Generating and distributing encryption keys via chaos synchronization of optical systems is a promising method for achieving secure and fast real-time encryption of large data volumes. However, current state-of-the-art systems based on lasers subjected to time-delayed feedback have exhibited serious limitations in regard to stability and speed due to their inherent phase sensitivity and their fundamental bandwidth limitation by the laser relaxation oscillation frequency. Here, we propose, simulate, and build a fundamentally different concept based on optoelectronic oscillators (OEOs) to generate and distribute encryption keys. We demonstrate both theoretically and experimentally that by injecting chaotic OEOs with a common external chaotic signal, chaos synchronization can be achieved. The key distribution signal shared between sender and receiver is in the optical domain and can thus be transmitted over a standard fiber-optic network. As the optoelectronic feedback is phase insensitive, stable synchronization becomes possible without any need for active stabilization, resulting in a compact and inexpensive setup. From the chaotic time traces, identical random bit sequences can be generated on the sender's and receiver's sides at rates of up to 6 GBit/s, which is comparable to current state-of-the-art systems of the same bandwidth. Since OEOs are not bandwidth limited by relaxation oscillations, the key generation can be further increased compared to laser-based systems by increasing the OEO bandwidth, thus presenting a promising platform for achieving fast and secure real-time encryption.