By Jacques Janssen, Raimondo Manca
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Additional resources for Security with Noisy Data - On Private Biometrics, Secure Key Storage and Anti-Counterfeiting
9, respectively. 4). 8. The secret-key rate of a tripartite probability distribution PXY Z is deﬁned by KA =⇒ SK1 ). S(PXY Z ) := rate(Source(PXY Z ) × AuthA↔B ∞ Similarly, the one-way secret-key rate is KA =⇒ SK1 ). S→ (PXY Z ) := rate(Source(PXY Z ) × AuthA→B ∞ 6 A fuzzy extractors as deﬁned in  can generally be seen as a one-way keyagreement protocol where the generation and the reproduction procedure correspond to Alice’s and Bob’s programs, respectively. The helper string generated by the generation procedure of a secure sketch corresponds to the message sent from Alice to Bob in a one-way key-agreement protocol.
We conclude from this example that the possibility of feedback from Bob to Alice can substantially improve the legitimate partners’ situation toward a wire-tapping adversary. Maurer  proposed the following interactive model of secret-key agreement by public discussion from common information (see Fig. 5). The parties Alice and Bob who want to establish a mutual secret key have access to realizations of random variables X and Y , respectively, whereas the adversary knows a random variable Z.
It thus suﬃces to show that DF (F (X)) contains no other element, except with probability |XE |/|U|; that is, Pr |DF (F (X))| > 1 ≤ |XE | . 4) By the deﬁnition of two-universality, Pr F (x) = F (x′ ) ≤ 1/|U|, for any x = x′ . Consequently, by the union bound, for any ﬁxed x ∈ X , Pr ∃x′ ∈ XE : (x = x′ ) ∧ (F (x) = F (x′ )) ≤ |XE | . 4) and thus concludes the proof. 2. Let X and Y be random variables and let F be chosen at random from a two-universal family of functions from X to U, where |U| = 2ℓ .
Security with Noisy Data - On Private Biometrics, Secure Key Storage and Anti-Counterfeiting by Jacques Janssen, Raimondo Manca