Is it secure to encrypt a 1 GB data file with AES-CTR by ECIES? I have a file system with share resources over the network (like a shared FTP)


Is it possible to use the client's ECC public key to encrypt the AES key, and then use the AES in CRT mode for the file encryption?  File size can be 1GB to 1TB.
I do not believe there would be any issues, as long as:


The problem you are attempting to solve is that you want to encrypt a file so that the client can decrypt it, but no one else can
The client has a public/private key pair
The encryptor has the client's public key and you somehow know that it's the client's public key
The encryptor has access to randomness (as the security of ECIES depends on it)
You add some integrity transform (along with the AES-CTR), to make sure that no one can modify the encrypted message without being detected.  If you need a suggestion about which integrity transform to use, perhaps HMAC-SHA256 would work; alternatively, you could replace AES-CTR with (say) AES-GCM.


You appear to be concerned about the size of the file being encrypted; the public key portions could care less about how long the message is (it does the same thing regardless), and the AES-CTR portion can easily handle a terabyte without an issue.

You may want to consider breaking the file up into smaller pieces and encrypt and send each piece separately, but that is for purely practical reasons (e.g. if one of the smaller pieces get corrupted, the receiver can ask for that specific piece to be resent, and not the entire 1Tb file); however the cryptographical security would not depend on that.