B-5 GLev

A GLev ciphertext is a list of GLWE ciphertexts which encrypts the list of plaintext ${\displaystyle \frac{q}{{\beta }^1}}M,{\displaystyle \frac{q}{{\beta }^2}}M,\cdots ,{\displaystyle \frac{q}{{\beta }^l}}M$, where $M$ is a plaintext encoded in a polynomial. Note a GLev ciphertext’s each $i$-th GLWE ciphertext uses a different plaintext scaling factor, which is: ${\mathrm{\Delta }}_i={\displaystyle \frac{q}{{\beta }^i}}$. The structure of GLev ciphertext is visually depicted in Figure 9.

Note that $\beta$ should be some value between $t$ and $q$. Especially, $t$ should be smaller than $\beta$, because if $t$ is greater than $\beta$, then the higher bits of $M$ will overflow beyond $q$ when computing ${\displaystyle \frac{q}{{\beta }^1}}M$.