  An attacker can gain information of a user by analyzing its network traffic.
The size of transferred data leaks information about the file being transferred
or the service being used, and this is particularly revealing when the attacker
has background knowledge about the files or services available for transfer. To
prevent this, servers may pad their files using a padding scheme, changing the
file sizes and preventing anyone from guessing their identity uniquely. This
work focuses on finding optimal padding schemes that keep a balance between
privacy and the costs of bandwidth increase. We consider R\'enyi-min leakage as
our main measure for privacy, since it is directly related with the success of
a simple attacker, and compare our algorithms with an existing solution that
minimizes Shannon leakage. We provide improvements to our algorithms in order
to optimize average total padding and Shannon leakage while minimizing
R\'enyi-min leakage. Moreover, our algorithms are designed to handle a more
general and important scenario in which multiple servers wish to compute
padding schemes in a way that protects the servers' identity in addition to the
identity of the files.
