Canonical Byte-String Encoding for Finite-Ring Cryptosystems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910208584843264 |
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| author | Riabov, Kyrylo Kryvyi, Serhii |
| author_facet | Riabov, Kyrylo Kryvyi, Serhii |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23364 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Canonical Byte-String Encoding for Finite-Ring Cryptosystems Riabov, Kyrylo Kryvyi, Serhii Cryptography and Security Information Theory 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. |
| title | Canonical Byte-String Encoding for Finite-Ring Cryptosystems |
| topic | Cryptography and Security Information Theory |
| url | https://arxiv.org/abs/2603.23364 |