Security Analysis of LBlock and Its Application Based on Deep Learning
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摘要: 目前通过深度学习对轻量级分组密码进行安全性分析正成为一个全新的研究热点。Gohr在2019年的美密会上首次将深度学习应用于分组密码安全性分析(doi:
10.1007/978-3-030-26951-7_6 )，利用卷积神经网络学习固定输入差分的密文差分分布特征，从而构造出高精度的神经网络区分器。LBlock算法是一种具有优良软硬件实现效率的轻量级分组密码算法，自算法发表以来受到了研究者的广泛关注。该文基于残差网络，构造了减轮LBlock差分神经网络区分器，所得7轮和8轮区分器模型的精度分别是0.999和0.946。进一步利用构造的9轮区分器，提出了针对11轮LBlock的密钥恢复攻击方案。实验结果表明，当密码算法迭代轮数较少时，该方案进行攻击时无需单独考虑S盒，相比于传统攻击方案具有方案流程简单和易于实现等特点，并且在数据复杂度和时间复杂度方面具有较大的优越性。Abstract: Currently, the security analysis of lightweight block ciphers by using deep learning is becoming a new research hotspot. At the Crypto2019, Gohr first applied deep learning to the security analysis of block ciphers, the high-accuracy neural distinguisher is constructed, which used convolutional neural networks to learn the ciphertext distribution of the given input differentials. LBlock is a lightweight block cipher with excellent software and hardware implementation efficiency, which attracted extensive attention from scholars since its publication. In this paper, with the application of the residual network, a round-reduced neural differential distinguisher of LBlock is constructed, in which the accuracy of the 7-round and 8-round distinguishers reach 0.999 and 0.946, respectively. Moreover, based on the 9-round neural distinguisher, a key recovery attack scheme against 11-round LBlock is proposed. Experiment results show that under the case of the number of iteration rounds of the algorithm is small, the scheme need not consider the S-box separately. Compared with the traditional attack schemes, the new scheme is not only simpler and easy to be implemented, but also possess great advantages on data complexity and time complexity.-
Key words:
- LBlock /
- Differential distinguisher /
- Deep learning /
- Key recovery attack
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算法1 神经网络区分器的构造 输入：样本数量$ n $，输入差分${\varDelta _x}$ 输出：$ {\text{model}} $ (1) 随机生成数量为$ n $的$ ({P_0},{P_1}) $和$ K $，$({P'_0} ,{P'_1}) = ({P_0},{P_1}) \oplus {\varDelta _x}$ (2) 通过密钥扩展算法生成子密钥$ {K^i} $ (3) 分别对$ ({P_0},{P_1}),({P_0}^\prime ,{P_1}^\prime ) $使用LBlock加密，得到相对应的
密文$ ({C_0},{C_1}),({C_0}^\prime ,{C_1}^\prime ) $，构成训练集和验证集的数据部分(4) 将$ ({C_0},{C_1}) $的标签$ Y $标为0，为负样本；$ ({C_0}^\prime ,{C_1}^\prime ) $的标签
$ Y $标为1，为正样本(5) $ {\text{Traindata}} \leftarrow (({C_0},{C_1},{C_0}^\prime ,{C_1}^\prime ),Y) $ (6) $ {\text{model}} \leftarrow {\text{TrainDistinguisher}}({\text{Traindata}}) $ (7) return $ {\text{model}} $ 
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表 2 LBlock 7～9轮区分器模型的性能指标
迭代轮数(r) 训练轮数(epoch) 输入差分${\varDelta _x}$ 精度(acc) (%) 损失率(loss) (%) 训练时间(s) 7 20 0x0/0x1 99.63 0.37 1 240 0x0/0x2 99.57 0.44 574 0x0/0x4 99.96 0.05 1 251 0x0/0x8 99.91 0.10 1 220 0x0/0x40 99.91 0.10 1 212 0x0/0x80 99.93 0.07 1 211 8 30 0x0/0x1 94.34 4.67 1 812 0x0/0x2 94.58 4.53 1 828 0x0/0x4 93.57 5.27 1 820 0x0/0x8 93.58 5.37 1 810 0x0/0x40 93.94 5.09 1 815 0x0/0x80 93.54 5.39 1 821 9 50 0x0/0x1 65.53 21.05 2 926 0x0/0x2 65.43 21.09 3 000 0x0/0x4 62.53 22.06 3 068 0x0/0x8 61.68 22.26 1 832 0x0/0x40 64.79 21.48 2 934 0x0/0x80 64.61 21.48 3 015
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算法2 密钥恢复攻击 输入：样本数量$ n $，输入差分${\varDelta _x}$，$ {\text{model}} $ 输出：候选密钥的概率 (1) 随机生成数量为$ n $的$ ({P_0},{P_1}) $和$ K $，$({P'_0} ,{P'_1} ) = ({P_0},{P_1}) \oplus {\varDelta _x}$ (2) 通过密钥扩展算法生成子密钥$ {K^i} $ (3) $({P'_0} ,{P'_1} )$使用LBlock加密，得到相对应的密文$({C'_0} ,{C'_1} )$ (4) for $ i \in \{ 1,{\text{ }}n\} $ do (5) 对密文对$({C'_0} ,{C'_1})$分别使用LBlock解密一轮，得到$ ({x_0},{x_1}) $ (6) 将$ ({x_0},{x_1}) $放入$ {\text{model}} $中，得到概率$ {\omega ^i} $ (7) end for (8) 按$ {\omega ^i} $的大小降序排列
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