An Application of <i>p</i>-Fibonacci Error-Correcting Codes to Cryptography
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 cryptogr...
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doaj-799dda5275a340debebc15f62765eb0c2021-04-06T23:03:38ZengMDPI AGMathematics2227-73902021-04-01978978910.3390/math9070789An Application of <i>p</i>-Fibonacci Error-Correcting Codes to CryptographyEmanuele Bellini0Chiara Marcolla1Nadir Murru2Cryptography Research Centre, Technology Innovation Institute, P.O. Box 9639, Masdar City, Abu Dhabi, United Arab EmiratesCryptography Research Centre, Technology Innovation Institute, P.O. Box 9639, Masdar City, Abu Dhabi, United Arab EmiratesDepartment of Mathematics, University of Trento, 38123 Povo, Trento, ItalyIn 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.https://www.mdpi.com/2227-7390/9/7/789code-based cryptographysignature schemeidentification protocolFiat–Shamir transformFibonacci codesproof of knowledge signature |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Emanuele Bellini Chiara Marcolla Nadir Murru |
spellingShingle |
Emanuele Bellini Chiara Marcolla Nadir Murru An Application of <i>p</i>-Fibonacci Error-Correcting Codes to Cryptography Mathematics code-based cryptography signature scheme identification protocol Fiat–Shamir transform Fibonacci codes proof of knowledge signature |
author_facet |
Emanuele Bellini Chiara Marcolla Nadir Murru |
author_sort |
Emanuele Bellini |
title |
An Application of <i>p</i>-Fibonacci Error-Correcting Codes to Cryptography |
title_short |
An Application of <i>p</i>-Fibonacci Error-Correcting Codes to Cryptography |
title_full |
An Application of <i>p</i>-Fibonacci Error-Correcting Codes to Cryptography |
title_fullStr |
An Application of <i>p</i>-Fibonacci Error-Correcting Codes to Cryptography |
title_full_unstemmed |
An Application of <i>p</i>-Fibonacci Error-Correcting Codes to Cryptography |
title_sort |
application of <i>p</i>-fibonacci error-correcting codes to cryptography |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2021-04-01 |
description |
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. |
topic |
code-based cryptography signature scheme identification protocol Fiat–Shamir transform Fibonacci codes proof of knowledge signature |
url |
https://www.mdpi.com/2227-7390/9/7/789 |
work_keys_str_mv |
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