改进Simon32/64和Simeck32/64神经网络差分区分器

doi:10.3969/j.issn.1671-1122.2025.02.006

摘要/Abstract

摘要：

神经网络差分区分器具备良好的泛化能力和强大的学习能力，但目前仍缺乏完善且具有普适性的神经网络差分区分模型。为提升Simon32/64和Simeck32/64神经网络差分区分器的准确率和普适性，文章提出3个改进方向。首先，采用多密文对作为Simon32/64和Simeck32/64的输入，并将Inception网络模块引入神经网络模型，以改善过拟合现象。然后，将Simon32/64和Simeck32/64倒数第二轮的差分信息加入多密文对输入样本中，构造7~10轮和7~11轮神经网络差分区分器。最后，将多密文对与多面体差分结合，根据Simon32/64和Simeck32/64两种密码构造改进多面体差分区分器，提高已有多面体神经网络差分区分器的准确率。实验结果表明，8轮Simon32/64和Simeck32/64新型多面体神经网络差分区分器的准确率分别达到99.54%和99.67%。此外，利用10轮神经网络差分区分器对12轮Simon32/64和Simeck32/64开展最后一轮子密钥恢复攻击，在100次攻击实验中，攻击成功率分别达到86%和97%。

关键词: 深度学习, Inception模块, 多密文对, 多面体差分, 密钥恢复攻击

Abstract:

Neural distinguishers have good generalisation ability as well as powerful learning ability, but there is still a lack of perfect and universal neural network distinguishing model. In order to increase the accuracy of the neural distinguishers of Simon32/64 and Simeck32/64, increase the generalizability of the neural differential distinguishers, this paper proposed three improvement directions. First, multiple ciphertext pairs were used as inputs to the Simon32/64 and Simeck32/64 neural distinguishers, and the Inception network module was added to the neural network model to improve the overfitting phenomenon. Then, added Simon32/64 and Simeck32/64 penultimate round difference information to the multi-ciphertext pair input samples, constructed the netural distinguishers of 7 to 10 rounds of Simon32/64 and 7 to 11 rounds of Simeck32/64. Finelly, multiple ciphertext pairs were combined with polyhedral difference, constructed polyhedral differential distinguishers for Simon32/64 and Simeck32/64. The accuracy of the polyhedral neural distinguishers were improved. The experimental results show that the new polyhedral netural distinguishers of 8-round of Simon32/64 reach the accuracy of 99.54% and 8-round of Simeck32/64 reach the accuracy of 99.67%. In addition, the improved netural distinguishers of the 10-round of Simon32/64 and Simeck32/64 are applied to the final round of key recovery attacks of 12-round of Simon32/64 and Simeck32/64, the success rate of the attacks respectively reaches 86% and 97% in 100 attack experiments.

Key words: deep learning, Inception module, multiple ciphertext pairs, polyhedral difference, key recovery attack

中图分类号:

TP309

武浩莹, 陈杰, 刘君. 改进Simon32/64和Simeck32/64神经网络差分区分器[J]. 信息网络安全, 2025, 25(2): 249-259.

WU Haoying, CHEN Jie, LIU Jun. Improved Neural Network Differential Distinguisher of Simon32/64 and Simeck32/64[J]. Netinfo Security, 2025, 25(2): 249-259.

图/表 16

图1

图2

图3

图4

表1

Simon32/64和Simeck32/64多密文对神经网络差分区分器的准确率对比

密码	轮数	$N{{D}_{k=1}}$ (文献[10]方法)	$N{{D}_{k=2}}$	$N{{D}_{k=4}}$	$N{{D}_{k=8}}$	$N{{D}_{k=16}}$
Simon32/64	7	96.73 %	99.22 %	99.51 %	99.16 %	99.12 %
Simon32/64	8	76.76 %	77.36 %	80.38 %	85.46 %	89.21 %
Simon32/64	9	62.70 %	64.38 %	67.17 %	62.84 %	62.50 %
Simeck32/64	7	98.75 %	99.78 %	99.81 %	99.96 %	99.99 %
Simeck32/64	8	86.77 %	91.38 %	97.13 %	97.31 %	97.92 %
Simeck32/64	9	67.26 %	68.58 %	67.95 %	66.98 %	66.90 %

表1

图5

表2

Simon32/64改进神经网络差分区分器的准确率对比

轮数	old测试准确率	$N{{D}_{\mathbf{1}}}$ 测试准确率	$N{{D}_{\mathbf{2}}}$ 测试准确率
7	96.73 %	99.82 %	99.80 %
8	76.76 %	92.92 %	91.49 %
9	62.70 %	72.85 %	71.85 %
10	50.02 %	59.26 %	58.67 %

表2

表3

Simeck32/64改进神经网络差分区分器的准确率对比

轮数	old测试准确率	$N{{D}_{\mathbf{1}}}$ 测试准确率	$N{{D}_{\mathbf{2}}}$ 测试准确率
7	98.75 %	99.97 %	99.97 %
8	86.77 %	97.46 %	97.03 %
9	67.26 %	78.88 %	78.34 %
10	54.69 %	60.33 %	59.72 %
11	—	52.07 %	—

表3

图6

图7

图8

9轮Simon32/64 $N{{D}_{1}}$ 训练与验证准确率

图8

图9

9轮Simon32/64 $N{{D}_{2}}$ 训练与验证准确率

图9

图10

表4

密钥恢复攻击成功率

密码	轮数	数据复杂度	计算复杂度	攻击成功率	结果来源
Simon32/64	11	${{2}^{25}}$	${{2}^{30.9}}$	100% （1000次攻击）	文献[23]
Simon32/64	11	${{2}^{9}}$	—	95.6% （1000次攻击）	文献[24]
Simon32/64	12	${{2}^{9}}$	${{2}^{25}}$	86% （100次攻击）	本文
Simeck32/64	10	${{2}^{7.6}}$	${{2}^{29.4}}$	80% （50次攻击）	文献[19]
Simeck32/64	12	${{2}^{9}}$	${{2}^{25}}$	97% （100次攻击）	本文

表4

表5

Simon32/64三类神经网络差分区分器模型对比

轮数	$N{{D}_{3}}$ 测试准确率	$N{{D}_{1}}$ 测试准确率	$ND'_{1}$ 测试准确率
7	99.99 %	99.82 %	99.44 %
8	99.54 %	92.92 %	92.51 %
9	83.62 %	72.85 %	63.73 %
10	63.44 %	59.26 %	50.17 %
11	51.65 %	—	—

表5

表6

Simeck32/64三类神经网络差分区分器模型对比

轮数	模型	测试准确率
7	$N{{D}_{3}}$	99.99 %
7	$N{{D}_{1}}$	99.97 %
8	$N{{D}_{3}}$	99.67 %
8	$N{{D}_{1}}$	97.46 %
8	$ND'_{2}$	96.77 %
9	$N{{D}_{3}}$	86.37 %
9	$N{{D}_{1}}$	78.88 %
9	$ND'_{2}$	75.85 %
10	$N{{D}_{3}}$	63.50 %
10	$N{{D}_{1}}$	60.33 %
11	$N{{D}_{3}}$	52.30 %
11	$N{{D}_{1}}$	52.07 %

表6

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