xRSA: Construct Larger Bits RSA on Low-Cost Devices

Fan Dang, Lingkun Li, Jiajie Chen
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Abstract

As the most widely applied public-key cryptographic algorithm, RSA is now integrated into many low-cost devices such as IoT devices. Due to the limited resource, most low-cost devices only ship a 2048-bit multiplier, making the longest supported private key length as 2048 bits. Unfortunately, 2048-bit RSA keys are gradually considered insecure. Utilizing the existing 2048-bit multiplier is challenging because a 4096-bit message cannot be stored in the multiplier. In this paper, we perform a thorough study of RSA and propose a new method that achieves the 4096-bit RSA cryptography with the existing hardware. We use the Montgomery modular multiplication and the Chinese Remainder Theorem to reduce the computational cost and construct the necessary components to compute the RSA private key operation. To further validate the correctness of the method and evaluate its performance, we implement this method on a micro-controller and build a testbed named CanoKey with three commonly used cryptography protocols. The result shows that our method is over 200x faster than the naive method, a.k.a., software-based big number multiplications.
xRSA:在低成本设备上构造大比特RSA
RSA作为目前应用最广泛的公钥加密算法,已被集成到物联网设备等许多低成本设备中。由于资源有限,大多数低成本设备只提供2048位乘法器,因此支持的最长私钥长度为2048位。不幸的是,2048位RSA密钥逐渐被认为是不安全的。利用现有的2048位乘法器具有挑战性,因为4096位消息不能存储在乘法器中。本文对RSA进行了深入的研究,提出了一种利用现有硬件实现4096位RSA加密的新方法。我们使用Montgomery模乘法和中国剩余定理来减少计算成本,并构造计算RSA私钥操作所需的组件。为了进一步验证该方法的正确性并评估其性能,我们在微控制器上实现了该方法,并构建了一个名为CanoKey的测试平台,其中包含三种常用的加密协议。结果表明,我们的方法比基于软件的大数乘法的朴素方法快200倍以上。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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