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A fast and secure public-key image encryption scheme based on Mordell elliptic curves

机译：基于Mordell椭圆曲线的快速安全公共键图像加密方案

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Encryption schemes based on elliptic curves (ECs) have shown high resistance against modern cryptanalysis. However, these schemes involve heavy computation for the generation of points over ECs, and therefore they are not suitable for communication systems such as sensor networks and Internet of Things. Thus, we propose a fast and secure public-key image encryption scheme. In this scheme, the sender and receiver agree on a public EC. Then the scheme performs pixel-masking and pixel-scrambling procedures using random numbers and a dynamic substitution box over ECs that are isomorphic to the public EC. For a fixed public EC, we prove that our scheme has a computational complexity that is a polylogarithmic function of the size of the plain text. In other words, the computational complexity of our scheme is independent of the point generation over ECs. We tested the security of our scheme against modern attacks by encrypting all standard images in the USC-SIPI image database. Compared to some state-of-the-art cryptosystems, our scheme is fast and has high security.
机译：基于椭圆曲线（ECS）的加密方案表现出高抗现代密码分析的电阻。然而，这些方案涉及对ECS的产生点的重量计算，因此它们不适合传感器网络和物联网等通信系统。因此，我们提出了一种快速安全的公钥图像加密方案。在本计划中，发件人和接收者在公共EC上达成一致。然后，该方案使用随机数和对公共EC同性构的ECS上的随机数和动态替代框执行像素屏蔽和像素 - 扰箱。对于固定的公共EC，我们证明我们的方案具有计算复杂性，这是纯文本大小的波动力学函数。换句话说，我们的方案的计算复杂性与ECS上的点一代无关。我们通过加密USC-SIPI图像数据库中的所有标准图像来测试我们的计划对现代攻击的安全性。与某些最先进的密码系统相比，我们的计划是快速的，安全性高。

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