An O(n) procedure for hiding m bits of signal inside of n−m bits of quantum random noise is introduced. When the signal and quantum noise have a uniform probability distribution, and the signal size is fixed, the security of a single, hidden signal transmission can be made arbitrarily close to perfect secrecy. Our hiding procedures are implemented with commercially available quantum random number generators, and current TCP/IP infrastructure. A random nonce helps unpredictably change the bit locations of the signal: a prior hidden signal transmission does not reveal information to Eve on where the current signal is hidden. This security property enables a new key exchange that hides public keys in quantum randomness; introduces a post-quantum key exchange with substantially smaller key sizes; offers a substantially greater classical complexity than the underlying public keys; and provides quantum complexity that is comparable to Grover’s quantum computing algorithm.