With the advancement of technology in the last few decades, leading to the widespread availability of miniaturized sensors and internet-connected things (IoT), security of electronic devices has become a top priority. Side-channel attack (SCA) is one of the prominent methods to break the security of an encryption system by exploiting the information leaked from the physical devices. Correlational power attack (CPA) is an efficient power side-channel attack technique, which analyses the correlation between the estimated and measured supply current traces to extract the secret key. The existing countermeasures to the power attacks are mainly based on reducing the SNR of the leaked data, or introducing large overhead using techniques like power balancing. This paper presents an attenuated signature AES (AS-AES), which resists SCA with minimal noise current overhead. AS-AES uses a shunt low-drop-out (LDO) regulator to suppress the AES current signature by 400x in the supply current traces. The shunt LDO has been fabricated and validated in 130 nm CMOS technology. System-level implementation of the AS-AES along with noise injection, shows that the system remains secure even after 50K encryptions, with 10x reduction in power overhead compared to that of noise addition alone.