Security of Rep Sample Clauses

Security of Rep. Even if the adversary modifies P , the string produced by Rep has high entropy: for all (adversarial) functions A and suitable (W, W', E), if (R, P ) ← Gen(W ), P' ← A(P, E), and R' ← Rep(W',P'), then H˜ ∞(R' | E, P ) ≥ hR' . We can build weakly robust fuzzy conductors out of any secure sketch (SS, Rec). We use the secure sketch constructions of [DORS08] to build weakly robust fuzzy conductors for Hamming, set difference, and edit distance metrics. Namely, in Appendix B, we easily obtain • for Hamming distance over an alphabet of size F , given an [n, κ, 2t + 1] linear error-correcting code for the alphabet, we get hR = hW − (n − κ) log F , hR' = hW − 2(n − κ) log F , and η = t. • for set difference, with sets whose elements come from a universe of size U , we get hR = hW − η log(U + 1) and hR' = hW − 2η log(U + 1) for any η. • for edit distance over an alphabet of size we get hR = hW − [ n| log(n − c + 1) − α, and hR' = hW − [ n| log(n − c + 1) − 2α, where α = (2c − 1)η[log(F c + 1)|, for any constant c and