<p>This paper presents an optimized approach to the implementation of the Gallant–Lambert–Vanstone method for scalar multiplication on elliptic curves, with special emphasis on BLS curves. The optimization is based on the insight that only half of the look-up table needs to be explicitly computed, while the rest can be derived by means of an efficient endomorphism. Precise algorithms, including lookup table construction, unified recoding/alignment, and efficient multiplication loops, are meticulously presented. The corresponding regular implementations are also provided. The effectiveness of the approach is demonstrated through a comparative analysis with the standard method. This includes a comprehensive evaluation of their computational advantages compared to conventional methods. The proposed implementation prioritizes regularity and optimization, aiming to provide resilience against potential cryptographic vulnerabilities, particularly side-channel attacks due to its regular implementation.</p>