Unique Information and Secret Key Agreement

The partial information decomposition (PID) is a promising framework for decomposing a joint random variable into the amount of influence each source variable Xi has on a target variable Y, relative to the other sources. For two sources, influence breaks down into the information that both X0 and X1 redundantly share with Y, what X0 uniquely shares with Y, what X1 uniquely shares with Y, and finally what X0 and X1 synergistically share with Y. Unfortunately, considerable disagreement has arisen as to how these four components should be quantified. Drawing from cryptography, we consider the secret key agreement rate as an operational method of quantifying unique informations. Secret key agreement rate comes in several forms, depending upon which parties are permitted to communicate. We demonstrate that three of these four forms are inconsistent with the PID. The remaining form implies certain interpretations as to the PID's meaning---interpretations not present in PID's definition but that, we argue, need to be explicit. These reveal an inconsistency between third-order connected information, two-way secret key agreement rate, and synergy. Similar difficulties arise with a popular PID measure in light the results here as well as from a maximum entropy viewpoint. We close by reviewing the challenges facing the PID.Comment: 9 pages, 3 figures, 4 tables; http://csc.ucdavis.edu/~cmg/compmech/pubs/pid_skar.htm. arXiv admin note: text overlap with arXiv:1808.0860

Gait-Based Smart Pairing System for Personal Wearable Devices

With the rapid development of embedded technology and mobile computing, we have seen a growing number of Internet of Things (IoT) devices on the market. As the number of wearable devices belonging to the same user increases rapidly, secure pairing between legitimate devices becomes an important research problem. In this chapter, we propose the first gait-based shared key generation system that assists two devices to generate a common secure key by exploiting the user’s unique walking pattern. The system is based on the fact that sensors on different positions of the same user exhibit similar accelerometer signal when the user is walking. Therefore, the acceleration can be used as a shared secret information to generate a common key on different devices independently. Our experimental results show that the key generated by two independent devices on the same body is able to achieve 100% bit agreement rate. The proposed key generation protocol can establish a 128-bit key in 5 s (about 10 steps) with entropy varying from 0.93 to 1. We also find that the proposed scheme can run in real time on modern smartphone and require low system cost

Compressed Secret Key Agreement: Maximizing Multivariate Mutual Information Per Bit

The multiterminal secret key agreement problem by public discussion is formulated with an additional source compression step where, prior to the public discussion phase, users independently compress their private sources to filter out strongly correlated components for generating a common secret key. The objective is to maximize the achievable key rate as a function of the joint entropy of the compressed sources. Since the maximum achievable key rate captures the total amount of information mutual to the compressed sources, an optimal compression scheme essentially maximizes the multivariate mutual information per bit of randomness of the private sources, and can therefore be viewed more generally as a dimension reduction technique. Single-letter lower and upper bounds on the maximum achievable key rate are derived for the general source model, and an explicit polynomial-time computable formula is obtained for the pairwise independent network model. In particular, the converse results and the upper bounds are obtained from those of the related secret key agreement problem with rate-limited discussion. A precise duality is shown for the two-user case with one-way discussion, and such duality is extended to obtain the desired converse results in the multi-user case. In addition to posing new challenges in information processing and dimension reduction, the compressed secret key agreement problem helps shed new light on resolving the difficult problem of secret key agreement with rate-limited discussion, by offering a more structured achieving scheme and some simpler conjectures to prove