State of the fhe The good Huge impact on the field -Solid 1 Given a generic group G Unconditionally secure PKE and even secure computation -Major. Not known to be helpful for FHE The not so goo Narrow set of assumptions and underlying structures all related to lattices Susceptible to lattice reduction attacks and other attacks Concrete efficiency still leaves much to be desired
State of the FHE • The good – Huge impact on the field – Solid foundations [BV11,GSW13,…] – Major progress on efficiency [BGV12,HS15,DM15,CGGI16,…] • The not so good – Narrow set of assumptions and underlying structures, all related to lattices • Susceptible to lattice reduction attacks and other attacks – Concrete efficiency still leaves much to be desired Given a generic group G: • Unconditionally secure PKE and even secure computation • Not known to be helpful for FHE
THERE HAS GOT TOBEA IN SOME SENSE FFERENT WAY
IN SOME SENSEDIFFERENT
Recall: ehe (x) sk Dec [P(x)] Eval E Enc
Recall: FHE Dec P(x) sk [x] Enc x pk Eval [P(x)] P
“1/2FHE sk Dec [P(x)]1 [P(×)]2 Eval Eval computationally computationally hi Ides x hides x Enc
“1/2 FHE” Dec P(x) sk [x]1 Enc x pk Eval [P(x)]1 P Eval [P(x)]2 P [x]2 computationally hides x computationally hides x
2-Party) Homomorphic Secret Sharing [P(x)]1 [P(×)]2 Eval Eval Share
(2-Party) Homomorphic Secret Sharing Dec P(x) [x]1 Share x Eval [P(x)]1 P Eval [P(x)]2 P [x]2