How difficult is it to design a high bypass turbofan given a military derived core?
As of 2015, the #1 selling jet engine, the CFM56, is exactly that.

The core is from the General Electric F101, which powers the Rockwell B-1 Lancer no less.

The development was shrouded in secrecy, and politics were involved, and at least at one point only the Americans had access to the core details, while the French built around it (the new LP spool – which does include the turbines).


  Engines assembled in France were subject to the initially strict export agreement, which meant that GE's core was built in the U.S., then shipped to the Snecma plant in France where it was placed in a locked room into which even the President of Snecma was not allowed.


The linked Wikipedia featured article is a must read, and trying to summarize it here wouldn't do it any justice. But yes, it's not only possible, it's been done. Judging by the specifications, the civilian CFM56 has higher OPR (a jump from 26.8 to upwards of 27.5–38.3 depending on the variant).



According to the image above and this webpage, technology from the CFM56 fed back into the F110, which went on to power the F-14, F-15, and F-16.