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Open AccessArticle

An Application of p-Fibonacci Error-Correcting Codes to Cryptography

1
Cryptography Research Centre, Technology Innovation Institute, P.O. Box 9639, Masdar City, Abu Dhabi, United Arab Emirates
2
Department of Mathematics, University of Trento, Povo, 38123 Trento, Italy
*
Author to whom correspondence should be addressed.
Academic Editors: Gabriel Eduard Vilcu and Patrick Solé
Mathematics 2021, 9(7), 789; https://doi.org/10.3390/math9070789
Received: 31 January 2021 / Revised: 24 February 2021 / Accepted: 26 March 2021 / Published: 6 April 2021
(This article belongs to the Special Issue Algebra and Number Theory)
In addition to their usefulness in proving one’s identity electronically, identification protocols based on zero-knowledge proofs allow designing secure cryptographic signature schemes by means of the Fiat–Shamir transform or other similar constructs. This approach has been followed by many cryptographers during the NIST (National Institute of Standards and Technology) standardization process for quantum-resistant signature schemes. NIST candidates include solutions in different settings, such as lattices and multivariate and multiparty computation. While error-correcting codes may also be used, they do not provide very practical parameters, with a few exceptions. In this manuscript, we explored the possibility of using the error-correcting codes proposed by Stakhov in 2006 to design an identification protocol based on zero-knowledge proofs. We showed that this type of code offers a valid alternative in the error-correcting code setting to build such protocols and, consequently, quantum-resistant signature schemes. View Full-Text
Keywords: code-based cryptography; signature scheme; identification protocol; Fiat–Shamir transform; Fibonacci codes; proof of knowledge signature code-based cryptography; signature scheme; identification protocol; Fiat–Shamir transform; Fibonacci codes; proof of knowledge signature
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MDPI and ACS Style

Bellini, E.; Marcolla, C.; Murru, N. An Application of p-Fibonacci Error-Correcting Codes to Cryptography. Mathematics 2021, 9, 789. https://doi.org/10.3390/math9070789

AMA Style

Bellini E, Marcolla C, Murru N. An Application of p-Fibonacci Error-Correcting Codes to Cryptography. Mathematics. 2021; 9(7):789. https://doi.org/10.3390/math9070789

Chicago/Turabian Style

Bellini, Emanuele; Marcolla, Chiara; Murru, Nadir. 2021. "An Application of p-Fibonacci Error-Correcting Codes to Cryptography" Mathematics 9, no. 7: 789. https://doi.org/10.3390/math9070789

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