Yuval Ishai and AnatPaskin (IP) Scheme

In 2007, Yuval et al. have expanded the set of branching programs which are directed acyclic graphs in such a way that every node has two outgoing edges with labeled binary 0 and 1. Furthermore, they proposed a public key encryption scheme by evaluating the branching programs on the encrypted data. In addition, Melchor et al. proposed a generic construction method to obtain a chained encryption scheme that allowing the homomorphic evaluation of constant depth circuit over ciphertext. The chained encryption scheme is obtained from well-known encryption schemes with some homomorphic properties. For example, they showed how to obtain a combination of BGN and KTX (kawachi et. al. suggested an additively homomorphic encryption scheme over a large cyclic group, which depends on the hardness of underlying lattice problems.). Hence, the resulting combined scheme allows arbitrary additions and two multiplicati-ons.