B-2.1 Setup

Let $[0,t-1)$ be the plaintext range, and $[0,q-1)$ the ciphertext range, where $t<q$ ($t$ is much smaller than $q$). Randomly pick a vector $S$ of length $k$ comprising $k$ binary numbers as a secret key (denoted as $S\underset{}{\overset{\$}{\leftarrow }}{\mathbb{Z}}_2^k$). Let $\mathrm{\Delta }={\displaystyle \frac{q}{t}}$, the scaling factor of plaintext.