A method of shared key generation between three nodes through a shared communication medium includes performing, with a processor in a first node communicatively connected to a second node and a third node through a shared communication medium, a one-way function using a first shared key between the first node and the second node stored in a memory of the node and a predetermined counter as inputs to generate a first plurality of pseudo-random bits. The method includes generating, with the processor and a transceiver in the first node, a second shared key between the first node and the third node by transmitting each bit in the first plurality of pseudo-random bits to the third node through the shared communication medium simultaneously to transmission of random bits from the third node to the first node.