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

Author

Listed:
  • Emanuele Bellini

    (Cryptography Research Centre, Technology Innovation Institute, P.O. Box 9639, Masdar City, Abu Dhabi, United Arab Emirates)

  • Chiara Marcolla

    (Cryptography Research Centre, Technology Innovation Institute, P.O. Box 9639, Masdar City, Abu Dhabi, United Arab Emirates)

  • Nadir Murru

    (Department of Mathematics, University of Trento, Povo, 38123 Trento, Italy)

Abstract

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.

Suggested Citation

  • Emanuele Bellini & Chiara Marcolla & Nadir Murru, 2021. "An Application of p -Fibonacci Error-Correcting Codes to Cryptography," Mathematics, MDPI, vol. 9(7), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:789-:d:530913
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    References listed on IDEAS

    as
    1. Stakhov, A.P., 2006. "Fibonacci matrices, a generalization of the “Cassini formula”, and a new coding theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 56-66.
    2. Basu, Manjusri & Prasad, Bandhu, 2009. "The generalized relations among the code elements for Fibonacci coding theory," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2517-2525.
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