Compressed sensing (CS) has recently emerged as an effective and efficient way to encrypt data. Under certain conditions, it has been shown to provide some secrecy notions. In theory, it could be considered to be a perfect match for constrained devices needing to acquire and protect the data with computationally cheap operations. However, the theoretical results on the secrecy of compressive cryptosystems only hold under the assumption of infinite precision representation. With this work, we aim to close this gap and lay the theoretical foundations to support this practical framework. We provide theoretical upper bounds on the distinguishability of the measurements acquired through finite precision sensing matrices and experimentally validate them. Our main result is that the secrecy of a CS cryptosystem can be exponentially increased with a linear increase in the representation precision. This result confirms that the CS can be an effective secrecy layer and provides tools to use it in practical settings.

中文翻译：

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有限精度压缩密码系统的保密性分析


压缩感知 (CS) 最近已成为一种有效且高效的数据加密方法。在某些条件下，它已被证明可以提供一些保密概念。从理论上讲，它可以被认为是需要通过计算成本低的操作来获取和保护数据的受限设备的完美匹配。然而，压缩密码系统保密性的理论结果仅在无限精度表示的假设下成立。通过这项工作，我们的目标是缩小这一差距，并为支持这一实践框架奠定理论基础。我们提供了通过有限精度传感矩阵获得的测量结果的可区分性的理论上限，并通过实验验证了它们。我们的主要结果是，随着表示精度的线性增加，CS 密码系统的保密性可以呈指数级增加。这一结果证实了 CS 可以成为一个有效的保密层，并提供了在实际环境中使用它的工具。