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Full homomorphic encryption (FHE) supports arbitrary computation on the ciphertext without the requirement of decryption,which provides protection for privacy security in cloud computing.However,the current FHE scheme constructed using the approximate eigenvector method requires complex matrix multiplications,which is computationally complicated and cannot resist subfield attacks.In this paper,a new FHE scheme was proposed by using the power-of-prime cyclotomic ring instead of a power-of-two cyclotomic ring,and the complex matrix multiplications in homomorphic multiplications were effectively avoided by modifying the ciphertext form and decryption structure.Compared with similar schemes,the proposed scheme improves the efficiency at least by a factor of <i>lφ(x)/2d</i> and is secure against IND-CPA attacks.