[Resource Topic] 2024/861: A new multivariate primitive from CCZ equivalence

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A new multivariate primitive from CCZ equivalence

Authors: Marco Calderini, Alessio Caminata, Irene Villa


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.

ePrint: https://eprint.iacr.org/2024/861

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