University of Brighton
In 1996, researchers introduced an efficient lattice based encryption scheme dubbed NTRUEncrypt. Unfortunately, this scheme lacks a proof of security. However, in 2011, other researchers showed how to modify NTRUEncrypt to reduce security to standard problems in ideal lattices. In 2012, they proposed a fully homomorphic scheme based on this modified system. However, to allow homomorphic operations and prove security, a non-standard assumption is required. In this paper, the authors show how to remove this non-standard assumption via techniques introduced and construct a new fully homomorphic encryption scheme from the version based on standard lattice assumptions and a circular security assumption.