In the dynamic landscape of securing online communication in the context of blockchain applications, Internet of Things (IoT) systems, and online shopping platforms, where integrity data, authentication, and non-repudiation are crucial, digital signature schemes are necessary. Among these, Elliptic Curve Cryptography has been outstanding due to the ability to provide high level of security with lowest key sizes and computational cost. However, increased sophistication of Internet-based threats and the weaknesses in the implementation-level have raised concerns on the effectiveness of elliptic curve digital signature variants that are widely in use. Present literature is more inclined to discuss these schemes in isolation rather than a holistic scheme of comparing security and performance. The chasm in this paper is that it will offer a comprehensive security analysis of the major elliptic curve signature plans like the Elliptic Curve Digital Signature Algorithm, EdDSA and Schnorr Signature. The study methodology includes mathematical modeling, threat analysis (such as the EUF-CMA, side-channel, and fault attacks) and performance analysis with the measurement of such aspects as the computational efficiency, the security strength, the key size efficiency, and the scalability, and the resources consumption. It has been found out that ECDSA is still widely used, but is more prone to nonce-based attacks and is considerably more expensive to compute. Nevertheless, EdDSA and Schnorr signatures are safest and more effective, and Schnorr has the optimal overall balance, based on the measured metrics.