Efficient scalar multiplication of ECC using SMBR and fast septuple formula for IoT

In order to solve the problem between low power of Internet of Things devices and the high cost of cryptography, lightweight cryptography is required. The improvement of the scalar multiplication can effectively reduce the complexity of elliptic curve cryptography (ECC). In this paper, we propose a fast formula for point septupling on elliptic curves over binary fields using division polynomial and multiplexing of intermediate values to accelerate the computation by more than 14%. We also propose a scalar multiplication algorithm based on the step multi-base representation using point halving and the septuple formula we proposed, which significantly reduces the computational cost. The experimental results show that our method is more efficient over binary fields and contributes to reducing the complexity of ECC.