# Tag Info

Homomorphic cryptosystems are cryptsystems in which, given $c_1\mathcal{E}(m_1)$ and $c_2\mathcal{E}(m_2)$, another party can compute some function of $c_1$ and $c_2$. For example, say the other party wants to compute $m_1\cdot m_2$, the cryptosystem allows them to compute $c_1\odot c_2$ such that $\mathcal{D}(c_1\odot c_2) = m_1\cdot m_2$. Not that $\odot$ is not necessarily multiplication (and in fact often is not).
A system is said to be homomorphic with respect to addition if $m_1+m_2$ can be computed from $\mathcal{E}(m_1)$ and $\mathcal{E}(m_2)$. Homomorphic with respect to multiplication is similarly defined. A fully homomorphic cryptosystem would support any finite sequence of additions and multiplications.