We study the Rössler system with a delayed feedback $k z(t-t(z))$ in the $z$-equation and state-dependent delay $t(z) = t_0 + c_1 z^2$. The linearization coincides with that of a constant delay $t^* = t_0 + c_1 z^{*2}$, so the Hopf curves in the $(k,t_0)$ plane are shifted exactly by $c_1 z^{*2}$ (verified by a pseudospectral method and by direct simulation). In a regime that possesses a stable equilibrium, the state dependence alone switches the Hopf bifurcation from subcritical to supercritical: the first Lyapunov coefficient computed with the normal-form theory for SD-DDEs changes sign at $c_1^* \approx 0.389$, and continuation of periodic orbits (DDE-BIFTOOL) confirms the picture, including the folds of the subcritical branches. In the chaotic regime, an ensemble of 16 initial conditions with six Lyapunov exponents shows a small but statistically detectable decrease of the chaotic fraction with $c_1$ (from 0.53 to 0.48), while individual parameter points are reclassified at a rate comparable to the initial-condition variability; no hyperchaos is found. When $c_1$ is regarded as a chaos-based key it produces logarithmic sensitivity, yet a least-squares attack on the observed signal $z(t)$ recovers $(t_0,c_1)$ even when $a,b,c,k$ are also unknown and the channel adds noise, band-limiting and quantization; the scheme is therefore not secure by itself.