A new multivariate primitive from CCZ equivalence
<|reference_start|>A new multivariate primitive from CCZ equivalence: Multivariate Cryptography is one of the main candidates for Post-quantum Cryptography. Multivariate schemes are usually constructed by applying two secret affine invertible transformations $\mathcal S,\mathcal T$ to a set of multivariate polynomials $\mathcal{F}$ (often quadratic). The secret polynomials $\mathcal{F}$ posses a trapdoor that allows the legitimate user to find a solution of the corresponding system, while the public polynomials $\mathcal G=\mathcal S\circ\mathcal F\circ\mathcal T$ look like random polynomials. The polynomials $\mathcal G$ and $\mathcal F$ 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.<|reference_end|>
@article{calderini2024a,
    title={A new multivariate primitive from CCZ equivalence},
    author={Marco Calderini and Alessio Caminata and Irene Villa},
    journal={arXiv preprint arXiv:2405.20968},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.20968},
    primaryClass={cs.CR}
}