Minimizing hamming weight based on 1's complement of binary numbers over GF(2^m)

Elliptic curve cryptosystems have been the focus of much attention as the benefits of elliptic curve cryptography (ECC) become many such as a small software footprint, low hardware implementation costs, linear scalability, low bandwidth requirements, and high performance, which have been drawn great attentions in particular wireless sensor networks. Many papers have investigated various algorithms for fast calculations due to the wireless sensor networks are always limited power energy, constrict computing capacity, and other tighten resources such as storage capacity limited, etc. In this paper a novel algorithm is first presented, with which the hamming weight will be minimized therefore the calculation cost will be dropped and the cryptographic algorithm has gained the natures of ECC. This makes ECC more suitable for use in constrained environment such as mobile sensor information applications, where computing resources and power availability are limited. The final results show that, in comparison with popular algorithms, such as NAF, MOF and complementary algorithms, the proposed algorithm significantly improved (average about 12.5% decreasing comparing with complementary algorithms).