Privacy-preserving cryptocurrency exchanges (shielded AMMs, batched swap auctions, sealed-bid order-flow auctions) alter what the pricing mechanism observes about order flow. We derive the unique linear Kyle equilibrium when a committed Bayesian market maker observes order flow perturbed by independent Gaussian privacy noise. The price-impact coefficient and informed-trader strategy both rescale by a single factor in the privacy parameter, and their product is invariant. A welfare decomposition then identifies a closed-form per-period transfer from the protocol's LP pool to traders -- the "privacy subsidy", the break-even fee any privacy-aggregated exchange must charge. The result is the single-period closed-form privacy-noise analog of Loss-Versus-Rebalancing (Milionis et al. 2022). The primary application is shielded AMMs with explicit additive-noise injection (e.g., differential privacy); related designs (batched swaps, sealed-bid auctions, oracle-pegged crossings) require separate frameworks that we leave to future work.

翻译：隐私保护的加密货币交易所（屏蔽型 AMM、批量交换拍卖、密封订单流拍卖）改变了定价机制对订单流的观测内容。我们推导出了当承诺的贝叶斯做市商观测到被独立高斯隐私噪声扰动的订单流时，唯一的线性 Kyle 均衡。价格影响系数和知情交易者策略均按隐私参数的单因子重新缩放，且它们的乘积保持不变。福利分解随后识别出从协议流动性池到交易者的每期封闭式转移——即“隐私补贴”，这是任何隐私聚合交易所必须收取的盈亏平衡费用。这一结果等价于单期封闭式隐私噪声版本的“再平衡损失”（Milionis 等人，2022）。主要应用场景为具有显式加性噪声注入（例如差分隐私）的屏蔽型 AMM；相关设计（批量交换、密封订单拍卖、预言机锚定交叉）需要独立的分析框架，我们将其留待后续研究。