In this paper we give a survey of the main methods used in attacks against the RSA cryptosystem. We describe the main factoring methods, attacks on the underlying mathematical function, as well as attacks that exploit details in implementations of the algorithm. While many attacks exist, the system has proven to be very secure, and most problems arise as a result of misuse of the system, bad choice of parameters or flaws in implementations. To conclude, we list a couple of countermeasures that can be used to prevent many of the attacks described.
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