发表机构
RPTU University Kaiserslautern-Landau; Beijing Huairou Laboratory; Princeton University; German Research Center for Artificial Intelligence (DFKI)（凯泽斯劳滕-兰道理工大学; 北京怀柔实验室; 普林斯顿大学; 德国人工智能研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对相位键控傅里叶曲线调制，发现密钥重用导致谐波关系泄漏，提出关系矩攻击，并量化了编码链路上满足安全所需的密钥刷新成本。
AI 中文摘要
键控调制的安全性通常依据密钥空间大小和无密钥接收机的误码率来论证。当密钥被重用且波形具有谐波耦合时，这一证据失效。对于相位键控傅里叶曲线星座，其$k$个音调共享一个数据参数，谐波索引之间的整数关系产生接收音调的消数据混合矩，从而暴露密钥字符。模关系格刻画了暴露的字符；对于连续谐波，三阶矩恢复相对相位，四阶矩在系数非零时（如所有评估设置中）完成密钥直至循环重标号。非数据辅助的关系矩估计器将此泄漏转化为攻击，且从不枚举密钥空间。在常规$(3,6)$ LDPC编码链路上，每个168符号码字一个密钥使得窃听者在中等噪声水平下的块错误率低于$0.04$，攻击在十二个操作点中的十一个满足预先声明的$0.1$泄露标准。切线人工噪声和低于四阶无关系的谐波集在中间重用长度下提高了她的测量错误率，但并未消除单码字漏洞。对于中等噪声水平下$2^{128}$协议密钥的网格，等长刷新调度保持她的块错误率95%置信下限高于$0.9$，每个信息比特至少消耗$1.52$个新密钥比特，是数据一次性密码本熵率的$1.52$倍。
英文摘要
The security of keyed modulation is often argued from the key-space size and the error rate of a key-less receiver. This evidence fails when the key is reused and the waveform is harmonically coupled. For a phase-keyed Fourier-curve constellation, whose $k$ tones share one data parameter, integer relations among the harmonic indices yield data-cancelling mixed moments of the received tones that expose key characters. A modular relation lattice characterizes the exposed characters; for consecutive harmonics, third-order moments recover the relative phases and a fourth-order moment completes the key up to cyclic relabeling whenever its coefficient is nonzero, as in all evaluated settings. A non-data-aided relation-moment estimator turns this leakage into an attack that never enumerates the key space. On a regular $(3,6)$ LDPC-coded link, one key per 168-symbol codeword leaves the eavesdropper a block error rate below $0.04$ at the middle noise level, and the attack meets a predeclared $0.1$ compromise criterion in eleven of twelve operating points. Tangent artificial noise and a harmonic set without relations below order four raise her measured error rate at intermediate reuse lengths but do not remove the one-codeword vulnerability. For a grid of $2^{128}$ protocol keys at the middle noise level, equal-length refresh schedules that keep a $95\%$ lower confidence bound of her block error rate above $0.9$ consume at least $1.52$ fresh key bits per information bit, $1.52$ times the entropy rate of a one-time pad on the data.
CommentsSubmitted to IEEE for publication
