Scalable and Unified Hardware to Compute Montgomery Inverse in GF(p) and GF(2)
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Efficient scalable VLSI architecture for Montgomery inversion in GF(p)
Integration, the VLSI Journal
A Carry-Free Architecture for Montgomery Inversion
IEEE Transactions on Computers
Parallel Itoh---Tsujii multiplicative inversion algorithm for a special class of trinomials
Designs, Codes and Cryptography
Hardware organization to achieve high-speed elliptic curve cryptography for mobile devices
Mobile Networks and Applications
Efficient hardware multiplicative inverters
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
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Abstract: Among the basic arithmetic operations over finite fields, the computation of a multiplicative inverse is the most time consuming operation. In this article, a number of methods are presented to efficiently compute the inverse using the extended Euclidean algorithm. The proposed methods can significantly reduce the computation time over large fields where the field elements are represented using a multi-precision format. A hardware structure for the inverter is also presented. The structure is area efficient and is suitable for resource constrained systems. Additionally, an application of the proposed inversion algorithm is given in the context of elliptic curve cryptography.