Elliptic Curve Cryptography with Efficiently Computable Endomorphisms and Its Hardware Implementations for the Internet of Things
Elliptic Curve Cryptography with Efficiently Computable Endomorphisms and Its Hardware Implementations for the Internet of Things
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DOI：
10.1109/tc.2016.2623609
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发表时间：
2017-05
影响因子：
3.7
通讯作者：
Zhe Liu;J. Großschädl;Zhi Hu;K. Järvinen;Husen Wang;I. Verbauwhede
中科院分区：
文献类型：
--
作者：
Zhe Liu;J. Großschädl;Zhi Hu;K. Järvinen;Husen Wang;I. Verbauwhede
ECDSA 签名的验证需要椭圆曲线上的双标量乘法。在这项工作中，我们研究了在扭曲的爱德华兹曲线上使用有效可计算的自同态来计算此操作，与传统实现相比，该操作可以将点加倍的数量减少大约 50%。特别是，我们关注在 207 位素数域 $\mathbb {F}_p$ 上定义的曲线，其中 $p = 2^{207}-5{,}131$ 。我们对操作进行了多种优化，并描述了用于计算操作的两种硬件架构。第一个架构是在 0.13 $\mu$ m CMOS ASIC 中实现的小型处理器，适用于物联网 (IoT) 应用的资源受限设备。第二种架构旨在通过使用 FPGA 加速进行快速签名验证，可用于这些应用程序的服务器端。我们的设计在性能和资源需求之间提供了各种权衡和优化，它们对于物联网应用很有价值。
Verification of an ECDSA signature requires a double scalar multiplication on an elliptic curve. In this work, we study the computation of this operation on a twisted Edwards curve with an efficiently computable endomorphism, which allows reducing the number of point doublings by approximately 50 percent compared to a conventional implementation. In particular, we focus on a curve defined over the 207-bit prime field $\mathbb {F}_p$ with $p = 2^{207}-5{,}131$ . We develop several optimizations to the operation and we describe two hardware architectures for computing the operation. The first architecture is a small processor implemented in 0.13 $\mu$ m CMOS ASIC and is useful in resource-constrained devices for the Internet of Things (IoT) applications. The second architecture is designed for fast signature verifications by using FPGA acceleration and can be used in the server-side of these applications. Our designs offer various trade-offs and optimizations between performance and resource requirements and they are valuable for IoT applications.