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A new path to code-based signatures via identification schemes with restricted errors

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Bibliographic Details
Title: A new path to code-based signatures via identification schemes with restricted errors
Authors: Baldi, Marco, Battaglioni, Massimo, Chiaraluce, Franco, Horlemann, Anna-Lena, Persichetti, Edoardo, Santini, Paolo, Weger, Violetta
Contributors: Baldi, Marco, Battaglioni, Massimo, Chiaraluce, Franco, Horlemann, Anna-Lena, Persichetti, Edoardo, Santini, Paolo, Weger, Violetta
Publication Year: 2025
Collection: Università Politecnica delle Marche: IRIS
Subject Terms: Coding theory, decoding problems, restricted errors, bounds
Description: 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.
Document Type: article in journal/newspaper
File Description: ELETTRONICO
Language: 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
Availability: 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
Accession Number: edsbas.C84F0C2E
Database: BASE
Description
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.
DOI:10.3934/amc.2024058