In modern critical infrastructure such as power grids, it is crucial to ensure security of data communications between network-connected devices while following strict latency criteria. This necessitates the use of cryptographic hardware accelerators. We propose a high-performance unified elliptic curve cryptography accelerator supporting NIST standard Montgomery curves Curve25519 and Curve448 at 128-bit and 224-bit security levels respectively. Our accelerator implements extensive parallel processing of Karatsuba-style large-integer multiplications, restructures arithmetic operations in the Montgomery Ladder and exploits special mathematical properties of the underlying pseudo-Mersenne and Solinas prime fields for optimized performance. Our design ensures efficient resource sharing across both curve computations and also incorporates several standard side-channel countermeasures. Our ASIC implementation achieves record performance and energy of 10.38 $μ$s / 54.01 $μ$s and 0.72 $μ$J / 3.73 $μ$J respectively for Curve25519 / Curve448, which is significantly better than state-of-the-art.