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Inversion over GF(2m) is crucial for cryptographic applications such as elliptic curve cryptography. The commonly used Itoh-Tsujii algorithm (ITA) computes the inversion by an entirely sequential process consisting of multiplications and squarings. In this paper, we first propose a modified ITA algorithm (MITA) for inversion with polynomial basis (PB). The MITA reduces the required clock cycles of...
This paper proposes an efficient pipelined architecture of elliptic curve scalar multiplication (ECSM) over GF(${2}^{m}$ ). The architecture uses a bit-parallel finite-field (FF) multiplier accumulator (MAC) based on the Karatsuba-Ofman algorithm. The Montgomery ladder algorithm is modified for better sharing of execution paths. The data path in the architecture is well designed, so that the critical...
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