In this paper, we apply the Sumcheck protocol to verify the Euclidean (resp. Hamming) distance computation in the case of facial (resp. iris) recognition. In particular, we consider a border crossing use case where, thanks to an interactive protocol, we delegate the authentication to the traveller. Verifiable computation aims to give the result of a computation and a proof of its correctness. In our case, the traveller takes over the authentication process and makes a proof that he did it correctly leaving to the authorities to check its validity. We integrate privacy preserving techniques to avoid that an eavesdropper gets information about the biometric data of the traveller during his interactions with the authorities. We provide implementation figures for our proposal showing that it is practical.