Is it necesary to introduce noise in building fully homomorphic encryption?
At present, almost all formally published FHE schemes are based on noisy approach. However, there are some noise-free FHE constructions posted at ePrint or arXiv. But all these noise-free FHE schemes have not been formally published, due to --- partially --- lack of provable security reductions. Gentry also published his position paper "Computing on the edge of chaos: Structure and randomness in encrypted computation" in ECCC. These progress urges me to think the above question.