Self-Renewing One-Time Pad: Information-Theoretic Messaging Beyond Initial Pad Exhaustion

The classical limitation of one-time-pad (OTP) cryptography is the key-distribution problem: to send n bits of plaintext, the parties must already share n bits of pre-distributed key. Once the pad is exhausted, the parties must meet again to exchange new pad material. This is widely viewed as making pure OTP impractical for sustained communication. We present a protocol that resolves this limitation: once an initial pad of size N is shared in person, subsequent pad material is generated by one party from a true-random source and transmitted as encrypted payload over the existing OTP channel itself. The receiver decrypts using existing pad and appends the recovered random bytes to its local pad. Net pad balance after a refill operation is unchanged — bytes of old pad are spent to deliver an equal number of bytes of new pad — but the new material is fresh, secret, and uncompromised. We prove inductively that information-theoretic security of the new pad is preserved across arbitrary refill chains. The result is a protocol with all the security guarantees of classical OTP and none of its practical key-distribution limitation, given a single in-person bootstrap.