Looping for Encryption Key Generation Over the Internet: A New Frontier in Physical Layer Security

Current key sharing techniques rely on the hardness of solving a solvable, but complex, mathematical problem. This entails, in Information Theoretical sense, the encryption key is not secret, it can be found by solving the underlying mathemat-ical problem. Sensitive data we encrypt today using traditional techniques can be recorded by malicious parties and be deciphered in the future whenever improved hacking techniques and supporting computing technology permit. Information Theory proves the existence of methods for sharing of encryption keys that are unconditionally secure, but does not show how to bring such theoretical results to practical use. One of the central information theoretical approaches to key sharing is based on exploiting common randomness. This theoretical result states that if two dependent random variables,$A$and B, are available at Alice and Bob, then, by communicating through a public channel between$A$and B, it is possible to securely share a key of size I(A;B). To bridge the gap between theory and practice, one needs a method to generate two sets of dependent random variables, one at Alice‘s side and the other one at the Bob’ side, as well as a method to extract two identical keys from these dependent random variables. This article presents a novel technique to achieve this goal over the Internet. Dependent random variables are generated by measuring packet travel times between Alice and Bob, and error-free key extraction from dependent random variables is realized by using a randomized Low Density Parity Check Code (LDPC). Through looping of packets between Alice and Bob, the mutual information between random variables is increased. Finally, methods are presented to measure the likelihood values required in decoding the underlying LDPC. It is shown that the key rate is approximately equal to$0.5\log_{9}(4L^{2}/(4L-1))\approx 0.5\log_{2}(L)$where$L$is the number of round trips (loops). Test results (based on measurements between distant nodes over the Internet) are presented, demonstrating the feasibility of the proposed technique. The proposed method is implemented entirely in software (through high-level programming, e.g., using C-language, at the application layer). This operation does not require modifying the underlying network.

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