This document proposes a secure scheme for secret sharing and key distribution using Pell's equation. It begins with an introduction to key distribution problems and secret sharing schemes. It then presents an algorithm that uses Pell's equation to generate a secret exponent S, which is used to distribute shares of a key to users. Each user's share allows them to collectively compute the key when a minimum number of users combine their shares, but individual shares reveal no information about the key. The algorithm provides perfectly secure secret sharing against coalitions of k or fewer users.