# Elliptic Curve Cryptography with Efficiently Computable Endomorphisms and Its Hardware Implementations for the Internet of Things

Research output: Contribution to journalArticleScientificpeer-review

### Researchers

• Zhe Liu
• Johann Großschädl
• Zhi Hu
• Kimmo Järvinen
• Husen Wang
• Ingrid Verbauwhede

### Research units

• Nanjing University of Aeronautics and Astronautics
• University of Waterloo
• University of Luxembourg
• Central South University
• KU Leuven

### Abstract

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.

### Details

Original language English 7727929 773-785 13 IEEE Transactions on Computers 66 5 Published - 1 May 2017 A1 Journal article-refereed

### Research areas

• elliptic curve cryptography, Internet-of-Things, multiple-precision arithmetic, signature verification, VLSI designs

ID: 12965302