Improved Differential Meet-in-the-Middle Attack against Cipher SIMECK

ZHANG Yi; LÜ Guangqiu; JIN Chenhui; CUI Ting

doi:10.12263/DZXB.20251191

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Improved Differential Meet-in-the-Middle Attack against Cipher SIMECK

PAPERS | 更新时间：2026-07-30

- Improved Differential Meet-in-the-Middle Attack against Cipher SIMECK
- ACTA ELECTRONICA SINICA Vol. 54, Issue 4, Pages: 1789-1801(2026)
- 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：
- 基金信息：
  
  National Natural Science Foundation of China(62372463;62302518);Young Elite Scientists Sponsorship Program of Henan(2025HYTP036)
- DOI：10.12263/DZXB.20251191
  CLC： TN918.1;TP309.7
- Received：03 February 2026，
  
  Accepted：25 March 2026，
  
  Online First：11 May 2026，
  
  Published：25 April 2026
- 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]. 电子学报, 2026, 54(04): 1789-1801.

ZHANG Yi, LÜ Guangqiu, JIN Chenhui, et al. Improved Differential Meet-in-the-Middle Attack against Cipher SIMECK[J]. Acta Electronica Sinica, 2026, 54(04): 1789-1801.
张奕, 吕广秋, 金晨辉, 等. SIMECK密码的差分中间相遇攻击改进[J]. 电子学报, 2026, 54(04): 1789-1801. DOI：10.12263/DZXB.20251191

ZHANG Yi, LÜ Guangqiu, JIN Chenhui, et al. Improved Differential Meet-in-the-Middle Attack against Cipher SIMECK[J]. Acta Electronica Sinica, 2026, 54(04): 1789-1801. 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为

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=114275768&type=

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3.72533321

2.53999996

经常小于

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=114275778&type=

4.91066647

2.45533323

（

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=114275770&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=114275779&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地结合。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=114275804&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=114275780&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

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=114275755&type=

3.72533321

2.53999996

is often below

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=114275769&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=114275778&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 part

itioning 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=114275804&type=

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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

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