Sure, here is a detailed explanation of Elliptic Curve Cryptography (ECC) key generation, encryption, and decryption in bullet points:

Key Generation:

Choose a prime number p that is large enough to resist attacks.

Choose an elliptic curve E over the finite field Fp with a point G on it.

Choose a random integer n such that 1 < n < p-1.

Calculate the public key point Q = nG.

The private key is the integer n.

Encryption:

Choose a random integer k such that 1 < k < n-1.

Calculate the public key point P = kG.

Compute the shared secret point S = kQ.

Convert the plaintext message M into a point on the curve.

Calculate the ciphertext C = (M + S)P.

Decryption:

Compute the shared secret point S = nP.

Calculate the plaintext message M = C - S.

Convert the point M back into the original plaintext message.

It's worth noting that ECC has several advantages over other public-key cryptography algorithms, including smaller key sizes and faster computations, making it an attractive choice for resource-limited environments such as mobile devices and IoT devices. However, it is important to note that proper implementation and key management are critical for the security of the system.