Secret-Key capacity of compound source models with one-way public communication

Abstract

In the classical Secret-Key generation model, Common Randomness is generated by two terminals based on the observation of correlated components of a common source, while keeping it secret from a non-legitimate observer. It is assumed that the statistics of the source are known to all participants. In this work, the Secret-Key generation model based on a compound source is studied where the source realization is unknown. The protocol should guarantee the security and reliability of the generated Secret-Key, simultaneously for all possible realizations of the compound source. A single-letter lower-bound of the Secret-Key capacity is derived for the case where the public communication rate is limited. Furthermore, a multi-letter capacity formula is computed for the case where the public communication is unconstrained.

Secret-Key Generation Using Compound Sources and One-Way Public Communication

“…Thus, Lemma 2 together with (19) implies for all τ ∈ (0, R − I(Uŝ; Xŝ)), all ζ > 0 sufficiently small, all n ∈ N sufficiently large, and all…”

“…For a given (i, j) ∈ I × J , the number of chosen random sequences v ij pq n is Nŝ ,3 Nŝ ,4 = exp(nR ), where R is the rate of choosing the random sequences. Similar to (19), conditions (14) and (15) imply that R = I(Vŝ; Xŝ|Uŝ) + δ. Furthermore, as a result of Lemma 1.1, from (u n ij (ŝ), x n ) ∈ T n [U X,ŝ]ζ follows T n [U V X,ŝ]σ (u n ij (ŝ), x n ) = ∅.…”

“…Furthermore, for R being the rate of choosing the random sequences {u n ij (ŝ)} (i,j)∈I×J , it holds by (12) and (13) where the last inequality follows by (19) and Lemma 1.4.…”

“…In the present paper, in contrast, we give the complete proofs of both theorems as well as the proofs for random coding and security lemmas. The third and main result of this work which is not available in [19] gives a single-letter SK capacity formula for a degraded compound source, where the set of source states may be infinite and the set of marginal states is finite. Compared with previous theorems, this result which is stated in Theorem 3 is more practical in the sense that the SK capacity is single-letter and also valid for sources with an infinite set of source states S. The complete formal proofs are given in Section IV.…”

“…A multi-letter SK capacity formula is computed as well for the case where the public communication rate is unconstrained. We proposed these two results which are stated in Theorems 1 and 2, originally in [19] in which the proof ideas have been outlined. In the present paper, in contrast, we give the complete proofs of both theorems as well as the proofs for random coding and security lemmas.…”