Min-Entropy Leakage of Channels in Cascade

Barbara Espinoza, Geoffrey Smith

Alexandra Musat, Andrei Tănăsescu, Pantelimon George Popescu

Geoffrey Smith

Quantitative theories of information flow are of growing interest, due to the fundamental importance of protecting confidential information from improper disclosure, together with the unavoidability of "small" leaks in practical systems. But while it is tempting to measure leakage using classic information-theoretic concepts like Shannon entropy and mutual information, these turn out not to provide very satisfactory security guarantees. As a result, several researchers have developed an alternative theory based on Renyi's min-entropy. In this theory, uncertainty is measured in terms of a random variable's vulnerability to being guessed in one try by an adversary, note that this is the complement of the Bayes Risk. In this paper, we survey the main theory of min-entropy leakage in deterministic and probabilistic systems, including comparisons with mutual information leakage, results on min-capacity, results on channels in cascade, and techniques for calculating min-entropy leakage in systems.

Stefan Dziembowski, Tomasz Kazana, Maciej Zdanowicz

Ching–Yi Lai, Kai-Min Chung

The leakage chain rule for quantum min-entropy quantifies the change of min-entropy when one party gets additional leakage about the information source. Herein we provide an interactive version that quantifies the change of min-entropy between two parties, who share an initial classical-quantum state and are allowed to run a two-party protocol. As an application, we prove new versions of lower bounds on the complexity of quantum communication of classical information.

Tomer Avrahami, Ofer Amrani, Avishai Wool

A shared secret key is necessary for encrypted communications. Since Wi-Fi relies on OFDM, we suggest a method for generating such key by utilizing Wi-Fi’s channel state information (CSI). The channel is typically reciprocal but very sensitive to location: while (legitimate) Alice and Bob should observe the same CSI, an eavesdropper Eve shall observe uncorrelated CSI when positioned over 0.5 wavelength away from either node.We show that if endpoint Bob is shaken, sufficient diversity is induced in the CSI, thus rendering it a true source for randomness. We then show that the CSI among neighboring sub-carriers is correlated, so we select a small set of judiciously-spaced sub-carriers, and decide on a value based on a majority rule about each. Consequently, Alice and Bob observe a 5-15% bit mismatch rate (BMR) in the extracted bitstream while Eve experiences a BMR of around 50% even when placed 10cm away from Alice.We employ the cryptography-oriented definition of min-entropy to estimate the number of secure bits in the received bitstream, and employ the so-called Cascade algorithm of quantum-key-distribution to reconcile Alice and Bob’s bitstreams while quantifying the number of bits leaked by the algorithm. Accounting for both the min-entropy and the Cascade-based leakage we quantify the Secured Bit Generation Rate realized by our method.Extensive set of experiments have been conducted in an indoor environment revealing secure bit generation rate of 1.2–1.6 bits per packet, for endpoint distances ranging from 0.5m–9m; a (128-bit) secured shared-key is generated in 20sec of device shaking.