Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation
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We propose a compact architecture of a Montgomery elliptic curve scalar multiplier in a projective coordinate system over GF(2m). To minimize the gate area of the architecture, we use the common Z projective coordinate system where a common Z value is kept for two elliptic curve points during the calculations, which results in one register reduction. In addition, by reusing the registers we are able to reduce two more registers. Therefore, we reduce the number of registers required for elliptic curve processor from 9 to 6 (a 33%). Moreover, a unidirectional circular shift register file reduces the complexity of the register file, resulting in a further 17% reduction of total gate area in our design. As a result, the total gate area is 13.2k gates with 314k cycles which is the smallest compared to the previous works.