Efficient hardware structure for extended Euclidean‐based inversion over

Abstract

In this study, an efficient hardware structure for implementation of extended Euclidean algorithm (EEA) inversion based on a modified algorithm is presented. In the proposed algorithm, one iteration performs the operations corresponding to two iterations in previously reported EEA-based inversion algorithm. The proposed structure is implemented based on a modified algorithm with low path-delay and hardware consumption. The circuit performs one iteration of the algorithm in one clock cycle. Furthermore, to increase speed and reduce the latency of the structure, the authors applied the loop unrolling technique by replicating the body of the loop. Loop unrolling replaces a loop body by several copies of the body. The authors chose the number of copies based on the trade-off between hardware resources, critical path delay and the number of clock cycles. Therefore, the time and area parameters can be adjusted by different choices. The proposed architecture is simple, low cost and also the number of clock cycles in the structure are reduced compared to existing EEA-based works. The structure over two binary finite fields F 2 163 and F 2 233 has been successfully verified and implemented on Virtex-5 XC5VLX110 fieldprogrammable gate array. The comparison with other previous implementations of the inversion operation verifies that the proposed method has better improvement in terms of area × time complexity.

A Hex Itoh-Tsujii inversion algorithm for FPGA platforms

“…Several attempts have been made to fasten the inverse operation [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] using squarer and quad circuits on FPGA platforms. There are two useful approaches for finding an inversion over GF (2 m ) which includes Extended Euclidean Algorithm (EEA) [14,23] and Fermat's Little Theorem (FLT) [24]. EEA requires more additional logic to compute the Greatest Common Divisor of the polynomial and is not much suitable for area efficient hardware implementation.…”