A Low-Latency and Low-Complexity Point-Multiplication in ECC

Elliptic curve cryptography (ECC) has received attention, because it can achieve the same security level as other asymmetric methods while using a key with smaller length. Although ECC is more efficient compared with other asymmetric methods, the fast computation of ECC is always desirable. In this paper, a fixed-base comb point multiplication method has been used to perform regular point multiplication. In addition, two low-complexity (LC) and low-latency (LL) architectures for the regular point multiplication using fixed-base comb method have been proposed. The point multiplication architectures have been implemented using field-programmable gate array and application-specific integrated circuit (ASIC). The LC architecture implementation results over <inline-formula> <tex-math notation="LaTeX">$GF(2^{233})$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$GF(2^{163})$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$GF(2^{283})$ </tex-math></inline-formula> show 62%, 46%, and 152% efficiency improvement, respectively. In addition, the LL architecture has 55%, 44%, and 76% reduction in point multiplication required time, respectively, over <inline-formula> <tex-math notation="LaTeX">$GF(2^{233})$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$GF(2^{163})$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$GF(2^{283})$ </tex-math></inline-formula>. Moreover, ASIC results show 100% energy improvement for the LC architecture implementation results over <inline-formula> <tex-math notation="LaTeX">$GF(2^{163})$ </tex-math></inline-formula>. In addition, the LL architecture has 99% reduction in point multiplication required time, respectively, using a pentanomial.

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