ACORN v3 is a lightweight authenticated encryption cipher, which was selected as one of the seven nalists of CAESAR competition in March 2018. It is intended for lightweight applications (resource-constrained environments). By using the technique numeric mapping proposed at CRYPTO 2017, an e cient algorithm for algebraic degree estimation of ACORN v3 is proposed. As a result, new distinguishing attacks on 647, 649, 670, 704, and 721 initialization rounds of ACORN v3 are obtained, respectively. So far, as we know, all of our distinguishing attacks on ACORN v3 are the best. e e ectiveness and accuracy of our algorithm is con rmed by the experimental results.