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In this article, we study the problem of secret key generation in themultiterminal source model, where the terminals have access to correlatedGaussian sources. We assume that the sources form a Markov chain on a tree. Wegive a nested lattice-based key generation scheme whose computationalcomplexity is polynomial in the number, N , of independent and identicallydistributed samples observed by each source. We also compute the achievablesecret key rate and give a class of examples where our scheme is optimal in thefine quantization limit. However, we also give examples that show that ourscheme is not always optimal in the limit of fine quantization.

A Lattice Coding Scheme for Secret Key Generation from Gaussian Markov Tree Sources