Aimed at the problems that the homomorphous signature schemes based on the latticebased theory can resist the quantum computer attacks, however, the existing homomorphous signature schemes based on the standard latticebased theory are inefficient due to their large key storage and complex structure, failing to be used for the equipment support cloud service, a first antiquantum computing linear homomorphism authentication scheme for equipment assurance cloud service is designed based on the NTRU. The algorithm generated by the key of the NTRU is utilized for simplifying the system key quantity and avoiding the huge key quantity. And then the linear homomorphism authentication value is produced by using the simple structure of the NTRU lattice preimage sampleable algorithm. The results show that the scheme satisfies the weak context hiding property. And the scheme achieves existential unforgeability against adaptive chosen message under the NTRUSIS (small integer solution) assumption in the random oracle model. Compared with the current scheme in effect, the new scheme is superior in the key quantity, the certification cost and the communication cost.