Variable-Length Secret Key Agreement via Random Stopping Time
Junda Zhou, Cheuk Ting Li
TL;DR
The paper addresses secret-key agreement from correlated sources under a variable-length, randomly stopped framework, proposing a less stringent uniformity criterion that enables longer average keys. It develops computationally efficient schemes across three models: a common randomness case (X=Y), an almost common randomness case, and a general correlated case, with analysis tying the achievable key length to the mutual information $I(X;Y)$. The results show that, in the common and almost-common models, near-optimal lengths can be achieved (within constant or small-logarithmic gaps), and in the general model the key length approaches $I(X;Y)$ up to a logarithmic term, via a two-stage construction that combines existing extraction methods with a variable-length coding approach. This has potential impact for practical key agreement where adaptivity to source realizations and efficient encoding are crucial, drawing connections to Huffman coding and Knuth–Yao random-number generation through the random-stopping paradigm.
Abstract
We consider a key agreement setting where two parties observe correlated random sources, and want to agree on a secret key via public discussions. In order to allow the key length to adapt to the realizations of the random sources, we allow the key to be of variable length, subject to a novel variable-length version of the uniformity constraint based on random stopping time. We propose simple, computationally efficient key agreement schemes under the new constraint. The proposed scheme can be considered as the key agreement analogue of variable-length source coding via Huffman coding, and the Knuth-Yao random number generator.