diff --git a/lec_15_FHE.md b/lec_15_FHE.md index 5c80e8d..76e435a 100644 --- a/lec_15_FHE.md +++ b/lec_15_FHE.md @@ -80,7 +80,7 @@ We focus on encryption for single bits. This is without loss of generality for Let $\mathcal{F} = \cup \mathcal{F}_\ell$ be a class of functions where every $f\in\mathcal{F}_\ell$ maps $\{0,1\}^\ell$ to $\{0,1\}$. An _$\mathcal{F}$-homomorphic public key encryption scheme_ is a CPA secure public key encryption scheme $(G,E,D)$ such that there exists a polynomial-time algorithm $EVAL:\{0,1\}^* \rightarrow \{0,1\}^*$ such that for every $(e,d)=G(1^n)$, $\ell=poly(n)$, $x_1,\ldots,x_\ell \in \{0,1\}$, and $f\in \mathcal{F}_\ell$ of description size $|f|$ at most $poly(\ell)$ it holds that: -* $c=EVAL_e(f,E_e(x_1),\ldots,E_e(x_\ell))$ has length at most $n$. +* $c=EVAL_e(f,E_e(x_1),\ldots,E_e(x_\ell))$ has length at most $p(n)$ for $p=poly(\cdot)$ that does not grow with $\ell$ or $|f|$. * $D_d(c)=f(x_1,\ldots,x_\ell)$. :::