Abstract Channels and Their Robust Information-Leakage Ordering
Abstract Channels and Their Robust Information-Leakage Ordering
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抽象通道及其鲁棒信息泄漏排序
DOI：
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发表时间：
2014
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通讯作者：
L. Meinicke
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作者：
Annabelle McIver;Carroll Morgan;Geoffrey Smith;Barbara Espinoza;L. Meinicke
处理秘密输入的概率系统的可观察输出可能会揭示有关该输入的一些信息。系统可以建模为一个信息论的通道，它指定给定每个输入的每个输出的概率。给定这些输入的先验分布，类似熵的测量可以量化由通道引起的信息泄漏量。但事实证明，传统的通道表示，作为一个矩阵，包含了相对于泄漏的冗余结构，比如列的标记，以及互为标量倍数的列。因此，我们通过引用这些冗余来引入抽象通道。从泄漏的角度来看，通道的一个基本问题是一个通道是否比另一个更差。但是，考虑到大量可能的先验分布和泄漏措施，很难可靠地回答这个问题。事实上，越来越多的人认识到，不同的泄漏措施适用于不同的情况，这导致了最近提出的g泄漏措施，该措施使用增益函数g来模拟通道运行的操作场景：对于任何先验和任何增益函数，强g泄漏预顺序要求通道a永远不会比通道B泄漏更多。这里我们证明，在抽象通道上，强g泄漏预阶是反对称的，因此是偏阶。先前已经证明，强g漏序是由一种称为复合细化的结构有序隐含的，该结构有序要求a = BR，对于某些通道R；但相反的情况并没有得到全面的证实，而是留下了所谓的“革质猜想”。利用b[2]的观点，我们在这里证实了皮质猜想。因此，强g-泄漏排序和成分精化是一致的，使得我们的偏序在结构和泄漏测试上都具有重要意义。
The observable output of a probabilistic system that processes a secret input might reveal some information about that input. The system can be modelled as an information-theoretic channel that specifies the probability of each output, given each input. Given a prior distribution on those inputs, entropy-like measures can then quantify the amount of information leakage caused by the channel. But it turns out that the conventional channel representation, as a matrix, contains structure that is redundant with respect to that leakage, such as the labeling of columns, and columns that are scalar multiples of each other. We therefore introduce abstract channels by quotienting over those redundancies. A fundamental question for channels is whether one is worse than another, from a leakage point of view. But it is difficult to answer this question robustly, given the multitude of possible prior distributions and leakage measures. Indeed, there is growing recognition that different leakage measures are appropriate in different circumstances, leading to the recently proposed g-leakage measures, which use gain functions g to model the operational scenario in which a channel operates: the strong g-leakage pre-order requires that channel A never leak more than channel B, for any prior and any gain function. Here we show that, on abstract channels, the strong g-leakage pre-order is antisymmetric, and therefore a partial order. It was previously shown [1] that the strong g-leakage ordering is implied by a structural ordering called composition refinement, which requires that A = BR, for some channel R; but the converse was not established in full generality, left open as the so-called Coriaceous Conjecture. Using ideas from [2], we here confirm the Coriaceous Conjecture. Hence the strong g-leakage ordering and composition refinement coincide, giving our partial order both structural- and leakage-testing significance.