The adversary will then decrypt any communications with the proper key, and encrypt them with the other key for sending to the other party. The parties will think that they are communicating securely, but in fact the adversary is hearing everything. The recipient then verifies that the signature came from the desired other party, and that the hash in the signature matches that computed locally. This method is used e.g. in Photuris . It is relevant to at least RSA , Diffie-Hellman , and Elliptic Curve methods .
More information is available in the original paper and various followup articles.
There are many other cryptographic attacks and cryptanalysis techniques. However, these are probably the most important ones for a practical system designer. Anyone contemplating to design a new encryption algorithm should have a much deeper understanding of these issues. One place to start looking for information is the excellent book Applied Cryptography by Bruce Schneier. Any opinions and evaluations presented here are speculative, and the author cannot be held responsible for their correctness.