Updatable encryption (UE) allows a third-party server to update outsourced encrypted data without exposing keys and plaintexts. The server can update ciphertexts to ones under a new key using an update token provided by the client. UE can realize efficient key rotation and is effective against key compromise. The standard security notions of UE capture the property that even if keys or update tokens are compromised, the confidentiality of messages is maintained by the key update and ciphertext update. In general, the randomnesses used in the encryption and ciphertext update algorithms must be kept secret in the same way as the keys. On the other hand, while key compromise is considered in existing security notions, randomness compromise is not. In this paper, we define a new security notion for UE, \(\textsf{IND}\text {-}\textsf{UE}\text {-}\textsf{R}\) security, that is resilient to the compromise of randomnesses used to generate or update ciphertexts. Furthermore, we prove that the UE construction \(\textsf{RISE}\) (EUROCRYPT’18) satisfies our proposed security notion.