B-5.2 Decryption

We decrypt the first GLWE ciphertext ($i=1$) using the secret $S$, with the scaling factor ${\mathrm{\Delta }}_1={\displaystyle \frac{q}{\beta }}$. This is because while the ciphertext contains $l$ encryptions, the higher indices $i>1$ have progressively smaller scaling factors ${\mathrm{\Delta }}_i=q∕{\beta }^i$. If ${\mathrm{\Delta }}_i$ becomes smaller than the noise threshold, those specific components cannot be decrypted correctly.