基于矩阵方法的减轮<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><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-M001.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-M001c.jpg"><?fx-imagestate width="5.50333309" height="5.58799982"?></graphic></alternatives></inline-formula>算法不可能差分分析

杜小妮; 余恬; 贾美纯; 梁丽芳

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

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基于矩阵方法的减轮

μ^{2}

算法不可能差分分析

学术论文 | 更新时间：2024-12-24

- 基于矩阵方法的减轮 $μ^{2}$ 算法不可能差分分析
- Impossible differential cryptanalysis of reduced-round $μ^{2}$ algorithm based on matrix method
- 通信学报 2024年45卷第11期页码：106-113
- 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：
  
  [ "杜小妮（1972- ），女，甘肃庆阳人，博士，西北师范大学教授、博士生导师，主要研究方向为密码学与信息安全等。" ]
  [ "余恬（2001- ），女，安徽安庆人，西北师范大学硕士生，主要研究方向为密码学与信息安全等。" ]
  [ "贾美纯（1998- ），女，河南南阳人，西北师范大学硕士生，主要研究方向为密码学与信息安全等。" ]
  [ "梁丽芳（1995- ），女，甘肃定西人，西北师范大学博士生，主要研究方向为密码学与信息安全等。" ]
- 基金信息：
  
  国家自然科学基金资助项目;The National Natural Science Foundation of China(62172337);甘肃省自然科学基金重点资助项目;Key Project of Gansu Natural Science Foundation(23JRRA685);甘肃省基础研究创新群体基金资助项目(23JRRA684)
- DOI：10.11959/j.issn.1000-436x.2024196
  中图分类号： TP309.7
- 收稿日期：2024-07-02，
  
  修回日期：2024-10-22，
  
  纸质出版日期：2024-11-25
- 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.

基于矩阵方法的减轮

μ^{2}

算法不可能差分分析

PDF下载

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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2.45533323

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个选择明文，时间复杂度为

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2.45533323

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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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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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and the time complexity of 13 rounds of algorithm encryptions is

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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

WU W L , ZHANG L . LBlock: a lightweight block cipher [C ] // Applied Cryptography and Network Security: 9th International Conference . Berlin : Springer , 2011 : 327 - 344 .

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 .

BEIERLE C , JEAN J , KÖLBL S , et al . The SKINNY family of block ciphers and its low-latency variant MANTIS [C ] // Annual International Cryptology Conference . Berlin : Springer , 2016 : 123 - 153 .

BANIK S , PANDEY S K , PEYRIN T , et al . GIFT: a small present: towards reaching the limit of lightweight encryption [C ] // Cryptographic Hardware and Embedded Systems . Berlin : Springer , 2017 : 321 - 345 .

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 .

SHI J L , LI C , LIU G Q . Differential attack with constants on μ2 block cipher [J ] . The Computer Journal , 2024 , 67 ( 1 ): 195 - 209 .

KNUDSEN L R . DEAL-a 128-bit block cipher [J ] . Complexity , 1998 , 258 ( 2 ): 216 .

BIHAM E , BIRYUKOV A , SHAMIR A . Cryptanalysis of skipjack reduced to 31 rounds using impossible differentials [J ] . Journal of Cryptology , 2005 , 18 ( 4 ): 291 - 311 .

WU W L , ZHANG W T , FENG D G . Impossible differential cryptanalysis of reduced-round ARIA and camellia [J ] . Journal of Computer Science and Technology , 2007 , 22 ( 3 ): 449 - 456 .

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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基于矩阵方法的减轮μ2算法不可能差分分析

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

基于矩阵方法的减轮 $μ^{2}$ 算法不可能差分分析

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