# Is a cryptosystem based on hardness of factorization of polynomials, as defined below valid? [closed]

I'm proposing a cryptosystem as defined below:

• Private Key: $$(R, A, R^{-1})$$, where $$R = \left(\mathbf{r_1}, \cdots, \mathbf{r_n}\right)$$ is full-rank, with $$n \geq 4$$, even; $$A = \left(a_1\mathbf{e_1}, \cdots, a_n\mathbf{e_n} \right)$$ and $$a_i \neq 0$$;
• Public Key: $$B = RAR^{-1}$$;
• Plaintext: $$P \in \mathbb{F}_p^{n\times n}$$ represents an ordered basis over $$\mathbb{F}_p^n$$;
• Ciphertext: $$C = PBP^{-1}$$;
• Decription: $$VR^{-1}$$, where $$V = \left(\mathbf{v_1}, \cdots, \mathbf{v_n}\right)$$, where $$C\mathbf{v_i} = a_i\mathbf{v_i}$$;
• Document: $$d \in \mathbb{F}_p$$;
• Signature: $$s = \Pi_{i = 1}^{n/2} (x-a_{\pi(i)}^d) \in \mathbb{F}_p[x]$$, where $$\pi(\cdot) \in S_n$$;
• Verification: $$s | b_d$$, where $$b_d = det\left(B^d-xI\right) \in \mathbb{F}_p[x]$$;

where:

• $$\mathbb{F}_p$$ refers to the finite field of order $$p$$;
• $$\mathbb{F}_p[x]$$ refers to the set of polynomials over $$\mathbb{F}_p$$;
• $$\left(\mathbf{m_1},\cdots,\mathbf{m_n}\right)$$ signifies a matrix having $$\mathbf{m_i}$$ as its $$i$$th column vector;
• $$\mathbf{e_i}$$ refers to the $$i$$th canonical vector of $$\mathbb{F}_p$$;
• $$p|q$$ means '$$p$$ divides $$q$$';
• $$S_n$$ is the symmetric group of $$n$$ elements;

Is it original? Is the premise of soundess based on hardness of factorization of polynomials over finite fields valid?

References: White Paper