The invention relates to a sum and product computing method for protecting data privacy security of an arbitrary user group. The computing method comprises the following steps of system initialization, user private key generation, secret key generation, sum encryption, product encryption, sum decryption, and product decryption. To be specific, according to the system initialization, a security parameter is specified; and a corresponding integer group and a system public key are generated by the security parameter. According to the user private key generation, participants in the user group compute private keys independently and respectively, so that the product of the private keys is equal to one after modulus operation. According to the secret key generation, a sum secret key and a product secret key for encryption data are generated for the participants based on combination of the system public key and the user private keys. According to the sum encryption, during the sum computing, the participants utilize the obtained secret keys to carry out encryption on the sum computing and send obtained sum ciphertexts to other participants in the user group. According to the product encryption, during product computing, the participants utilize the obtained secret keys to carry out encryption on the product computing and send obtained product ciphertexts to other participants in the user group. According to the sum decryption, the participants in the user group combine the received ciphertexts to obtain a final sum. And according to the product decryption, the participants in the user group combine received ciphertexts to obtain a final product.