Side-Channel Analysis of Complete ZUC Algorithm Keys Using Maximum Likelihood Extraction and Multi-Task Learning
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摘要: 针对ZUC算法侧信道分析中的密钥字节等价关系导致猜测熵难以收敛与多S盒结构未充分利用两个问题，该文提出一种结合最大似然函数值提取与多任务学习的侧信道分析方法。首先，针对第6轮三个密钥字节模加重叠导致的等价类问题，提出基于最大似然函数值提取的猜测熵范围压缩策略，将猜测熵从224量级压缩至28量级。其次，利用ZUC算法四个S盒共享同一密钥字节的结构特点，设计多任务学习网络，通过对数似然概率融合提升攻击效果。实验表明，该方法在软件实现上仅需2条能量迹即可恢复全部密钥，优于单任务深度学习侧信道分析的8条能量迹及相关功耗分析的185条能量迹。针对硬件实现，在消耗
10000 条测试集数据的条件下，该方法成功恢复全部16字节密钥，而传统相关功耗分析仅能恢复3字节，单任务深度学习侧信道分析恢复12字节。本文揭示的密钥字节等价类问题表明，密码算法的代数结构会对侧信道分析构成限制，攻击需结合代数分析。此外，攻击者需考虑多路并行泄露的融合效应，而非仅局限于单一攻击路径，从而提高攻击效率。Abstract:Objective This paper addresses two issues in side-channel analysis of the ZUC algorithm: slow guessing entropy convergence caused by key-byte equivalence relations, and the underutilization of its multi-S-box structure. A method combining maximum likelihood extraction with multi-task learning is proposed to enable efficient complete key recovery. Methods First, to tackle the equivalence class problem caused by modular addition overlap of three key bytes in round 6, a guess entropy range compression strategy based on maximum likelihood value extraction is introduced, reducing the candidate space from 224 to 28. Second, leveraging the structural feature of the ZUC algorithm where four S-boxes share the same key byte, a multi-task learning network is designed. This network is trained using multi-branch cross-entropy joint loss, and the attack effectiveness is improved by fusing multiple log-likelihood probabilities. Results and Discussions For the 224 equivalence class space caused by modular addition and bit overlap among three key bytes in round 6, the proposed maximum likelihood extraction strategy stably compresses the guessing entropy range to a single-byte scale, overcoming the convergence difficulty of direct global sorting. For software implementation, this method requires only two power traces to recover the entire 128-bit key, outperforming single-task deep learning side-channel analysis, which requires eight traces, and traditional correlation power analysis, which requires 185 traces. For hardware implementation, when 10000 test traces are consumed, traditional correlation power analysis can only recover three key bytes, single-task deep learning side-channel analysis recovers 12, whereas the proposed method successfully recovers all 16 bytes.Conclusions Sometimes, the algebraic structure of cryptographic algorithms imposes constraints on side-channel analysis, requiring attackers to incorporate algebraic analysis during an attack. In addition, attackers should consider the combined effect of multiple parallel leakages, rather than only focusing on the attack results of a single path, so as to improve attack efficiency. -
Key words:
- ZUC Algorithm /
- Side-Channel Analysis /
- Deep Learning /
- Multi-Task Learning
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表 1 超参数设置
超参数 搜索范围 DLSCA MTLSCA 学习率 0.00001 ～0.0010.0001 0.0001 批处理大小 50～500 100 200 激活函数 relu, tanh, selu relu relu 迭代次数 10～200 10～200 10～200 卷积核数量 16, 32, 64, 128 64 64 卷积核大小 5～50 10 10 池化窗口大小 2～10 2 2 
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