1. A system for organizing without central administration of a network of non-trusting computing devices so that the computing devices can securely share network resources and communicate with each other, comprising: a recipient computing device; and a sending computing device that sends a signed circuit establishment request to the recipient computing device via the network of non-trusting computing devices, wherein the sending computing device communicates a first identity document to the recipient computing device, wherein the first identity document identifies the sending computing device to the recipient computing device, wherein the first identity document includes a first public key signed by the sending computing device, and wherein the first public key is associated with a first private key known only to the sending computing device; wherein the recipient computing device communicates a second identity document to the sending computing device, wherein the second identity document identifies the recipient computing device to the sending computing device, wherein the second identity document includes a second public key signed by the recipient computing device, and wherein the second public key is associated with a second private key known only to the recipient computing device; wherein the first private key, the second private key, the first public key, and the second public key uniquely identify the sending computing device to the recipient computing device; and wherein a communications circuit is established between the sending computing device and the recipient computing device in response to identifying the sending computing device based on the first private key, the second private key, the first public key, and the second public key.