1. I had some difficulty understanding how the treaty verification worked. It raises the question to me is RSA still secure if you compute d and let (n,d) be public but keep e private? It seems me that country B can just gather their own x data and then use it to find d. After that country B can do what they want.
There was also some difficulty understanding the method of authentication and non-repudiation. I didn't follow their explanation.
2. The RSA challenge if funny. I think it would take me a little more than $100 to put in a serious effort to try to decrypt the message. The people that worked on it must have been looking for a challenge. Trapdoors are interesting. They seem like a very easy security breach on a cryptosystem if word ever got, but after reading and thinking about it that is pretty much the case with any cryptosystem.
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