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Physical Unclonable Functions (PUFs) are circuits designed to extract physical randomness from the underlying circuit. This randomness depends on the manufacturing process. It differs for each device enabling chip-level authentication and key generation applications. We present a protocol utilizing a PUF for secure data transmission. Parties each have a PUF used for encryption and decryption; this is facilitated by constraining the PUF to be commutative. This framework is evaluated with a primitive permutation network - a barrel shifter. Physical randomness is derived from the delay of different shift paths. Barrel shifter (BS) PUF captures the delay of different shift paths. This delay is entangled with message bits before they are sent across an insecure channel. BS-PUF is implemented using transmission gates; their characteristics ensure same-chip reproducibility, a necessary property of PUFs. Post-layout simulations of a common centroid layout 8-level barrel shifter in 0.13 {\mu}m technology assess uniqueness, stability and randomness properties. BS-PUFs pass all selected NIST statistical randomness tests. Stability similar to Ring Oscillator (RO) PUFs under environment variation is shown. Logistic regression of 100,000 plaintext-ciphertext pairs (PCPs) failed to successfully model BS- PUF behavior.