Fully Homomorphic Encryption

Encryption supporting arbitrary computation on ciphertexts: its definitions, what composing evaluations requires, and what bootstrapping costs.

Status	Statement	Tags
	Two-scheme key cycle Open in both directions, and the source paper says why the existing separations miss it: the counterexamples fix both schemes, whereas here the second is chosen after the first. Two hypotheses left implicit in the printed statement have to be added before it is even non-vacuous. 7 open	Circular Security Fully Homomorphic Encryptionassumption
	Composability implies circular security Open with no partial result in either direction. The converse – circular security plus limited homomorphism gives full composability – is the source paper’s Theorem 6; this direction, which would make the two properties essentially equivalent, is conjectured there and nothing has been published towards it. 7 open	Circular Security Fully Homomorphic Encryptionequivalence