GMiMC

The GMiMC$_\textsf{erf}$ defined over $\mathbb{F}_q$, is unbalanced Feistel network with an expanding round function (ERF). One round of GMiMC$_\textsf{erf}$ is depicted as in the following figure (b)

It can be described as

$$(x_0, x_1, \dots, x_{t-1}) \leftarrow (x_1 + F(x_0), x_2 + F(x_0), \dots, x_{t-1} + F(x_0), x_0).$$

The round function \(F(\cdot)\) in round \(i\) defined as

$$F(x) = (x + k_i + c_i)^3$$

where \(k_i\) and \(c_i\) denote the round constant and the round key in round (i), respectively. When the secret key $k \in \mathbb{F}_q$, the round key $k_i = (i+1)\cdot k$.