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.

翻译：多元密码学是后量子密码学的主要候选方案之一。多元密码方案通常通过将两个秘密的可逆仿射变换$\mathcal S,\mathcal T$作用于一组多元多项式$\mathcal{F}$（通常为二次型）来构造。秘密多项式$\mathcal{F}$包含陷门结构，使得合法用户能够求解相应方程组，而公开多项式$\mathcal G=\mathcal S\circ\mathcal F\circ\mathcal T$则呈现随机多项式的外观。此时多项式$\mathcal G$与$\mathcal F$被称为仿射等价。本文提出一种更通用的多元密码方案构造方法，通过引入在向量布尔函数领域已被深入研究的CCZ等价性来实现方案构建。