Key Encapsulation Mechanism

Key Encapsulation Mechanism, also known as KEM, is a triple of algorithms ${\mathcal {K}}=\{{\text{KeyGen}},{\text{Encaps}},{\text{Decaps}}\}$ and a corresponding key space $K$, a ciphertext space ${\text{C}}$ with

1. The ${\text{KeyGen}}(n)$ algorithm takes a public parameter $n$ as an input and returns a public and secret-key pair (${\text{pk}},{\text{sk}}$).
2. The probabilistic ${\text{Encaps}}(pk)$ (encapsulation) algorithms takes ${\text{pk}}$ as an input and returns a ciphertext $c\in C$ and a key $k\in K$.
3. The deterministic ${\text{Decaps}}(sk,c)$ (decapsulation) algorithm takes ${\text{sk}},{\text{c}}$ as inputs and returns a key $k\in K\cup \{\perp \}$, with $\perp$ denoting as a failure.