Efficient RSA Key Generation Protocol in the Two-Party Setting

The goal of this thesis is the implementation of a fully distributed multiparty computation protocol in a Two-Party setting, secure in the semi-honest model. For each single step in the protocol is expected the participation of two and only two parties. This is among the first implementations of a complete distributed protocol for RSA Composite generation in this setting, on top of which several Secure Multiparty Computation protocols have also been implemented. In this paper it has been shown that using standards approaches the problem turns to be intractable. From this first result, the research moves in several directions, adopting Elliptic Curve-based solutions, avoiding where possible the use of expensive cryptographic operations, and using different cheaper approaches. This has brought to the implementation of the last version of the protocol, which permits to the two parties to securely compute an RSA Composite of at least 2048 bits in 15 minutes in average. Thus, it has practically been demonstrated that many of the different applications of the SMPC model that have been studied in the rich literature on the argument have a chance of being used in real-world environment.