The computational discrete entropoid root hardness conjecture

Let $\mathbb{E}_{p^2}$ be an entropoid, with $p=2q+1$ a safe prime having $\lambda$ bits, and let $g$ generate $\mathbb{E}^*_{(p-1)^2}$. Let $\mathcal{A}$ be an algorithm for CDERP. The CDERP hardness conjecture. Over uniformly chosen $(\mathbf{B},\mathfrak{b})\xleftarrow{\mathbf{r}}\mathbb{L}$, the probability that

$$\mathcal{A}\left(x^{(\mathbf{B},\mathfrak{b})},(\mathbf{B},\mathfrak{b})\right)=x$$

is $\mathtt{negl}(\lambda)$. This conjectures the computational difficulty of extracting non-associative entropoid roots; the paper gives no proof or resolution.