Conference Paper

# Providing secrecy with lattice codes

Electr. Eng. Dept., Pennsylvania State Univ., University Park, PA

DOI: 10.1109/ALLERTON.2008.4797696 Conference: Communication, Control, and Computing, 2008 46th Annual Allerton Conference on Source: IEEE Xplore

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**ABSTRACT:**Bidirectional relaying, where a relay helps two user nodes to exchange messages has been an active area of recent research. In the compute-and-forward strategy for bidirectional relaying, the relay computes a function of the two messages using the naturally-occurring sum of symbols simultaneously transmitted by user nodes in a Gaussian Multiple Access Channel (MAC), and the computed function value is forwarded to the user nodes in an ensuing broadcast phase. In this work, we consider the Gaussian MAC in bidirectional relaying with the messages taking values in a finite Abelian group and the relay computing the sum within the group under an additional secrecy constraint for protection against a honest but curious relay. The secrecy constraint is that, while the relay should decode the group sum, the individual message of each user should be perfectly secure from the relay. We exploit the symbol addition that occurs in a Gaussian MAC to design explicit modulations at the user nodes that achieve independence between the received symbols at the relay and each of the two individual transmitted messages under an average transmit power constraint. We provide a lattice coding strategy for reliable computation of the group sum at the relay with perfect secrecy, and study rate versus average power trade-offs in the large-dimension regime. Our results for secure compute-and-forward are significant because we achieve perfect security with finite average transmit power, and this has been done using a novel approach involving Fourier-analytic tools.06/2012; - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, we propose opportunistic jammer selection in a wireless security system for increasing the secure degrees of freedom (DoF) between a transmitter and a legitimate receiver (say, Alice and Bob). There is a jammer group consisting of $S$ jammers among which Bob selects $K$ jammers. The selected jammers transmit independent and identically distributed Gaussian signals to hinder the eavesdropper (Eve). Since the channels of Bob and Eve are independent, we can select the jammers whose jamming channels are aligned at Bob, but not at Eve. As a result, Eve cannot obtain any DoF unless it has more than $KN_{j}$ receive antennas, where $N_{j}$ is the number of each jammer's transmit antenna, and hence $KN_{j}$ can be regarded as defensible dimensions against Eve. For the jamming signal alignment at Bob, we propose two opportunistic jammer selection schemes and find the scaling law of the required number of jammers for target secure DoF by a geometrical interpretation of the received signals.IEEE Transactions on Signal Processing 01/2014; 62(4):828-839. · 2.81 Impact Factor -
##### Conference Paper: The Gaussian many-to-one interference channel with confidential messages

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**ABSTRACT:**We investigate the K-user many-to-one interference channel with confidential messages in which the Kth user experiences interference from all other K - 1 users, and is at the same time treated as an eavesdropper to all the messages of these users. We derive achievable rates and an upper bound on the sum rate for this channel and show that the gap between the achievable sum rate and its upper bound is log<sub>2</sub>(K - 1) bits per channel use under very strong interference, when the interfering users have equal power constraints and interfering link channel gains. The main contributions of this work are: (i) nested lattice codes are shown to provide secrecy when interference is present, (ii) a secrecy sum rate upper bound is found for strong interference regime and (iii) it is proved that under very strong interference and a symmetric setting, the gap between the achievable sum rate and the upper bound is constant with respect to transmission powers.Information Theory, 2009. ISIT 2009. IEEE International Symposium on; 08/2009

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