We propose a generalization of Zhandry's compressed oracle method to random permutations, where an algorithm can query both the permutation and its inverse. We show how to use the resulting oracle simulation to bound the success probability of an algorithm for any predicate on input-output pairs, a key feature of Zhandry's technique that had hitherto resisted attempts at generalization to random permutations. One key technical ingredient is to use strictly monotone factorizations to represent the permutation in the oracle's database. As an application of our framework, we show that the one-round sponge construction is unconditionally preimage resistant in the random permutation model. This proves a conjecture by Unruh.

翻译：我们提出了一种将Zhandry压缩预言机方法推广至随机置换的框架，其中算法可同时查询置换及其逆映射。我们展示了如何利用所得预言机模拟来界定算法对任意输入-输出对谓词的成功概率，这是Zhandry方法的关键特性，此前该特性在向随机置换推广的尝试中始终难以实现。一个关键技术要素是采用严格单调分解在预言机数据库中表示置换。作为我们框架的应用，我们证明在随机置换模型中，单轮海绵构造具有无条件原像抵抗性，从而证实了Unruh的猜想。