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

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.

Multidimensional Fibonacci Coding

“…In addition, compared with other variable-length codes for the integers such as logarithmic ramp [12] and Elias codes [13], Fibonacci codes provide much better resistance against insertion and deletion errors. Other applications of the Fibonacci sequence in information science include the study of Morse code as a monoid [14,15], Wavelet trees [16], and zero-knowledge cryptography [17].…”