We introduce a new cryptographic primitive, called insubvertible encryption, that produces ciphertexts which can be randomized without the need of any key material. Unlike plain universal re-encryption schemes, insubvertible encryption prevents against adversarial exploitation of hidden channels, by including certificates proving that the ciphertext can only be decrypted by authorized parties. The scheme can be applied to RFID tags, providing strong protection against tracing. This enables post-sale applications of manufacturer-issued RFID tags while preserving the privacy of consumers. The functionality required of the RFID tags is minimal, namely that they be re-writable (many-writable). No cryptographic capabilities are required of the tags themselves, as the readers perform all necessary computations. Categories and Subject Descriptors: K.6.5 [Security and Protection] General Terms: Algorithms, Security.