8. This problem is about the NTRU cryptosystem with parameters N-7, p-3, d-2, q-41. We use the convention that the plaintext has coefficients in the set 0,1,...,p (a) Check that these integers are indeed valid NTRU parameters (b) Compute the public key h corresponding to the private key (c) Write down the matrix associated to the NTRU cryptosystem with the given param- eters and public key h- 20r6 +40r52382382 +26a +30. (d) Write down a basis for the lattice associated to the NTRU cryptosystem with the given parameters and public key h- 20r6 +40243882 +26r +30. 8. This problem is about the NTRU cryptosystem with parameters N-7, p-3, d-2, q-41. We use the convention that the plaintext has coefficients in the set 0,1,...,p (a) Check that these integers are indeed valid NTRU parameters (b) Compute the public key h corresponding to the private key (c) Write down the matrix associated to the NTRU cryptosystem with the given param- eters and public key h- 20r6 +40r52382382 +26a +30. (d) Write down a basis for the lattice associated to the NTRU cryptosystem with the given parameters and public key h- 20r6 +40243882 +26r +30