Browsing by Author "Poostindouz, Alireza"

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    Contributions to Information Theoretic Multiterminal Secret Key Agreement
    (2022-01) Poostindouz, Alireza; Safavi-Naeini, Reyhaneh; Ghaderi, Majid; Gour, Gilad; Fapojuwo, Abraham O.; Sprintson, Alex
    A multiterminal secret key agreement (SKA) protocol is used to establish a shared se- cret key among a group of terminals. We study SKA protocols with information-theoretic security. In the source model of SKA, each terminal can sample from a correlated random variable. In the channel model of SKA, terminals instead are connected through an un- derlying noisy channel that is used for distributing the correlated variables. The terminals arrive at a shared secret key by establishing correlation (as per the presumed source/channel model) and communicating over a noiseless authenticated public channel. In the general models of SKA, it is assumed that terminals’ variables are partially leaked to the adversary, Eve, in the form of a random variable which we call Eve’s wiretap side information. Eve has unlimited computational power and has read access to all public communication mes- sages. The key rate of an SKA protocol is given by the key length divided by the terminals’ variables length, and the maximum possible key rate calculated for an SKA model is called the wiretap secret key (WSK) capacity of that model. Finding a general expression for the WSK capacity continues to be one of the hardest open problems within the context of information-theoretic key agreement. Our contributions include proving the WSK capacity and proposing capacity achieving SKA protocols for the wiretapped PIN, Tree-PIN, and Polytree-PIN models, that are special multiterminal SKA models of interest in practice. Also, we introduce a new channel model of SKA that we call the transceiver model for which we prove multiple upper and lower bounds on key capacity under various assumptions. Furthermore, we note that traditionally the key capacity was studied and calculated for SKA models, while in the actual implementation of SKA protocols, the achievable key length as a function of terminals’ variables length is needed. Compared to calculating WSK capacity, finding the key length requires different information-theoretic techniques for evaluating the protocols. We prove finite-length upper and lower bounds on the maximum achievable key length for some of the models that we have considered. In the concluding sections, we outline directions for future research.
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    Fine-Grained Quantum Uncertainty Relations
    (2016) Poostindouz, Alireza; Gour, Gilad; Høyer, Peter; Sanders, Barry
    Quantum theory predicts an inherent joint unpredictability for some pairs of measurements. For example, Heisenberg showed that the more precisely the position of a quantum particle is known, the less precisely its momentum can be known and vice versa. Uncertainty relations (URs) are mathematical expressions quantifying the constraints between the output probability distributions of the given sets of measurements. Typically, URs are expressed in terms of uncertainty quantifiers such as entropies. Based on an information-theoretic approach, we discovered a characterization that unifies all uncertainty quantifiers and thus, generalizes a large class of URs into a single framework. We also prove new URs that are fundamentally different from typical URs in that they are fine-grained; i.e. they set restrictions directly on the output probability distributions without using any particular uncertainty quantifiers. We used Majorization theory and other techniques such as matrix analysis to prove our fine-grained uncertainty relations.
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    Path Hopping: An MTD Strategy for Long-Term Quantum-Safe Communication
    (2018-05-07) Safavi-Naini, Reihaneh; Poostindouz, Alireza; Lisy, Viliam
    Moving target defense (MTD) strategies have been widely studied for securing computer systems. We consider using MTD strategies to provide long-term cryptographic security for message transmission against an eavesdropping adversary who has access to a quantum computer. In such a setting, today’s widely used cryptographic systems including Diffie-Hellman key agreement protocol and RSA cryptosystem will be insecure and alternative solutions are needed. We will use a physical assumption, existence of multiple communication paths between the sender and the receiver, as the basis of security, and propose a cryptographic system that uses this assumption and an MTD strategy to guarantee efficient long-term information theoretic security even when only a single path is not eavesdropped. Following the approach of Maleki et al., we model the system using a Markov chain, derive its transition probabilities, propose two security measures, and prove results that show how to calculate these measures using transition probabilities. We define two types of attackers that we call risk-taking and risk-averse and compute our proposed measures for the two types of adversaries for a concrete MTD strategy. We will use numerical analysis to study tradeoffs between system parameters, discuss our results, and propose directions for future research.