pqNTRUSign is a lattice based, same-key aggregatable signature scheme. After three years of revision, during which period, the scheme has been submitted to, and rejected by, NIST PQC standardization process, the pqNTRUSign paper is finally accepted for publication by Design, Codes and Cryptography. In this paper, we finally come up with a proof for the existential unforgeablity of the signature, based on the short integer solution (SIS) problems over certain structured lattices.