Number Theoretic SETUPs for RSA Like Factoring Based Algorithms

For many years there was a very common misbelief that having embedded mechanisms in hardware, constitute the optimal solution not only in the usage and the performance for the encryption algorithms, but for their security as well. The idea that lead to this common belief was that by this way an attacker could not tamper the encryption algorithms, specially regarding the asymmetric ones. M. Young and Yung introduced kleptography, showing that there are more risks than the ones that are expected to be faced, when using cryptographic systems. This work summarizes the scope of kleptography and analyzes two new number theoretic SETUPs for factoring encryption algorithms, one based on Lagrange’s four square theorem and one based on Coppersmith’s theorem. Both SETUPs target public key encryption algorithms, whose key generation depends on the product of two primes, providing a robust and secure solution.