[en] 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 Fp with p = 2^207 - 5131. 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 μm 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.
Disciplines :
Computer science
Author, co-author :
Liu, Zhe ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > Computer Science and Communications Research Unit (CSC)
Groszschädl, Johann ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
Hu, Zhi; Central South University > School of Mathematics and Statistics
Järvinen, Kimmo; Katholieke Universiteit Leuven > Department of Electrical Engineering (ESAT)
Wang, Husen ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
Verbauwhede, Ingrid; Katholieke Universiteit Leuven > Department of Electrical Engineering (ESAT)
External co-authors :
yes
Language :
English
Title :
Elliptic Curve Cryptography with Efficiently Computable Endomorphisms and Its Hardware Implementations for the Internet of Things
Publication date :
May 2017
Journal title :
IEEE Transactions on Computers
ISSN :
1557-9956
Publisher :
Institute of Electrical and Electronics Engineers, Los Alamitos, United States - California