We obtain truncated restriction estimates of an unexpected form for discrete surfaces $$\begin{align*}S_N = \{\, (n_1 , \dots , n_d , R(n_1 , \dots, n_d)) \,,\, n_i \in [-N,N] \cap {\mathbb{Z}} \,\},\end{align*}$$ where |$R$| is an indefinite quadratic form with integer matrix.