using same symmetric key for multiple files

[Phillip Gardner]

I am using tar to create a backup file of important personal files on my hard disk. I want to store this tar file on another computer which is far away in case something bad happens to my apartment such as a hurricane. (I love in Florida!) Unfortunately, this distant computer is not very secure. So, I am using this command to encrypt my tar file:

gpg2 --symmetric --force-mdc --cipher-algo AES256 backup20130405.tar

I try to do a backup every day and copy the backup file to this distant computer. The result being, that there are lots of backup files stored on this distant computer, one for each day for the last 20 or 30 days. I am using the same key every time I encrypt the tar file.

Is it a problem using the same key when encrypting multiple files which will all be stored together? These files were very similar in content prior to being encrypted.

Thanks for your help!