The elliptic curve cryptography is based upon the efficient scalar multiplication, which directly affects the performance and security of a calculation. The article is an in-depth analysis of the advanced techniques of multiplication of scalars to reduce time complexity and resource consumption. It analyzes algorithmic optimization strategies, including, but not limited to, precomputation techniques, windowing techniques and memorycomputation trade-offs. The parallel processing and pipelining are addressed to enhance the throughput features of hardware and software programs. The use of the GLV and GLS methods of endomorphisms are examined with the aim of hastening the breakdown of scalars. The binary method and its computational complexity is also taken into consideration along with the optimized point addition and doubling algorithms in the context of the group law. According to the experimental findings, the time spent on execution, the amount of energy used, and the scalability have improved positively, which demonstrates the applicability of the proposed optimizations to the recent cryptographic systems.