Privacy-preserving cryptocurrency exchanges 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 rescale by reciprocal factors of the privacy parameter (one down, one up), so 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改变了定价机制对订单流的观测方式。我们推导出，当承诺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，存在唯一的线性Kyle均衡。价格影响系数与知情交易者策略分别按隐私参数的倒数因子重新缩放（一降一升），因而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形式转移——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。该结果是单期封闭形式的隐私噪声版本Loss-Versus-Rebalancing（Milionis等人，2022年）。主要应用场景是显式添加噪声注入（例如差分隐私）的屏蔽AMM；相关设计（批量交换、密封投标拍卖、预言机锚定交叉）需另立框架，留待后续研究。