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With the arrival of the era of big data, more and more users begin to adopt public cloud storage to store data and compute data. Sharing large amounts of sensitive data in the public cloud will arouse privacy concerns. Data encryption is a widely accepted method to prevent information leakage. How to achieve the cloud sharing and cloud computing of big data is a challenging problem. Conditional proxy re-encryption can solve cloud sharing, and homomorphic encryption can achieve cloud computing. In this paper, we combine conditional proxy re-encryption with homomorphic encryption to construct a lattice-based identity-based homomorphic conditional proxy re-encryption for secure big data computing in cloud environment. The scheme can not only realize the encrypted data sharing in the cloud, but also can realize the encrypted data computing in the cloud. That is, the homomorphic conditional proxy re-encryption scheme can homomorphically evaluate ciphertexts no matter ciphertexts are 'fresh' or re-encrypted (re-encrypted ciphertexts can come from different identities). The constructed scheme modifies the homomorphic proxy re-encryption scheme of Ma et al. We also use the approximate eigenvector method to manage the noise level and decrease the decryption complexity without introducing additional assumptions. At last, we prove that the scheme is indistinguishable against chosen-plaintext attacks, key privacy secure and master secret secure. [ABSTRACT FROM AUTHOR]