A new path to code-based signatures via identification schemes with restricted errors
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| Titel: | A new path to code-based signatures via identification schemes with restricted errors |
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| Autoren: | Baldi, Marco, Battaglioni, Massimo, Chiaraluce, Franco, Horlemann, Anna-Lena, Persichetti, Edoardo, Santini, Paolo, Weger, Violetta |
| Weitere Verfasser: | Baldi, Marco, Battaglioni, Massimo, Chiaraluce, Franco, Horlemann, Anna-Lena, Persichetti, Edoardo, Santini, Paolo, Weger, Violetta |
| Publikationsjahr: | 2025 |
| Bestand: | Università Politecnica delle Marche: IRIS |
| Schlagwörter: | Coding theory, decoding problems, restricted errors, bounds |
| Beschreibung: | In this paper, we introduce a new variant of the syndrome decoding problem (SDP), called restricted SDP (R-SDP), in which the entries of the solution vector live in a fixed subset of the underlying finite field. We prove the NP-completeness of R-SDP via a reduction from SDP and show how this new problem can be employed in identification schemes. We revisit some concepts of classical coding theory in light of this new setting, provide several bounds such as the Gilbert-Varshamov, the Singleton, and the Plotkin bound, and study the behavior of random codes. Resulting from this initial work, several proposals have arisen; in particular, the code-based digital signature scheme named CROSS, which is currently competing within NIST's additional call for post-quantum digital signatures, is based on R-SDP. |
| Publikationsart: | article in journal/newspaper |
| Dateibeschreibung: | ELETTRONICO |
| Sprache: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/wos/WOS:001388687500001; volume:19; issue:5; firstpage:1360; lastpage:1381; numberofpages:22; journal:ADVANCES IN MATHEMATICS OF COMMUNICATIONS; https://hdl.handle.net/11566/338732 |
| DOI: | 10.3934/amc.2024058 |
| Verfügbarkeit: | https://hdl.handle.net/11566/338732 https://doi.org/10.3934/amc.2024058 https://www.aimsciences.org/article/doi/10.3934/amc.2024058 |
| Rights: | info:eu-repo/semantics/closedAccess |
| Dokumentencode: | edsbas.C84F0C2E |
| Datenbank: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | In this paper, we introduce a new variant of the syndrome decoding problem (SDP), called restricted SDP (R-SDP), in which the entries of the solution vector live in a fixed subset of the underlying finite field. We prove the NP-completeness of R-SDP via a reduction from SDP and show how this new problem can be employed in identification schemes. We revisit some concepts of classical coding theory in light of this new setting, provide several bounds such as the Gilbert-Varshamov, the Singleton, and the Plotkin bound, and study the behavior of random codes. Resulting from this initial work, several proposals have arisen; in particular, the code-based digital signature scheme named CROSS, which is currently competing within NIST's additional call for post-quantum digital signatures, is based on R-SDP. |
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| DOI: | 10.3934/amc.2024058 |