From Bits to Mixed-Radix Keys: Horner Decomposition, Uniform Sampling, and the Information-Theoretic QKD Interface of the MR-OTP (opens in new tab)

The Mixed-Radix One-Time Pad (MR-OTP) extends the classical OTP to heterogeneous alphabets while preserving perfect secrecy. We provide a practical, bias-free method to convert raw binary entropy from a QKD source into uniform mixed-radix keys by identifying Horner's method and its inverse as the natural mapping between binary integers and mixed-radix tuples. We show that naive modular reduction induces bias and prove that rejection sampling res...