What was the greatest concern of the authors of the Federalist papers, preserving social liberties are ensuring national security?

They are more concerned about ensuring national security

Explanation:

The federalist  believed that by increasing the power of Central government, it will be easier for the government to accumulate various resources that can be used for their programs.  This include the mobilization of military that  will be a positive impact for national security.

But, this increase of Government power tend to act as a double edged sword.

As the power of government increase, the influence that it has over the people is also increased. This means that they will be able to create legislations that intervene with citizens' freedom.

the answer would be in this answer. someone already asked the question.