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Lecture notes in computer science

Common Randomness and Secret Key Capacities of Two-Way Channels

Hadi Ahmadi, Reihaneh Safavi–Naini

Published Jan 1, 2011• 4 citations
Publisher
DOI
10.1007/978-3-642-20728-0_8

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Abstract. Common Randomness Generation (CRG) and Secret Key Establishment (SKE) are fundamental primitives that are used in information-theoretic coding and cryptography. We study these two problems over the two-way channel model of communication, introduced by Shannon. In this model, the common randomness (CK) capacity is defined as the maximum number of random bits per channel use that the two parties can generate. The secret key (SK) capacity is defined similarly when the random bits are also required to be secure against a passive adversary. We provide lower bounds on the two capacities. These lower bounds are tighter than those one might derive based on the previously known results. We prove our lower bounds by proposing a two-round, two-level coding construction over the two-way channel. We show that the lower bound on the common randomness capacity can also be achieved using a simple interactive channel coding (ICC) method. We furthermore provide upper bounds on these capacities and show that the lower and the upper bounds coincide when the two-way channel consists of two independent (physically degraded) one-way channels. We apply the results to the case where the channels are binary symmetric.

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Identification is a new paradigm introduced for goal-oriented communication that verifies the semantics of the intended message rather than just transmitting the message bits, which is traditionally done in classical communication systems. One of the key techniques to improve randomized identification capacity is by introducing Common Randomness (CR). Physical Layer Secret Key (PLSK) is one such CR generation technique, where terminals generate secret keys based on changes in channel reciprocity between the wireless terminals and are mainly used for PHY layer encryption. However, the traditional way of evaluating PLSK techniques through bit discrepancies, bit generation rate, and entropy is not sufficient for evaluating their usefulness for identification. This paper proposes three key novel information theory paradigms that can be used alongside other mentioned parameters to evaluate key PLSK techniques for their usefulness in identification, i.e., CR rate, CR capacity, and cost function, followed by a supporting implementation using Software Defined Radio (SDR)s.

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Abstract. Common Randomness Generation (CRG) and Secret Key Establishment (SKE) are fundamental primitives that are used in information-theoretic coding and cryptography. We study these two problems over the two-way channel model of communication, introduced by Shannon. In this model, the common randomness (CK) capacity is defined as the maximum number of random bits per channel use that the two parties can generate. The secret key (SK) capacity is defined similarly when the random bits are also required to be secure against a passive adversary. We provide lower bounds on the two capacities. These lower bounds are tighter than those one might derive based on the previously known results. We prove our lower bounds by proposing a two-round, two-level coding construction over the two-way channel. We show that the lower bound on the common randomness capacity can also be achieved using a simple interactive channel coding (ICC) method. We furthermore provide upper bounds on these capacities and show that the lower and the upper bounds coincide when the two-way channel consists of two independent (physically degraded) one-way channels. We apply the results to the case where the channels are binary symmetric.
Ahlswede-Csiszar (1993) and Csiszar (see Problemy Peredacii Informatsii, 1996) have addressed problems of determining the common randomness (CR) capacity and the secret key (SK) capacity for a variety of models as they arise in information theory and cryptography. We study problems of common randomness and secret key generation by a pair of terminals called the "users" with help from a third terminal, called the "helper". Noiseless one-way communication from the helper to the users as also from one user to the other, subject to rate constraints, is permitted over public channels. A situation involving a wiretapper is also considered.
Identification is a new paradigm introduced for goal-oriented communication that verifies the semantics of the intended message rather than just transmitting the message bits, which is traditionally done in classical communication systems. One of the key techniques to improve randomized identification capacity is by introducing Common Randomness (CR). Physical Layer Secret Key (PLSK) is one such CR generation technique, where terminals generate secret keys based on changes in channel reciprocity between the wireless terminals and are mainly used for PHY layer encryption. However, the traditional way of evaluating PLSK techniques through bit discrepancies, bit generation rate, and entropy is not sufficient for evaluating their usefulness for identification. This paper proposes three key novel information theory paradigms that can be used alongside other mentioned parameters to evaluate key PLSK techniques for their usefulness in identification, i.e., CR rate, CR capacity, and cost function, followed by a supporting implementation using Software Defined Radio (SDR)s.