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Rename m to N here (#7)
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idk maybe there's a better letter
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vEnhance authored Aug 15, 2024
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14 changes: 7 additions & 7 deletions easy/src/fhe2.typ
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Expand Up @@ -157,16 +157,16 @@ imagine that $q approx 2^(sqrt(n))$.

For security, instead of adding $4$ rows of the public key, we want to add
at least $log (q^n) = n log q$ rows. To be safe, maybe a little bigger, say
$m = 2 n log q$ (of course, for this to work, the
public key has to have at least $m$ rows). The
$N = 2 n log q$ (of course, for this to work, the
public key has to have at least $N$ rows). The
encryption algorithm will be "select some subset of the rows at random,
and add them up".

Combining $m$ rows will have the effect of multiplying the
error by $m$, so if the initial $epsilon.alt$ was bounded by $1$, then
the error in the ciphertext will be at most $m$. But remember that $q$
is exponentially large compared to $m$ and $n$ anyway, so a mere factor
of $m$ should not scare us!
Combining $N$ rows will have the effect of multiplying the
error by $N$, so if the initial $epsilon.alt$ was bounded by $1$, then
the error in the ciphertext will be at most $N$. But remember that $q$
is exponentially large compared to $N$ and $n$ anyway, so a mere factor
of $N$ should not scare us!

To generalize our choice of $m$ in $\{0,5\}$, we could encode a single bit
by using either $0$ or $⌊q / 2⌋$ to obtain maximum separation and thus
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