A new multivariate primitive from CCZ equivalence

Marco Calderini; Alessio Caminata; Irene Villa

Paper 2024/861

A new multivariate primitive from CCZ equivalence

Marco Calderini

, University of Trento

Alessio Caminata

, University of Genoa

Irene Villa

, University of Genoa

Abstract

Multivariate Cryptography is one of the main candidates for Post-quantum Cryptography. Multivariate schemes are usually constructed by applying two secret affine invertible transformations $S, T$ to a set of multivariate polynomials $F$ (often quadratic). The secret polynomials $F$ posses a trapdoor that allows the legitimate user to find a solution of the corresponding system, while the public polynomials look like random polynomials. The polynomials and are said to be affine equivalent. In this article, we present a more general way of constructing a multivariate scheme by considering the CCZ equivalence, which has been introduced and studied in the context of vectorial Boolean functions.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Post-quantum Cryptography Multivariate Cryptography Boolean functions CCZ equivalence
Contact author(s): marco calderini @ unitn it
alessio caminata @ unige it
irene1villa @ gmail com
History: 2024-06-05: approved; 2024-05-31: received; See all versions
Short URL: https://ia.cr/2024/861
License: CC BY

BibTeX

@misc{cryptoeprint:2024/861,
      author = {Marco Calderini and Alessio Caminata and Irene Villa},
      title = {A new multivariate primitive from {CCZ} equivalence},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/861},
      year = {2024},
      url = {https://eprint.iacr.org/2024/861}
}