From Bits to Mixed-Radix Keys: Horner Decomposition, Uniform Sampling, and the Information-Theoretic QKD Interface of the MR-OTP

Computer Science > Cryptography and Security [Submitted on 16 Jun 2026] From Bits to Mixed-Radix Keys: Horner Decomposition, Uniform Sampling, and the Information-Theoretic QKD Interface of the MR-OTP Fabio F.G. Buono 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 restores uniformity with optimal expected cost. We establish end-to-end information-theoretic security for single and multi-session pipelines, quantify efficiency gains, present a batched extractor, and give unconditional and conditional results on the Base Recovery Problem. Subjects: Cryptography and Security (cs.CR); Information Theory (cs.IT) Cite as: arXiv:2606.18526 [cs.CR]   (or arXiv:2606.18526v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2606.18526 Focus to learn more Related DOI: https://doi.org/10.5281/zenodo.20723997 Focus to learn more Submission history From: Fabio Francesco Gabriele Buono [view email] [v1] Tue, 16 Jun 2026 22:40:49 UTC (30 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-06 Change to browse by: cs cs.IT math math.IT References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)