# Does AES encryption of a NTRU pivate key reduce security?

The NTRU crypto system requires quite long keys. For example with parameters N=439 and q=2048 the security is 128 bits and the key_size is 4829 bits. When the private key is encrypted with AES-256 and the ciphertext is made public, can an attacker learn something from that? Or is the 128 bit security of NTRU reduced by doing this?

Suppose 2 ciphertexts, 1 NTRU, 1 IES-ECC, both are 128-bit secure, what you have right now is 2 ciphertexts requiring $$2^{128}$$ work to recover the plaintext without having the corresponding private key. This is true even if the encoded private key is longer than 128 bits (because of non-generic attacks such as lattice-reduction or Pollard's rho algorithm)