Efficient multiplication of binary polynomials is a critical challenge in Elliptic Curve Cryptography (ECC) systems, especially for resource-constrained hardware environments. Standard Karatsuba multipliers, while effective, often result in suboptimal hardware resource utilization, limiting their suitability for compact FPGA implementations. To address this, this work explores a novel overlap-free Karatsuba multiplier designed to reduce hardware complexity. Both the standard and overlap-free designs were implemented for 256-bit binary polynomial multiplication on the Artix-7 AC701 Evaluation Platform (model xc7a200tfbg676-2). Experimental results reveal that the overlap-free Karatsuba multiplier achieves a 17.3% reduction in Slice LUT usage compared to the standard version, making it a highly efficient choice for ECC applications in resourcelimited settings.