Definition

An encryption scheme is perfectly indistinguishable if ∀m0,m1∈ℳ\forall m_0, m_1 \in \mathcal{M}, forallc∈𝒞forall c \in \mathcal{C},

Pr⁡[Enc𝐊⁡(m0)=c]=Pr⁡[Enc𝐊⁡(m1)=c]\Pr[\operatorname{Enc}_\mathbf{K}(m_0)=c] = \Pr[\operatorname{Enc}_\mathbf{K}(m_1)=c]

where 𝐊\mathbf{K} is uniform over 𝒦\mathcal{K}.

(with ℳ\mathcal{M} message space, 𝒦\mathcal{K} key space, 𝒞\mathcal{C} cipher space)