Deep learning-based side channel attacks are burgeoning due to their better efficiency and performance, suppressing the traditional side-channel analysis. To launch the successful attack on a particular public key cryptographic (PKC) algorithm, a large number of samples per trace might need to be acquired to capture all the minor useful details from the leakage information, which increases the number of features per instance. The decreased instance-feature ratio increases the computational complexity of the deep learning-based attacks, limiting the attack efficiency. Moreover, data class imbalance can be a hindrance in accurate model training, leading to an accuracy paradox. We propose an efficient Convolutional Neural Network (CNN) based approach in which the dimensionality of the large leakage dataset is reduced, and then the data is processed using the proposed CNN based model. In the proposed model, the optimal number of convolutional blocks is used to build powerful features extractors within the cost limit. We have also analyzed and presented the impact of using the Synthetic Minority Over-sampling Technique (SMOTE) on the proposed model performance. We propose that a data-balancing step should be mandatory for analysis in the side channel attack scenario. We have also provided a performance-based comparative analysis between proposed and existing deep learning models for unprotected and protected Elliptic curve (ECC) Montgomery Power ladder implementations. The reduced network complexity, together with an improved attack efficiency, promote the proposed approach to be effectively used for side-channel attacks.