The Elliptic Curve Primality Test (ECPT) is a method used to determine whether a number is prime. It leverages the properties of elliptic curves, which are mathematical structures defined by specific equations. By analyzing these curves, the test can efficiently identify prime numbers, making it useful in fields like cryptography. ECPT is based on the theory of elliptic curves and their group structures. It is often faster than traditional primality tests, especially for large numbers. This efficiency is crucial for applications in secure communications, where large prime numbers are essential for algorithms like those used in RSA and Diffie-Hellman key exchange.