Title: Adventures in RSA key recovery Abstract: Forty years after its invention, RSA remains one of the most widely used public key encryption and signature schemes in practice. Its prevalence has also made it a popular target of cryptanalytic attacks, both theoretical and applied. In this talk, I will survey old and new results on extracting RSA private keys under various attack models. RSA has a rich mathematical structure that seems to lend itself to a variety of interesting algorithmic approaches, and the problem of recovering keys from incomplete information crops up in some surprising ways and places.