SIMECK密码的差分中间相遇攻击改进

张奕; 吕广秋; 金晨辉; 崔霆

doi:10.12263/DZXB.20251191

您当前的位置：

首页 >

文章列表页 >

SIMECK密码的差分中间相遇攻击改进

更新时间：2026-05-11

- SIMECK密码的差分中间相遇攻击改进
- Improved Differential Meet-in-the-Middle Attack against Cipher SIMECK
- 电子学报 2026年页码：1-13
- 作者机构：
  
  网络空间部队信息工程大学，河南郑州450001
- 作者简介：
  
  [ "张奕男，1997年11月出生于江西省吉安市。现为网络空间部队信息工程大学网络空间安全专业博士研究生。主要研究方向为对称密码分析。E-mail: yizhang0796@foxmail.com" ]
  [ "吕广秋男，1994年6月出生于河北省衡水市。现为网络空间部队信息工程大学讲师。主要研究方向为对称密码的设计与分析、集成电路技术。E-mail: lgq_running@163.com" ]
  [ "金晨辉男，1965年3月出生于河南省周口市。现为网络空间部队信息工程大学教授。主要研究方向为密码学与信息安全。E-mail: jinchenhui@126.com" ]
  [ "崔霆男，1985年12月出生于安徽省铜陵市。现为网络空间部队信息工程大学教授。主要研究方向为密码理论与密码算法分析。E-mail: cuiting_1209@126.com" ]
- 基金信息：
  
  国家自然科学基金(62372463;62302518);河南省青年人才托举工程(2025HYTP036)
- DOI：10.12263/DZXB.20251191
  中图分类号： TN918.1;TP309.7
- 收稿：2026-02-03，
  
  录用：2026-03-25，
  
  网络首发：2026-05-11，
- 稿件说明：
移动端阅览
张奕, 吕广秋, 金晨辉, 等. SIMECK密码的差分中间相遇攻击改进[J/OL]. 电子学报, 2026,1-13.

ZHANG Yi, LV Guangqiu, JIN Chenhui, et al. Improved Differential Meet-in-the-Middle Attack against Cipher SIMECK[J/OL]. ACTA ELECTRONICA SINICA, 2026, 1-13.
张奕, 吕广秋, 金晨辉, 等. SIMECK密码的差分中间相遇攻击改进[J/OL]. 电子学报, 2026,1-13. DOI： 10.12263/DZXB.20251191.

ZHANG Yi, LV Guangqiu, JIN Chenhui, et al. Improved Differential Meet-in-the-Middle Attack against Cipher SIMECK[J/OL]. ACTA ELECTRONICA SINICA, 2026, 1-13. DOI： 10.12263/DZXB.20251191.

摘要

Boura等人在CRYPTO 2023上提出的差分中间相遇分析（Differential Meet-in-the-middle Cryptanalysis，DMC）是一种基于中间相遇思想实施差分攻击的新型密码分析方法。凭借概率扩展（Probabilistic Extension，PE）、限制条件（Imposed Condition，IC）与并行分割（Parallel Partition，PP）技术在降低时间、数据复杂性与扩展攻击轮数上的优势，差分中间相遇攻击已在多个采用线性密钥生成算法的分组密码上取得了显著效果。然而，目前的DMC还存在两点不足：一是概率扩展后的差分区分器概率

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633972&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633929&type=

3.72533321

2.53999996

经常小于

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633944&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633958&type=

4.91066647

2.45533323

（

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633973&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633930&type=

1.60866666

2.28600001

是密码的分组规模），会导致限制条件技术失效而无法将攻击的数据复杂性维持在非全码本（全码本攻击通常被认为是无效攻击）。虽然已有工作使用明文结构缓解这个问题，但其并没有与并行分割技术很好结合；二是受SIMECK密码中非线性密钥生成算法的影响，近期关于此密码的DMC无法有效恢复主密钥。具体来说，这些工作只恢复了轮次分散的子密钥，导致进一步推导主密钥的代价超出上界。围绕上述两个问题，本文提出了基于尾接技术的DMC模型。此模型不再按照密码算法头尾来分割待恢复的密钥，而是将尾部的部分密钥视作头部

密钥，使攻击中头部轮数减少而尾部轮数增加，从而获得三重优势：一是头部轮数减少会导致差分扩散不充分，便于使用明文结构降低攻击的数据复杂性；二是将更多的被分割密钥集中在密码算法尾部的连续轮，显著降低了推导主密钥的代价；三是利用尾部相邻子密钥间更清晰的制约关系提前排除掉不可能的密钥穷举值。基于上述模型，本文能够有效结合明文结构与并行分割技术，不仅解决了原有攻击在

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633945&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633959&type=

19.64266586

3.13266683

时无法实现非全码本复杂性的问题，还提升了DMC对于采用非线性密钥生成算法的密码的分析能力。作为应用，本文分别提出了对23轮SIMECK32、31轮SIMECK48和41轮SIMECK64的主密钥恢复攻击。据我们所知，在所有能够恢复主密钥的差分攻击中，本文对SIMECK三个版本的攻击均是轮数最长的攻击。

Abstract

Differential meet-in-the-middle cryptanalysis (DMC)

proposed by Boura et al. at CRYPTO 2023

is a novel method to mount differential attacks based on the meet-in-the-middle idea. Benefiting from the advantages of the probabilistic extension (PE)

imposed condition (IC) and parallel partition (PP) techniques in reducing time and data complexities and extending attack rounds

differential meet-in-the-middle attacks have achieved significantly improved results on many block ciphers employing linear key schedules. However

two limitations of the existing DMC remain. Firstly

the probability of the differential distinguisher under PE

denoted by

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633972&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633929&type=

3.72533321

2.53999996

is often below

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633974&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633931&type=

4.91066647

2.45533323

(where

is the block size)

causing the IC technique to fail to maintain the non-full-codebook data complexity—a scenario usually deemed invalid for attacks. Although the plaintext structure technique has been adopted in some studies as a mitigation

its integration with the PP technique remains inadequate. Secondly

owing to the nonlinear key schedule of the SIMECK cipher

recent DMC attacks have been unable to recover the master key effectively. Specifically

these attacks only recover round keys with scattered round numbers

making the cost of deriving the master key unacceptable. Motivated by the two issues above

this paper introduces a new DMC model based on the tail-jointing technique. Rather than partitioning the key bits to be enumerated according to position

this model treats some tail key bits as head key bits

yielding fewer head

rounds and more tail rounds

thereby offering three advantages. First

fewer head rounds cause insufficient differential diffusion

enabling the use of plaintext structures to reduce data complexity. Second

more key bits concentrated in consecutive tail rounds significantly lowers the cost of master key derivation. Third

more explicit constraints between adjacent tail key bits enable early elimination of impossible enumerations. Based on the above model

this paper effectively integrates the plaintext structure technique with the PP technique to achieve non-full-codebook data complexity when

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633946&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=107633960&type=

19.64266586

3.13266683

and strengthens DMC’s effectiveness in analyzing ciphers that adopt a nonlinear key schedule. As an application

this paper proposes master key recovery attacks on 23-round SIMECK32

31-round SIMECK48

and 41-round SIMECK64

respectively. As far as we know

among all differential attacks capable of recovering master keys

our attacks on the three versions of SIMECK achieve the longest rounds.

关键词

Keywords

references

Diffie W , Hellman M E . Special feature exhaustive cryptanalysis of the NBS data encryption standard [J ] . Computer , 1977 , 10 ( 6 ): 74 - 84 . DOI: 10.1109/c-m.1977.217750 http://dx.doi.org/10.1109/c-m.1977.217750

Biham E , Shamir A . Differential cryptanalysis of DES-like cryptosystems [J ] . Journal of Cryptology , 1991 , 4 ( 1 ): 3 - 72 . DOI: 10.1007/bf00630563 http://dx.doi.org/10.1007/bf00630563

Boura C , David N , Derbez P , et al . Differential meet-in-the-middle cryptanalysis [C ] // Proceedings of 43rd Annual International Cryptology Conference on Advances in Cryptology - CRYPTO 2023 . Cham : Springer , 2023 : 240 - 272 . DOI: 10.1007/978-3-031-38548-3_9 http://dx.doi.org/10.1007/978-3-031-38548-3_9

Ahmadian Z , Khalesi A , M'Foukh D , et al . Improved differential meet-in-the-middle cryptanalysis [C ] // Proceedings of 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology - EUROCRYPT 2024 . Cham : Springer , 2024 : 280 - 309 . DOI: 10.1007/978-3-031-58716-0_10 http://dx.doi.org/10.1007/978-3-031-58716-0_10

Song Ling , Liu Huimin , Yang Qianqian , et al . Generic differential key recovery attacks and beyond [C ] // Proceedings of 30th International Conference on the Theory and Application of Cryptology and Information Security on Advances in Cryptology - ASIACRYPT 2024 . Singapore : Springer , 2024 : 361 - 391 . DOI: 10.1007/978-981-96-0941-3_12 http://dx.doi.org/10.1007/978-981-96-0941-3_12

M'Foukh D , Naya-Plasencia M , Neumann P . The state-test technique on differential attacks: A 26-round attack on CRAFT and other applications [C ] // Proceedings of 31st International Conference on the Theory and Application of Cryptology and Information Security on Advances in Cryptology - ASIACRYPT 2025 . Singapore : Springer , 2025 : 253 - 284 . DOI: 10.1007/978-981-95-5018-0_9 http://dx.doi.org/10.1007/978-981-95-5018-0_9

Demirci H , Selçuk A A . A meet-in-the-middle attack on 8-round AES [C ] // Proceedings of 15th International Workshop , FSE 2008 on Fast Software Encryption . Berlin : Springer , 2008 : 116 - 126 . DOI: 10.1007/978-3-540-71039-4_7 http://dx.doi.org/10.1007/978-3-540-71039-4_7

Li Rongjia , Jin Chenhui . Meet-in-the-middle attacks on 10-round AES-256 [J ] . Designs, Codes and Cryptography , 2016 , 80 ( 3 ): 459 - 471 . DOI: 10.1007/s10623-015-0113-3 http://dx.doi.org/10.1007/s10623-015-0113-3

Beaulieu R , Shors D , Smith J , et al . The SIMON and SPECK lightweight block ciphers [C ] // Proceedings of the 52nd Annual Design Automation Conference . New York : ACM , 2015 : 175 . DOI: 10.1145/2744769.2747946 http://dx.doi.org/10.1145/2744769.2747946

Yang Gangqiang , Zhu Bo , Suder V , et al . The Simeck family of lightweight block ciphers [C ] // Proceedings of 17th International Workshop on Cryptographic Hardware and Embedded Systems -- CHES 2015 . Berlin : Springer , 2015 : 307 - 329 . DOI: 10.1007/978-3-662-48324-4_16 http://dx.doi.org/10.1007/978-3-662-48324-4_16

Kölbl S , Leander G , Tiessen T . Observations on the SIMON block cipher family [C ] // Proceedings of 35th Annual Cryptology Conference on Advances in Cryptology -- CRYPTO 2015 . Berlin : Springer , 2015 : 161 - 185 . DOI: 10.1007/978-3-662-47989-6_8 http://dx.doi.org/10.1007/978-3-662-47989-6_8

Matsui M . Linear cryptanalysis method for DES cipher [C ] // Proceedings of Workshop on the Theory and Application of Cryptographic Techniques on Advances in Cryptology - EUROCRYPT '93 . Berlin : Springer , 1993 : 386 - 397 . DOI: 10.1007/3-540-48285-7_33 http://dx.doi.org/10.1007/3-540-48285-7_33

Liu Zhengbin , Li Yongqiang , Wang Mingsheng . Optimal differential trails in SIMON-like ciphers [J ] . IACR Transactions on Symmetric Cryptology , 2017 , 2017( 1 ): 358 - 379 . DOI: 10.46586/tosc.v2017.i1.358-379 http://dx.doi.org/10.46586/tosc.v2017.i1.358-379

Leurent G , Pernot C , Schrottenloher A . Clustering effect in SIMON and SIMECK [C ] // Proceedings of 27th International Conference on the Theory and Application of Cryptology and Information Security on Advances in Cryptology - ASIACRYPT 2021 . Cham : Springer , 2021 : 272 - 302 . DOI: 10.1007/978-3-030-92062-3_10 http://dx.doi.org/10.1007/978-3-030-92062-3_10

Niu Chao , Li Muzhou , Zhang Jifu , et al . Improved differential and linear cryptanalysis on round-reduced SIMON [EB/OL ] . [ 2025-12-15 ] . https://eprint.iacr.org/2025/178 https://eprint.iacr.org/2025/178 .

成磊 , 沈璇 , 任传伦 . 广义类CLEFIA动态密码结构抵抗差分和线性密码分析的安全性评估 [J ] . 电子学报 , 2024 , 52 ( 8 ): 2571 - 2580 .

Cheng Lei , Shen Xuan , Ren Chuanlun . Security evaluation of generalized CLEFIA-like dynamic cipher structures against differential and linear cryptanalysis [J ] . Acta Electronica Sinica , 2024 , 52 ( 8 ): 2571 - 2580 . (in Chinese)

刘帅 , 任小广 , 王世雄 , 等 . 基于MILP的轻量级密码算法ACE与SPIX的线性分析 [J ] . 电子学报 , 2024 , 52 ( 9 ): 3065 - 3074 .

Liu Shuai , Ren Xiaoguang , Wang Shixiong , et al . Linear analysis of lightweight cipher ACE and SPIX based on mixed-integer linear programming [J ] . Acta Electronica Sinica , 2024 , 52 ( 9 ): 3065 - 3074 . (in Chinese)

Deng Weiqing , Zhang Jianing , Wang Haoyang . Improved differential meet-in-the-middle cryptanalysis on SIMON and Piccolo [C ] // Proceedings of 30th Australasian Conference, ACISP 2025 on Information Security and Privacy . Singapore : Springer , 2025 : 78 - 97 . DOI: 10.1007/978-981-96-9095-4_5 http://dx.doi.org/10.1007/978-981-96-9095-4_5

Chakraborty D , Sahoo S , Nguyen P H , et al . An automated model to search for differential meet-in-the-middle attack: Applications to AndRX ciphers [EB/OL ] . [ 2025-12-15 ] . https://eprint.iacr.org/2025/1249 https://eprint.iacr.org/2025/1249 . DOI: 10.1038/s41598-026-41390-w http://dx.doi.org/10.1038/s41598-026-41390-w

Wang Ning , Wang Xiaoyun , Jia Keting , et al . Differential attacks on reduced SIMON versions with dynamic key-guessing techniques [J ] . Science China Information Sciences , 2018 , 61 ( 9 ): 098103 . DOI: 10.1007/s11432-017-9231-5 http://dx.doi.org/10.1007/s11432-017-9231-5

Michel B , M'Foukh D , Naya-Plasencia M . Differential meet-in-the-middle attacks on Feistel ciphers [EB/OL ] . [ 2025-12-15 ] . https://eprint.iacr.org/2025/1911 https://eprint.iacr.org/2025/1911 .

Hao Yonglin , Meier W . Truncated differential based known-key attacks on round-reduced SIMON [J ] . Designs, Codes and Cryptography , 2017 , 83 ( 2 ): 467 - 492 . DOI: 10.1007/s10623-016-0242-3 http://dx.doi.org/10.1007/s10623-016-0242-3

Lee J K , Koo B , Kim W H . A general framework for the related-key linear attack against block ciphers with linear key schedules [C ] // Proceedings of 26th International Conference on Selected Areas in Cryptography - SAC 2019 . Cham : Springer , 2019 : 194 - 224 . DOI: 10.1007/978-3-030-38471-5_9 http://dx.doi.org/10.1007/978-3-030-38471-5_9

Zhang Yi , Zhang Kai , Cui Ting . Related-key zero-correlation linear attacks on block ciphers with linear key schedules [J ] . Chinese Journal of Electronics , 2024 , 33 ( 3 ): 672 - 682 . DOI: 10.23919/cje.2022.00.419 http://dx.doi.org/10.23919/cje.2022.00.419

Kondo K , Sasaki Y , Todo Y , et al . Analyzing key schedule of SIMON: Iterative key differences and application to related-key impossible differentials [C ] // Proceedings of 12th International Workshop on Security on Advances in Information and Computer Security . Cham : Springer , 2017 : 141 - 158 . DOI: 10.1007/978-3-319-64200-0_9 http://dx.doi.org/10.1007/978-3-319-64200-0_9

Su Ruitao , Ren Jiongjiong , Chen Shaozhen . Improved framework of related-key differential neural distinguisher and applications to the standard ciphers [EB/OL ] . [ 2025-12-15 ] . https://eprint.iacr.org/2025/537 https://eprint.iacr.org/2025/537 . DOI: 10.1109/jiot.2026.3671705 http://dx.doi.org/10.1109/jiot.2026.3671705

Song Ling , Yang Qianqian , Liu Huimin . Revisiting the differential meet-in-the-middle cryptanalysis [EB/OL ] . [ 2025-12-15 ] . https://eprint.iacr.org/2023/1302 https://eprint.iacr.org/2023/1302 .

Qiao Kexin , Hu Lei , Sun Siwei . Differential analysis on Simeck and Simon with dynamic key-guessing techniques [C ] // Proceedings of Second International Conference on Information Systems Security and Privacy . Cham : Springer , 2016 : 64 - 85 . DOI: 10.5220/0005684400740084 http://dx.doi.org/10.5220/0005684400740084

Qin Lingyue , Chen Huaifeng , Wang Xiaoyun . Linear hull attack on round-reduced Simeck with dynamic key-guessing techniques [C ] // Proceedings of 21st Australasian Conference on Information Security and Privacy . Cham : Springer , 2016 : 409 - 424 . DOI: 10.1007/978-3-319-40367-0_26 http://dx.doi.org/10.1007/978-3-319-40367-0_26

Song Ling , Yang Qianqian , Chen Yincen , et al . Probabilistic extensions: A one-step framework for finding rectangle attacks and beyond [C ] // Proceedings of 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology - EUROCRYPT 2024 . Cham : Springer , 2024 : 339 - 367 . DOI: 10.1007/978-3-031-58716-0_12 http://dx.doi.org/10.1007/978-3-031-58716-0_12

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

暂无数据