In recent years there there has been an increased interest in encryption systems that preserve certain algebraic structures. These encryption systems are referred to as homomorphic and have applications in electronic voting, network coding and secure processing. An important example of an homomorphic encryption is Paillier encryption, a probabilistic encryption system that preserves addition of plain-text messages.
In this talk we discuss Paillier encryption from the perspective of simple groups theory using the notions of split short exact sequences and the Chinese Remainder Theorem. From the obtained insights we introduce a modified version of the classical Paillier system that is slightly more efficient in terms of bandwidth.