Identity-based signature has become an important technique for lightweight authentication as soon as it was proposed in 1984.Thereafter,identity-based signature schemes based on the integer factorization problem and discrete logarithm problem were proposed one after another.Nevertheless,the rapid development of quantum computers makes them insecure.Recently,many efforts have been made to construct identity-based signatures over lattice assumptions against attacks in the quantum era.However,their efficiency is not very satisfactory.In this study,an efficient identity-based signature scheme is presented over the number theory research unit(NTRU) lattice assumption.The new scheme is more efficient than other lattice-and identity-based signature schemes.The new scheme proves to be unforgeable against the adaptively chosen message attack in the random oracle model under the hardness of the γ-shortest vector problem on the NTRU lattice. Identity-based signature has become an important technique for lightweight authentication as soon as it was proposed in 1984. Thereafter, identity-based signature schemes based on the integer factorization problem and discrete logarithm problem were proposed one after another.Nevertheless, the rapid development of quantum computers makes them insecure.Recently, many efforts have been made to construct identity-based signatures over lattice assumptions against attacks in the quantum era. However, their efficiency is not very satisfactory.In this study, an efficient identity-based signature scheme is presented over the number theory research unit (NTRU) lattice assumption. The new scheme is more efficient than other lattice-and identity-based signature schemes. The new scheme proves to be unforgeable against the adaptively chosen message attack in the random oracle model under the hardness of the γ-shortest vector problem on the NTRU lattice.