d04_d05 small fix

[heiheiha798]

No description provided.

[gogo9th]

I think we can fix as follows:

<<LINE 741>>
K''||{\infty}}{q_l'}
--> K''||{\infty}}{q_{l'}}.

<<LINE 741>>
The output of the \textsf{SlotToCoeff} step is $\textsf{RLWE}{S, \sigma}(M + K''p)$
--> The output of the \textsf{SlotToCoeff} step is $\textsf{RLWE}{S, \sigma}(M + K''p) \bmod q_{l'}$

<<LINE 741>>
where $||P||\infty$ denotes the maximum absolute coefficient value of polynomial $P$).
--> where $\hat{q} < q_l < q{l'} < q_L, and $||P||_\infty$ denotes the maximum absolute coefficient value of polynomial $P$).
(a little more details)

<<LINE 637>>
so that we can do \textsf{ModRaise} from $q_l \rightarrow q_l\cdot \hat{q}$ and then a modulus switch from $q_l\cdot \hat{q} \rightarrow \hat{q}$ (based on the technique learned in \autoref{subsec:bgv-modulus-switch})
--> so that we can do a modulus switch from $q_l\cdot \hat{q} \rightarrow \hat{q}$ (based on the technique learned in \autoref{subsec:bgv-modulus-switch})
(we should do a direct modulus swtich from q_l to \hat{q}) as described in \autoref{subsec:bgv-modulus-switch}

<<LINE 417>>
also smaller
--> also small

<<LINE 286>>
$\hat{q}$ only needs to satisfy the relationship: $\hat{q}$ and $q_l$ are co-prime, $\hat{q} &lt; q_l$ and $\hat{q} \equiv 1 \bmod t$.
--> $\hat{q}$ only needs to satisfy the relationship: $\hat{q} &lt; q_l$ and $\hat{q} \equiv 1 \bmod t$.
(The co-prime requirement does not make sense here, because \hat{q} is okay to be one of the multiplicative levels of the ciphertext modulus, in which case \hat{q} divides the modulus of the higher multiplicative levels. I think I was trying to say that it's also okay that \hat{q} is co-prime to q_l, which is the case where we do the initial modulus switch from q_l to \hat{q} in the bootstrapping procedure.)

<<LINE 449>>
Suppose we have the current ciphertext modulus $q_l$ and new ciphertext modulus $\hat{q}$ where $q_l \equiv \hat{q} \equiv 1 \bmod t$, $\hat{q} &lt; q_l$, and $\hat{q}$ and $\hat{q_l}$ are co-prime.
--> Suppose we have the current ciphertext modulus $q_l$ and new ciphertext modulus $\hat{q}$ where $q_l \equiv \hat{q} \equiv 1 \bmod t$, and $\hat{q} &lt; q_l$.
(For the same reason as line 286)

[gogo9th]

A few comments to d04-bgv.tex. d05-rns.tex is all good.

[gogo9th]

These are all correct