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 fixedbase 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 GF(2
²³³
), GF(2
¹⁶³
), and GF(2
²⁸³
) 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 GF(2
²³³
), GF(2
¹⁶³
), and GF(2
²⁸³
). Moreover, ASIC results show 100% energy improvement for the LC architecture implementation results over GF(2
¹⁶³
). In addition, the LL architecture has 99% reduction in point multiplication required time, respectively, using a pentanomial.