Might/could prove

"Elizabeth turned to her most trusted counsellors – Secretary of State William Cecil, now Lord Burghley, and her ambassador to France and ruthless spymaster, Francis Walsingham – who advised her to consider cultivating alliances at both ends of the Mediterranean with Portugal and the Ottomans. The Portuguese might prove difficult considering the recent rifts over Morocco, but there was at least a diplomatic presence in both countries that might allow some compromise to be reached. The Ottomans were a different case altogether... But at such a distance from London and with no resident English ambassador or merchants, any attempt to negotiate with the sultan could prove extremely difficult, even dangerous."

What does "could prove" and "might prove" mean here?