Fig. 1: Flow chart of our method of bounding the guessing probability.
The arrow between s and k indicates that the εk-secure n1-bit final key k can be distilled from the N-bit sifted key s using a random matrix \({R}_{{n}_{1}N}\), i.e., \({\bf{k}}={R}_{{n}_{1}N}{\bf{s}}\). The arrow between k and \({\bf{k}}^{\prime}\) indicates that there exists a map M that can map the key k into \({\bf{k}}^{\prime}\), i.e. \({\bf{k}}^{\prime} =M({\bf{k}})\). The arrow between the sifted key S and \({\bf{k}}^{\prime}\) indicates that if a random hashing matrix \({R}_{{n}_{2}N}\) is used to distill the final key, we have \({\bf{k}}^{\prime} ={R}_{{n}_{2}N}{\bf{s}}\). Then, if n2 satisfies the condition in Theorem 2, a tightened guessing probability of k can be obtained.
