Modern high-performance as well as power-constrained System-on-Chips (SoC) are increasingly using hardware accelerated encryption engines to secure computation, memory access, and communication operations. The electromagnetic (EM) emission from a chip leaks information of the underlying logical operations and can be collected using low-cost non-invasive measurements. EM based side-channel attacks (EMSCA) have emerged as a major threat to security of encryption engines in a SoC. This paper presents the concept of Blindsight where a high-frequency inductive voltage regulator (IVR) integrated on the same chip with an encryption engine is used to increase resistance against EMSCA. High-frequency (~100MHz) IVRs are present in modern microprocessors to improve energy-efficiency. We show that an IVR with a randomized control loop (R-IVR) can reduce EMSCA as the integrated inductance acts as a strong EM emitter and blinds an adversary from EM emission of the encryption engine. The EM measurements are performed on a test-chip containing two architectures of a 128-bit Advanced Encryption Standard (AES) engine powered by a high-frequency R-IVR and under two attack scenarios, one, where an adversary gains complete physical access of the target device and the other, where the adversary is only in proximity of the device. In both attack modes, an adversary can observe information leakage in Test Vector Leakage Assessment (TVLA) test in a baseline IVR (B-IVR, without control loop randomization). However, we show that EM emission from the R-IVR blinds the attacker and significantly reduces SCA vulnerability of the AES engine. A range of practical side-channel analysis including TVLA, Correlation Electromagnetic Analysis (CEMA), and a template based CEMA shows that R-IVR can reduce information leakage and prevent key extraction even against a skilled adversary.