Encrypt your ECDSA signature with NTRU to make them quantum secure, does that work? I have a general question about quantum security. ECDSA is suppose to be broken by quantum computers. Whilst something like NTRU is suppose to be secure.

My question is: if we sign with ECDSA and encrypt the signature NTRU. Does that make the signature safe? Because I can expose both ECDSA and NTRU public keys but if either of them is compromised it shouldn't compromise.

Is this a correct statement or am I missing something?
So you want to encrypt the message's ECDSA signature with NTRU. 

Firstly, if the NTRU is secure against the quantum computers, then anything under NTRU encryption is secure against the quantum computers.

Secondly, NTRU has also digital signature, instead of ECDSA use NTRUSign.

Depending on different mathematical and computational problems are not considered a good practice. 

update: by the comments of Maarten Bodewes

Remember that, public key encryption and signature require two separate keys; public key and private key. In your case;


the public encryption keys generated by the receiver as $PK_{rec},SK_{rec}$ 
the digital signature keys are generated by the signer as $PK_{sign},PK_{sign}$.


As a result, the two public keys, $PK_{rec}$ and $PK_{sign}$, are generated by different people.