A New SETUP for Factoring Based Algorithms

When using cryptography, there is frequently the misconception that if the keys are properly stored and are not given away, then the user is safe, if he uses a strong encryption algorithm. SETUPs exploit this common misconception, be embedding secret trapdoors in the key creation procedure of public key algorithms. The essential part of a SETUP, is to provide good statistical properties for the used parameters, while maintaining the security of the encryption algorithm. In this work, a new method for creating SETUPs for factoring based encryption algorithms is presented. The SETUP takes advantage of Coppersmith´s theorem in order to efficiently recover the needed parameters.