Key agreement in wireless networks with active adversaries

1. A network of computers with error correction code configured to transmit a key secretly and securely between a source node and a receiver node which do not a priori share a key, so as to establish a shared key between the source node and the receiver node, the network of computers comprising:

a first computer-based workstation operating as the source node and configured to encode the key into a plurality of distinct encoded source files, encoding being operatively implemented in one of: a) hardware, b) software, or c) a combination of hardware and software;

a plurality of computer-based workstations operating as a plurality of intermediate nodes and configured to each receive a distinct encoded source file of the plurality of distinct encoded source files and transmit, to the receiver node, the distinct encoded source file when requested by the receiver; and

a second computer-based workstation operating as the receiver node and configured to decode the plurality of distinct encoded source files and retrieve the key to establish the shared key, decoding being operatively implemented in one of: a) hardware, b) software, or c) a combination of hardware and software;

wherein the encoding of the key comprises the following steps:

generating the key to be transmitted from the source node to the receiver node,

generating one or more random packets independently and uniformly within the source node, and

generating a distinct encoded file of the plurality of distinct encoded files for each intermediate node in the network, the distinct encoded file comprising a linear combination of the key, the one or more random packets that were independently and uniformly generated and corresponding error detection information.

2. The network of computers of claim 1 , wherein an intermediate node of the plurality of intermediate nodes and corresponding intermediate transmission links that link the particular intermediate node to the source node and to the receiver node form a two-hop path between the source node and the receiver node.

3. The network of computers of claim 1 , wherein the encoded source files comprise linearly independent combinations of the following:

one or more randomly generated packets, and

a source message, the source message comprising a set or subset of keys and corresponding error detection information.

4. The network of computers of claim 3 , wherein the error detection information comprises hash information from each of the other encoded files, the hash information being defined in terms of random parameters generated by the source node.

5. The network of computers of claim 1 , wherein the network is a distributed wireless network.

6. A network of computers with error correction code configured to transmit a key pool secretly and securely comprising:

(i) a plurality of computer-based workstations operating as a plurality of intermediate nodes and configured to each:

receive one or more, but not all, individual keys of the key pool, the key pool comprising a plurality of individual keys,

encode independently from other nodes of the plurality of intermediate nodes, using network error correction codes, the one or more individual keys, wherein the encoded one or more individual keys are represented by a vector that contains random linear combinations of the one or more individual keys, encoding being operatively implemented in one of: a) hardware, b) software, or c) a combination of hardware and software, and

transmit the encoded one or more individual keys to a receiver node, when requested; and

(ii) a computer-based workstation operating as the receiver node and configured to decode encoded one or more individual keys received from a subset of the intermediate nodes, using a decoding algorithm to retrieve a specified subset of the key pool, decoding being operatively implemented in one of: a) hardware, b) software, or c) a combination of hardware and software;

wherein decoding of the encoded keys to retrieve the key pool in the receiver node comprises the following steps:

identifying two or more distinct groupings of intermediate nodes of the plurality of nodes, wherein each intermediate node within a particular distinct grouping of intermediate nodes shares a same set of individual keys of the key pool,

requesting each of the intermediate nodes of the two or more distinct groupings of intermediate nodes to forward their respective encoded vectors,

using error detection information to identify a number of compromised nodes within the two or more distinct grouping of intermediate nodes,

decoding each of the encoded vectors forwarded by each of the intermediate nodes,

determining a number of consistent decoded keys forwarded by the intermediate nodes within a particular grouping of the two or more distinct groupings of intermediate nodes, the number of consistent decoded keys is based on the number of compromised nodes, and

extracting the key pool by retrieving an error-free subset of the key pool from each of two or more distinct grouping of intermediate nodes.