Canonical Byte-String Encoding for Finite-Ring Cryptosystems
Тип публікації :
Препринт
Дата випуску :
24 березня 2026 р.
Автор(и) :
Kyrylo Riabov
Serhii Kryvyi
eKNUTSHIR URL :
Журнал :
arXiv (Cornell University)
Цитування :
[APA 7] Kyrylo, R., & Serhii, K. (2026). Canonical Byte-String Encoding for Finite-Ring Cryptosystems. arXiv (Cornell University),. https://ir.library.knu.ua/handle/15071834/34275
[ДСТУ] Kyrylo R., Serhii K. Canonical Byte-String Encoding for Finite-Ring Cryptosystems. arXiv (Cornell University). 2026. URL: https://ir.library.knu.ua/handle/15071834/34275 (дата звернення: 11.09.2026).
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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