In this article, we study the problem of secret key generation in the
multiterminal source model, where the terminals have access to correlated
Gaussian sources. We assume that the sources form a Markov chain on a tree. We
give a nested lattice-based key generation scheme whose computational
complexity is polynomial in the number, N , of independent and identically
distributed samples observed by each source. We also compute the achievable
secret key rate and give a class of examples where our scheme is optimal in the
fine quantization limit. However, we also give examples that show that our
scheme is not always optimal in the limit of fine quantization.Comment: 10 pages, 3 figures. A 5-page version of this article has been
submitted to the 2016 IEEE International Symposium on Information Theory
(ISIT
