Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Software Implementation of the NIST Elliptic Curves Over Prime Fields
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Fast Implementation of Elliptic Curve Arithmetic in GF(pn)
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
IEEE Transactions on Computers
A state-of-the-art elliptic curve cryptographic processor operating in the frequency domain
Mobile Networks and Applications
| Hi-index | 0.00 |
Elliptic curve cryptography (ECC) was discovered by Koblitz and Miller, and there has been a vast amount of research on its secure and efficient implementation. To implement ECC, three kinds of finite fields are being widely used, i.e. prime field GF(p), binary field GF(2m) and optimal extension field GF(pm). There is an extensive literature on hardware implementation of prime fields and binary fields, but almost nothing is known about hardware implementation of OEFs. At a first glance, this may seem natural because OEF has been devised originally for efficient software implementation of ECC. However, we still need its hardware implementation for the environments where heterogeneous processors are communicating with each other using a single cryptographic protocol. Since the ECC software implementation over the weaker processor may not guarantee reasonable performance, a customized ECC coprocessor would be a good solution. In this paper, we propose an ECC coprocessor over GF(pm) on an FPGA. Since the most resource-consuming operation is inversion, we focus on the efficient design of inversion modules. First we provide four different implementations for inversion operation, i.e. three variants of Extended Euclidian Algorithm and inversion using the iterative Frobenius map. We use them as the building blocks of our ECC coprocessor over OEF. According to our analysis, inversion using the iterative Frobenius map shows the best performance among the four choices, from the viewpoints of speed and area.