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The Itoh-Tsujii multiplicative inverse algorithm (ITA) forms an integral component of several cryptographic implementations such as elliptic curve cryptography. For binary fields generated by irreducible trinomials, this paper proposes a modified ITA algorithm for efficient implementations on field-programmable gate-array (FPGA) platforms. Efficiency is obtained by the fact that the adapted ITA algorithm uses FPGA resources better and requires shorter addition chains. Evidence is furnished and supported with experimental results to show that the proposed architecture outperforms reported results. The proposed method is also shown to be scalable with respect to field sizes.