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arXiv · 2603.23364

Canonical Byte-String Encoding for Finite-Ring Cryptosystems

Kyrylo Riabov·Serhii Kryvyi
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Abstract

Ring-mapping protocols need a canonical byte-to-residue layer before any algebraic encryption step can begin. This paper isolates that layer and presents the base-m length codec, a canonical map from byte strings of length less than 2^64 to lists of residues modulo m. The encoder builds on and adapts an rANS-based system proposed by Duda. Decoding is exact for all moduli satisfying the paper's parameter bounds. Because the encoding carries the byte length in its fixed-width header, decoding is also tolerant to appended valid suffix digits. The paper is accompanied by a Rust implementation of the described protocol, a Lean 4 formalization of the abstract codec with machine-checked proofs, and performance benchmarks. The Lean 4 formalization establishes fixed-width prefix inversion and payload-state bounds below 2^64, stream-level roundtrip correctness, and that every emitted symbol is a valid residue modulo m. We conclude with a complexity analysis and a discussion of practical considerations arising in real-world use of the codec.

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Kyrylo Riabov, Serhii Kryvyi. 2026-03-24. Canonical Byte-String Encoding for Finite-Ring Cryptosystems. https://arxiv.org/abs/2603.23364

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