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（遮蔽型AMM、批量交换拍卖、密封投标订单流拍卖）改变了定价机制对订单流的观测方式。我们推导了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，唯一的线性凯尔均衡。价格影响系数和知情交易者策略均按隐私参数的单一因子重新缩放，且其乘积保持恒定。随后，福利分解识别出从协议LP池到交易者的闭式每期转移——"隐私补贴"，即任何隐私聚合交易所必须收取的盈亏平衡费用。该结果对应Loss-Versus-Rebalancing（Milionis等人，2022）的单期闭式隐私噪声类比。主要应用为具有显式加性噪声注入（如差分隐私）的遮蔽型AMM；相关设计（批量交换、密封投标拍卖、预言机锚定交叉交易）需要单独框架，我们将这些留待未来工作。