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：我们针对高斯机制下的洗牌隐私放大理论，建立了一套精确的实验层面分析框架：采用具有完全支撑集的固定有限输出局部随机化器，并考虑仅相差一个用户的相邻二元数据集。我们首先证明了洗牌直方图的精确似然比恒等式，以及一个包含显式典型集余项的完全条件期望线性化定理。随后推导出尖锐的Jensen-Shannon散度展开式，确定了比例组合情形下的普适主导常数I_π/(8n)，并强调了正确的固定组合协方差矩阵Σ_π=(1-π)Σ_0+π*Σ_1。接着我们通过Berry-Esseen界建立了与高斯差分隐私的等价性，并获得了完整的极限(ε,δ)隐私曲线。最后，针对非捆绑式多消息洗牌机制，我们给出了精确的m阶似然比、渐近GDP公式以及严格的捆绑式与非捆绑式对比分析。进一步成果包括：具备量化Le Cam等价性的局部渐近正态性、精确的有限n隐私曲线、随机响应的边界Berry-Esseen定理，以及一个频率估计的应用实例。