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arXiv · 2405.20968

A new multivariate primitive from CCZ equivalence

Marco Calderini·Alessio Caminata·Irene Villa
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Abstract

Multivariate Cryptography is one of the 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 polynomials $\mathcal{F}$ possess 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.

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Marco Calderini, Alessio Caminata, Irene Villa. 2024-05-31. A new multivariate primitive from CCZ equivalence. https://arxiv.org/abs/2405.20968

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