Inspired by my answer to this question: How to take down the internet?.
Lets say that a small ideological country has recently broken one of the most common HTTPS encryption schemes for public-private key style encryption (I don't care which specifically). They can easily decrypt any message encrypted with this scheme so long as they have the public key used for the encryption. No one is aware that the scheme has been broken at this time.
The country wants to do two things.
Improve its standing in the larger community, gaining both more wealth and more political power without angering anyone enough to trigger an invasion, sanctions, or any other political suicide.
Terrorize, damage the economy of, or destroy one other technically capable country that it passionately hates for ideological reasons. Assume the country it hates is first world economically. The hated country is larger then the country that broke the encryption, but still small compared to say the USA. However, the hated countries military is still a significant threat and thus our small country does not want to risk triggering an overt war.
I know those two goals may seem counter to each other, and rationally they may well be. However, rationality is not always humanities strong suit. Thus assume that their hatred for the other country is significant enough for them to act against them, even if not acting would be smarter; and they are not willing to wait 20-30 years of planning before trying to destroy the economy of the other nation. However, they need to be careful not to do anything that will trigger a direct invasion, by the country they hate or by any larger nations. In addition, if people realize that the encryption algorithm is broken they can switch to an alternate algorithm in the future, negating the countries advantage.
Generally I'm more interested in the terrorism and other evil that the nation can do by breaking HTTPS then I am in how they would build their own nation, but the two issues seem closely enough related that I wanted to mention both goals and stress that terrorism goal need not result in foolish actions or prevent them from attempting to profit as well.
As a small nation they have little infrastructure in place for supporting their exploitation of the encryption algorithm. For instance they don't already have dozens of computers in place for man-in-the-middle attacks just waiting to be tapped. They are not above growing this capability, just don't assume it already exists. However, if necessary to make them able to do anything interesting, you may assume that the nation is physically located between two large first world nations or the hated nation and the rest of the world; thus making it possible that data will often be routed through them.
What strategies do they have available to exploit their ability to see through HTTPS in order to better themselves and destroy their hated country?
ps. I really should name these countries to make it clear the distinction, but the only names I can come up with are Foo and Bar. Any naming suggestions?