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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19654846 |
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| _version_ | 1866901194729848832 |
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| author | Nakano, Tatsuya |
| author_facet | Nakano, Tatsuya |
| contents | <p>We introduce the Matrix Cryptographic Tree (MCT), a reversible and structure-preserving</p> <p>authenticated structure based entirely on products of fixed 2×2 integer matrices. In contrast to</p> <p>Merkle trees and other hash-based constructions, MCT is fully invertible: every encoded matrix</p> <p>admits a unique decoding path determined solely by non-negativity constraints on intermediate</p> <p>matrices. This yields three fundamental properties that are unattainable in hash-based systems:</p> <p>(1) injective encoding without collisions, (2) deterministic and unique decoding, and (3) algebraic</p> <p>tamper detection in which any modification of a matrix entry necessarily violates the decoding</p> <p>rule.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19654846 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Matrix Cryptographic Tree and Matrix Cryptographic Signature: A Fully Reversible and Structure-Preserving Cryptographic Primitive Nakano, Tatsuya <p>We introduce the Matrix Cryptographic Tree (MCT), a reversible and structure-preserving</p> <p>authenticated structure based entirely on products of fixed 2×2 integer matrices. In contrast to</p> <p>Merkle trees and other hash-based constructions, MCT is fully invertible: every encoded matrix</p> <p>admits a unique decoding path determined solely by non-negativity constraints on intermediate</p> <p>matrices. This yields three fundamental properties that are unattainable in hash-based systems:</p> <p>(1) injective encoding without collisions, (2) deterministic and unique decoding, and (3) algebraic</p> <p>tamper detection in which any modification of a matrix entry necessarily violates the decoding</p> <p>rule.</p> <p> </p> |
| title | Matrix Cryptographic Tree and Matrix Cryptographic Signature: A Fully Reversible and Structure-Preserving Cryptographic Primitive |
| url | https://doi.org/10.5281/zenodo.19654846 |