Length-flexible additively homomorphic encryption ⇒ Additively homomorphic encryption

Fully-black-box reduction · standard model · folklore · security loss: none

Statement

Run at length $s=1$, a length-flexible additively homomorphic encryption scheme is an additively homomorphic encryption scheme with message space ${\mathbb{Z}}_{M_1}$ and ciphertexts in ${\mathbb{Z}}_{M_2}$, with the same IND-CPA advantage — folklore.