A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
An End-to-End Systems Approach to Elliptic Curve Cryptography
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
A Scalable Dual-Field Elliptic Curve Cryptographic Processor
IEEE Transactions on Computers
Proceedings of the conference on Design, Automation and Test in Europe - Volume 3
WEWoRC'11 Proceedings of the 4th Western European conference on Research in Cryptology
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In this paper we discuss approaches that allow to construct efficient polynomial multiplication units. Such multipliers are the most important components of ECC hardware accelerators. The proposed hRAIK multiplication improves energy consumption, the longest path, and required silicon area compared to state of the art approaches. We use such a core multiplier to construct an efficient sequential polynomial multiplier based on the known iterative Karatsuba method. Finally, we exploit the beneficial properties of the design to build an ECC accelerator. The design for GF(2233) requires about 1.4 mm2 cell area in a .25 μm technology and needs 80 μsec for an EC point multiplication.