&type=

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次13轮算法加密。相比之前的研究结果，该研究实现了最长的攻击轮数，且数据复杂度显著降低。

Abstract

To evaluate the security of

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3.13266683

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algorithm in impossible differential cryptanalysis

a 9-round impossible differential distinguisher of

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algorithm was constructed based on matrix method and meet-in-the middle technique firstly. Then

with the utilization of key-bridge technique

a 13-round key recovery attack was presented to

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algorithm by expanding the 9-round distinguisher forward and backward 2 rounds

respectively. The results show that the master key can be recovered 45 bit in the attack

the data complexity of plaintexts is

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2.45533323

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and the time complexity of 13 rounds of algorithm encryptions is

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=71157628&type=

2.45533323

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. Compared with the previous research

the study achieves the longest attack rounds

and the data complexity is effectively reduced.

关键词

Keywords

references

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BANIK S , BOGDANOV A , ISOBE T , et al . Midori: a block cipher for low energy [C ] // Proceedings of the 21st International Conference on the Theory and Application of Cryptology and Information Security . Berlin : Springer , 2015 : 411 - 436 .

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YEOH W Z , TEH J S , SAZALI M I S B M . µ2: a lightweight block cipher [C ] // Computational Science and Technology . Berlin : Springer , 2020 : 281 - 290 .

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WU W L , ZHANG L , ZHANG W T . Improved impossible differential cryptanalysis of reduced-round camellia [C ] // Selected Areas in Cryptography . Berlin : Springer , 2009 : 442 - 456 .

CHEN J Z , JIA K T , YU H B , et al . New impossible differential attacks of reduced-round camellia-192 and camellia-256 [C ] // Australasian Conference on Information Security and Privacy . Berlin : Springer , 2011 : 16 - 33 .

DU C H , CHEN J Z . Impossible differential cryptanalysis of ARIA reduced to 7 rounds [C ] // Cryptology and Network Security . Berlin : Springer , 2010 : 20 - 30 .

ZHANG K , GUAN J , HU B . Impossible differential cryptanalysis on DVB-CSA [J ] . KSII Transactions on Internet and Information Systems , 2016 , 10 ( 4 ): 1944 - 1956 .

BOURA C , NAYA-PLASENCIA M , SUDER V . Scrutinizing and improving impossible differential attacks: applications to CLEFIA, camellia, LBlock and Simon [C ] // International Conference on the Theory and Application of Cryptology and Information Security . Berlin : Springer , 2014 : 179 - 199 .

ZHANG K , LAI X J , GUAN J , et al . Research on the security level of μ2 against impossible differential cryptanalysis [J ] . KSII Transactions on Internet and Information Systems , 2022 , 16 ( 3 ): 972 - 985 .

胡斌 , 张贵显 . μ2算法的积分攻击和不可能差分攻击 [J ] . 电子与信息学报 , 2022 , 44 ( 9 ): 3335 - 3342 .

HU B , ZHANG G X . Integral cryptanalysis and impossible differential cryptanalysis of the μ2 algorithm [J ] . Journal of Electronics & Information Technology , 2022 , 44 ( 9 ): 3335 - 3342 .

KIM J , HONG S , LIM J . Impossible differential cryptanalysis using matrix method [J ] . Discrete Mathematics , 2010 , 310 ( 5 ): 988 - 1002 .

SOLEIMANY H , NYBERG K . Zero-correlation linear cryptanalysis of reduced-round LBlock [J ] . Designs, Codes and Cryptography , 2014 , 73 ( 2 ): 683 - 698 .

LUO Y Y , LAI X J , WU Z M , et al . A unified method for finding impossible differentials of block cipher structures [J ] . Information Sciences , 2014 , 263 : 211 - 220 .

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Related Institution

Department of Cryptogram Engineering, Information Engineering University

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Impossible differential cryptanalysis of reduced-round μ2 algorithm based on matrix method

DOI：10.11959/j.issn.1000-436x.2024196

摘要

Abstract

关键词

Keywords

references

Impossible differential cryptanalysis of reduced-round $μ^{2}$ algorithm based on matrix method