For two additive sets $A,B$ with respective ambient groups $G,F$, an order $2$ Freiman homomorphism from $A$ to $B$ is a map $\phi:A\to B$ with the property that, $$a_1+a_2=a'_1+a'_2 \Longrightarrow \phi(a_1)+\phi(a_2)=\phi(a'_1)+\phi(a'_2).$$
I'm interesting in building an injective map with anti-Freiman properties: For any distinct $a_1,a_2,a'_1, a'_2$, $$a_1+a_2=a'_1+a'_2 \Longrightarrow \phi(a_1)+\phi(a_2)\neq\phi(a'_1)+\phi(a'_2).$$ Is there any reference / names for such a map ?