A method for generation of a shared key comprising: 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; and 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 , the generation of each bit in the second shared key further comprising: transmitting, with a transceiver in the first node , a first signal corresponding to each bit through the shared communication medium to the third node; receiving, with the transceiver in the first node , a first signal level of the shared communication medium during transmission of the first signal corresponding to a simultaneous transmission from the third node; transmitting, with the transceiver in the first node , a second signal corresponding to a logical complement of each bit through the shared communication medium to the third node; receiving, with the transceiver in the first node , a second signal level of the shared communication medium during transmission of the second signal corresponding to another simultaneous transmission from the third node; and storing, with the processor in the first node , each bit in a memory in association with the second shared key only in response to the first signal level of the shared communication medium and the second signal level of the shared communication medium being the same, the each bit being a logical complement to a corresponding bit generated in the third node. 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; and 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 , the generation of each bit in the second shared key further comprising: transmitting, with a transceiver in the first node , a first signal corresponding to each bit through the shared communication medium to the third node; receiving, with the transceiver in the first node , a first signal level of the shared communication medium during transmission of the first signal corresponding to a simultaneous transmission from the third node; transmitting, with the transceiver in the first node , a second signal corresponding to a logical complement of each bit through the shared communication medium to the third node; receiving, with the transceiver in the first node , a second signal level of the shared communication medium during transmission of the second signal corresponding to another simultaneous transmission from the third node; and storing, with the processor in the first node , each bit in a memory in association with the second shared key only in response to the first signal level of the shared communication medium and the second signal level of the shared communication medium being the same, the each bit being a logical complement to a corresponding bit generated in the third node. <EOS>