对称加密流交换引理的信息论证明
An Information-Theoretic Proof of the Streaming Switching Lemma for Symmetric Encryption
摘要：
在密码学的一个基本范例的启发下，我们考虑了一个最近的变种的经典问题的边界之间的区别优势的随机函数和随机排列。具体来说，我们考虑的问题，决定是否一个序列的$q$值进行了采样均匀或不替换从$[N]$，其中的决定是由一个流算法限制使用最多$s$位的内部存储器。在这项工作中，这样的算法的显着优势是衡量的KL分歧之间的分布，其输出下诱导的两种情况下。我们表明，对于任何$s=Ω(\log N)$的区别优势是上限由$O(q \cdot s / N)$，甚至由$O(q \cdot s / N \log N)$时，$q \leq N^{1 - ε}$为任何常数$ε> 0$，它是近紧相对于KL分歧。
英文摘要：
Motivated by a fundamental paradigm in cryptography, we consider a recent variant of the classic problem of bounding the distinguishing advantage between a random function and a random permutation. Specifically, we consider the problem of deciding whether a sequence of $q$ values was sampled uniformly with or without replacement from $[N]$, where the decision is made by a streaming algorithm restricted to using at most $s$ bits of internal memory. In this work, the distinguishing advantage of such an algorithm is measured by the KL divergence between the distributions of its output as induced under the two cases. We show that for any $s=Ω(\log N)$ the distinguishing advantage is upper bounded by $O(q \cdot s / N)$, and even by $O(q \cdot s / N \log N)$ when $q \leq N^{1 - ε}$ for any constant $ε> 0$ where it is nearly tight with respect to the KL divergence.
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