diff --git a/easy/src/fhe2.typ b/easy/src/fhe2.typ index 0aea4b5..6cf6b07 100644 --- a/easy/src/fhe2.typ +++ b/easy/src/fhe2.typ @@ -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