Post-quantum crypto proposal using Transcendentals

Transcendental numbers expand as a series of random, non-repeating digits (think Pi). Assume Alice could find a new transcendental number between 0 and 1. (There are an infinite number of them). Assume Alice and Bob know that number. This is their shared, private key. PRIVATE To communicate, Alice creates a new transcendental number using the private key (for example by exponentiation, or some other offset method). This "offset" OFFSET is the public key. To encode, Alice starts with the private key, creates a new transcendental number using some random offset. Call the new transcendental number PAD = f(PRIVATE, OFFSET). Alice uses PAD as a one-time pad to encrypt the message SECRET = (MESSAGE xor PAD) Alice sends the pair (OFFSET,SECRET) to Bob. Bob uses OFFSET to compute the PAD from PRIVATE. Then uses (SECRET xor PAD) to recover MESSAGE. Transcendental numbers plus offset can generate an infinite set of one-time PADs. Knowing (MESSAGE xor SECRET) recovers the PAD so this in insecure against a known plaintext attack. Knowing PAD then PRIVATE can be recovered. However, if Alice and Bob share a secret method of choosing a new PRIVATE after each communication then they can continue the scheme. The key question is how to find transcendental numbers.