Encryption deduplication technology first encrypts the file or chunks of data, then detects and removes duplicate ciphertexts, storing only one copy on the cloud storage server (CSP). Although traditional encryption deduplication schemes have the function of ciphertext deduplication, they also have a serious problem. Since the key generation algorithm and the encryption algorithm are deterministic, the frequency of plaintext chunking will be leaked. It is possible for the attacker to infer the information of the plaintext. We propose a Randomized Encryption deduplication method against Frequency Attack (REFA) that provides high randomness in ciphertexts. The core idea of REFA is that after obtaining a convergence key generated with the aid of a key server, the user randomizes the convergence key with a random value of the same length. Then, REFA encrypts the plaintext chunk with a randomized key. Our scheme hides the random value in the ciphertext and encrypts the convergence key for user ownership verification. REFA perfectly masks the frequency of plaintext chunks and has high storage efficiency and data security. Furthermore, the CSP performs ciphertext updates with ciphertexts uploaded by subsequent users. REFA can effectively protect against frequency analysis attacks.