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In an advanced metering infrastructure (AMI), the utility collects power consumption data from smart meters to improve energy optimization and provides detailed information on power consumption to utility customers. However, AMI is vulnerable to data falsification attacks, which can be launched by organized adversaries. Such attacks can be detected by analysing fine-grained power consumption data from customers, however, they violate the privacy of each customer in the grid. To strike a balance between privacy and security, a framework for privacy-preserving anomaly-based attack detection was proposed in the previous work, which uses homomorphic encryption (HE) scheme to address the issue of data falsification.HE is a form of encryption that permits users to perform computations on the encrypted data without having to decrypt the data. However, the downside of HE is computational overhead in terms of execution time. This thesis proposes a method for privacy-preserving and attack detection of data generated by smart meters to shorten the execution time. Our method applies elliptic curve cryptography (ECC) based HE for anomaly-based attack detection for data falsification over encrypted data. Through ECC, we can achieve the same security as a 3,072-bit RSA key with a 256-bit ECC key. Therefore, ECC requires less memory space to implement the encryption and decryption algorithms, which in turn reduces the time required to perform encryption and decryption operations.The proposed scheme and the CKKS-based method are implemented on the same platform using Python 3.8.10 to compare the execution times for user-side computation, server-side computation, and utility-side computation. In the proposed scheme, the user side computation is 10 times faster and the server-side computation is more than 100 times faster compared to the CKKS (HE) scheme.