Secret Keys Sample Clauses

Secret Keys. K A SK is a collection of RVs K1, ..., Km, where the ith party gets Ki, that agree with probability close to 1 and are concealed, in effect, from an eavesdropper. Formally, the ith party computes a function Ki of (Ui, Xi, F). Traditionally, the RVs K1, ..., Km with a common range constitute an (s, δ)-SK if the following two conditions are satisfied (for alternative definitions of secrecy, see [20,11,13]) P (K1 = ··· = Km) ≥ 1 − s, (1) 2 ǁPK1FZ − Punif × PFZǁ≤ δ, (2) ǁ· ǁ where is the variational distance and Punif is the uniform distribution on K . The first condition above represents the reliable recovery of the SK and the second condition guarantees security. In this work, we use the following alterna- tive definition of a SK, which conveniently combines the recoverability and the security conditions (cf. [25]): Xxx XXx X0, ..., Xx above constitute an s-SK with common range K if unif where 1 P 2 KMFZ − P(M) × PFZ ≤ s, (3) P(M) (k ) = (k1 = ·· · = km) . unif M |K| In fact, the two definitions above are closely related. ≤ ≤
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