  We introduce a cryptographically motivated quantifier of entanglement in
bipartite Gaussian systems called Gaussian intrinsic entanglement (GIE). The
GIE is defined as the optimized mutual information of a Gaussian distribution
of outcomes of measurements on parts of a system, conditioned on the outcomes
of a measurement on a purifying subsystem. We show that GIE vanishes only on
separable states and exhibits monotonicity under Gaussian local
trace-preserving operations and classical communication. In the two-mode case
we compute GIE for all pure states as well as for several important classes of
symmetric and asymmetric mixed states. Surprisingly, in all of these cases, GIE
is equal to Gaussian R\'{e}nyi-2 entanglement. As GIE is operationally
associated to the secret-key agreement protocol and can be computed for several
important classes of states it offers a compromise between computable and
physically meaningful entanglement quantifiers.
