Privacy Amplification Clause Samples
Privacy Amplification. Comparing the security condition given in Definition 1.8 with ▇▇▇▇▇▇▇’▇ criterion of secu- rity (perfect security) given in Definition 1.6 implies that a secure communication is the sense of Definition 1.8 is not necessarily a secure communication in the sense of Defini- tion 1.
Privacy Amplification. [9] The transmitter and the legiti- mate receiver publicly agree on a deterministic function they apply to their common sequence to generate a secret key. In this work, we focus primarily on the first phase of the key- distillation process and we investigate the optimal transmission strategy to adopt when the terminals in the network deploy multiple antennas. of messages over the public channel. A secret-key rate is defined as the ratio between the number of key bits k obtained at the end of a key-distillation strategy and the number of noisy channel uses n required to obtain it. A secret-key rate R = k/n is achievable if there exists a secret-key distillation strategy such that, • on denoting the secret key distilled at the transmitter and that at the legitimate receiver by K and Kˆ, the error probability is zero asymptotically, that is: public communication channel W nR R + YnR B lim P hK =/ Kˆi = 0; (3) A XnT HE HR + ZnE E W • the mutual information between the secret key and the eavesdropper observations is arbitrarily low (strong se- crecy constraint [11]); that is, if we denote the messages sent on the public two-way channel by the the random variable F and we collect the outputs of the eavesdropper nE E
Fig. 1. Secret-key agreement over quasi-static MIMO fading channels.
Privacy Amplification. After information reconciliation, ▇▇▇▇▇ and ▇▇▇ both know x0 but cannot use it as key, since ▇▇▇ has some information about it (in fact, ▇▇▇ knows some positions of x0 with certainty in our setting). ▇▇▇▇▇ and ▇▇▇ rectify this situation in the next step, called privacy amplification. The simple idea is that ▇▇▇▇▇ and ▇▇▇ can apply a strong extractor: ▇▇▇▇▇ chooses a seed uniformly at random and sends it to Bob. Then, they both apply the extractor to x0. Since for Eve x0 has large min-entropy, this gives a bit string which is close to uniform with respect to ▇▇▇’s information.
Privacy Amplification. The Alices apply a privacy amplification protocol to generate the final key systems ▇▇▇ ▇▇▇ · · · ▇▇▇ . The winning condition for the M -partite parity-CHSH game is [RMW18] a1,j ⊕ a2,j = x1,j ∧ x2,j ⊕ Mi=3 ai,j ! 4 where a1,j, . . . , ▇▇,▇, ▇▇,▇, and x2,j are realizations of the random variables specified in round j of the RMW18 Protocol. The winning probability for an arbitrary classical strategy is PCHSH = 3 . The ▇▇▇▇ inequality corresponding to the classical–quantum threshold in the tripartite case is [HKB20] ν = O1O+O3 − O0O− ≤ 1, (3) where O± = (O0 ± O1)/2, i refers to the ith party, and O0 and O1 are observables corresponding to the inputs 0 and 1, respectively, and are defined in [HKB20].