There has been a growing interest in fully integrating Physical Unclonable Function (PUF) for cryptographic primitives, or keyless encryption. Keyless primitives do not store key information during the entire encryption and decryption phase, providing full security against volatile and non-volatile memory attacks. The concept of keyless encryption using ReRAM PUF is a relatively new concept, and the security aspect of the protocol has not been tested yet. In this paper, we use statistical models to analyze the randomness of the protocol and its resistance against frequency attacks.