We develop a sharp, experiment-level privacy theory for amplification by shuffling in the Gaussian regime: a fixed finite-output local randomizer with full support and neighboring binary datasets differing in one user. We first prove exact likelihood-ratio identities for shuffled histograms and a complete conditional-expectation linearization theorem with explicit typical-set remainders. We then derive sharp Jensen-Shannon divergence expansions, identifying the universal leading constant I_pi/(8n) for proportional compositions and emphasizing the correct fixed-composition covariance Sigma_pi=(1-pi)Sigma_0+pi*Sigma_1. Next we establish equivalence to Gaussian Differential Privacy with Berry-Esseen bounds and obtain the full limiting (epsilon,delta) privacy curve. Finally, for unbundled multi-message shuffling we give an exact degree-m likelihood ratio, asymptotic GDP formulas, and a strict bundled-versus-unbundled comparison. Further results include Local Asymptotic Normality with quantitative Le Cam equivalence, exact finite-n privacy curves, a boundary Berry-Esseen theorem for randomized response, and a frequency-estimation application.

翻译：我们发展了高斯机制下通过混洗实现放大的极值实验级隐私理论：具有完全支撑的固定有限输出局部随机化器及相差一个用户的相邻二元数据集。首先证明混洗直方图的精确似然比恒等式，以及带有显式典型集余项的完全条件期望线性化定理。进而推导出精确的Jensen-Shannon散度展开，识别出比例组合下的通用领先常数I_pi/(8n)，强调正确的固定组合协方差Sigma_pi=(1-pi)Sigma_0+pi*Sigma_1。接下来建立与高斯差分隐私的等价性并给出Berry-Esseen界，获得完整极限(epsilon,delta)隐私曲线。最后，针对解绑多消息混洗给出精确的度m似然比、渐近GDP公式及严格的有绑与无绑比较。进一步结果包括具有量化Le Cam等价的局部渐近正态性、精确有限n隐私曲线、随机化应答的边界Berry-Esseen定理及频率估计应用。