Solving quadratic congruences is a widely applied operation in cryptographic protocols to ensure the data secrecy in the Internet of Things (IoT). Yet it requires unaffordable computation resource for resource-constrained IoT devices when bulk of this type of operations need to be performed. How to efficiently and effectively solve quadratic congruences on IoT devices becomes a challenging issue. To address this problem, in this article, we propose two practical and secure outsourcing algorithms for solving quadratic congruences. Our proposed algorithms enable the IoT devices to outsource the heavy computation of solving quadratic congruences to a single cloud server, and therefore, achieve high efficiency for IoT devices. Meanwhile, we obscure the input and the output so that the outsourcing process does not leak the privacy of the computation, and the IoT devices in our algorithms can detect any misbehavior of the cloud server with a probability of 1. In addition, we take the Rabin encryption algorithm as an example to show how our proposed algorithms can be applied to IoT applications. The theoretical analysis and experimental results support the fact that our proposed algorithms are secure and efficient.

中文翻译：

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解决物联网二次一致性的实用且安全的外包算法

解决二次一致性是加密协议中广泛应用的操作，可确保物联网（IoT）中的数据保密。但是，当需要执行大量此类操作时，它需要资源受限的IoT设备无法承受的计算资源。如何有效地解决物联网设备上的二次一致性成为一个具有挑战性的问题。为了解决这个问题，在本文中，我们提出了两种实用且安全的外包算法来解决二次一致性。我们提出的算法使IoT设备可以将解决二次一致性的繁重计算工作外包给单个云服务器，从而实现IoT设备的高效率。同时，我们模糊了输入和输出，以使外包过程不会泄漏计算的私密性，而且我们算法中的IoT设备可以检测到云服务器的任何不当行为的可能性为1。此外，我们以Rabin加密算法为例来说明如何将我们提出的算法应用于IoT应用。理论分析和实验结果支持了我们提出的算法安全有效的事实。