Scalar multiplication is the core operation in traditional elliptic curve cryptography (ECC). Scalar representations determine the iterations in scalar multiplication algorithms, which directly affect the security and efficiency of the algorithms. This study proposes two new scalar representation algorithms. One algorithm is ordered window width non-adjacent form (OWNAF) which combines traditional window non-adjacent form with random key segmentation and can resist energy analysis attacks while yielding better efficiency. The other is called window joint regular form (wJRF), which is improved from the traditional joint regular form. The wJRF algorithm is applicable to multi-scalar multiplication algorithms, which can reduce computational costs and ensure sound security compared with the existing algorithms.