Applications Succinct secure computation FHE HSS a [Cb(a)l [ab)]1 [a,b)]2 Cla, b) Bonus features. [C(ab)]1 [c(a,b)2 Beats FHE for long outputs Useful for generating correlations BCGIO17, BCGI18 Cla, b
Applications Succinct Secure Computation FHE HSS sk a b [a] [Cb (a)] C(a,b) a b [(a,b)]1 [(a,b)]2 [C(a,b)]1 [C(a,b)]2 C(a,b) Eval Eval Bonus features: • Beats FHE for long outputs • Useful for generating correlations [BCGIO17,BCGI18]
Applications IAIn .,· Worst-case to average-case reductions Goal: reduce f(x to g x),gx )where if f is boolean then so is g x, x2 are individually"random Complexity of g comparable to that of f HSS-based solution g=Evalf Weaker solutions via fhe, or even unconditionally Useful for Fine-grained average-case hardness Verifiable computation
Applications Worst-case to average-case reductions • Goal: reduce f(x) to g(x1 ), g(x2 ) where: – if f is boolean then so is g – x 1 ,x2 are individually “random” – Complexity of g comparable to that of f • HSS-based solution: g=Evalf – Weaker solutions via FHE, or even unconditionally • Useful for – “Fine-grained” average-case hardness – Verifiable computation
Applications IAIn .,· Worst-case to average-case reductions y f(×)? 0524 )? f()=y
Applications Worst-case to average-case reductions f(x)? x f(x)=y! f(x)?!
Applications IAIn .,· Worst-case to average-case reductions SIy f(r1) Test on N5NO94/ random 05 nputs? x will not be one of them
Applications Worst-case to average-case reductions Test on random inputs? r1 f(r1 ) rn f(rn ) x will not be one of them…
Applications IAIn .,· Worst-case to average-case reductions y gx=y f(×)? 05 fx) g(x2)=y2
Applications Worst-case to average-case reductions f(x)? x 1 g(x1 )=y1 f(x) x 2 g(x2 )=y2