Diophantine and Lattice Cryptanalysis of the RSA Cryptosystem

The RSA cryptosystem, invented in 1977 is the most popular public cryptosystem for electronic commerce. Its three inventors Rivest, Shamir and Adleman received the Year 2002 Turing Award, the equivalent Nobel Prize in Computer Science. RSA offers both encryption and digital signatures and is deployed in many commercial systems. The security of RSA is based on the assumption that factoring large integers is difficult. However, most successful attacks on RSA are not based on factoring. Rather, they exploit additional information that may be encoded in the parameters of RSA and in the particular way in which RSA is used. In this chapter, we give a survey of the mathematics of the RSA cryptosystem focussing on the cryptanalysis of RSA using a variety of diophantine methods and lattice-reduction based techniques.

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