In this paper, we show efficient implementations of binary field multiplication over ARMv8.
We exploit an advanced 64-bit polynomial multiplication (\texttt{PMULL}) supported by ARMv8
and conduct multiple levels of asymptotically faster Karatsuba multiplication.
Finally, our method conducts binary field multiplication within 57 and 153 clock cycles for B-251 and B-571, respectively.
Our proposed method on ARMv8 improves the performance by a factor of $5.5 \sim 7.2$ times than previous techniques on ARMv7.
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