A Classification of Unimodular Lattice Wiretap Codes in Small Dimensions

• Published in: IEEE transactions on information theory 2013-06, Vol.59 (6), p.3295-3303
• Main Authors: Fuchun Lin, Oggier, F.
• Format: Article
• Language: English
• Subjects: Applied sciences; Argon; Classification; Coding theory; Coding, codes; Electronic eavesdropping; Encoding; Equations; Exact sciences and technology; Gain; Gaussian channel; Information theory; Information, signal and communications theory; Jacobian matrices; lattice codes; Lattice theory; Lattices; Normal distribution; Radiocommunications; secrecy gain; Secret; Signal and communications theory; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; theta series; Transmitters. Receivers; unimodular lattices; Vectors; wiretap codes
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2013.2246814

Lattice coding over a Gaussian wiretap channel, where an eavesdropper listens to transmissions between a transmitter and a legitimate receiver, is considered. A new lattice invariant called the secrecy gain is used as a code design criterion for wiretap lattice codes since it was shown to characterize the confusion that a chosen lattice can cause at the eavesdropper: the higher the secrecy gain of the lattice, the more confusion. In this paper, secrecy gains of extremal odd unimodular lattices as well as unimodular lattices in dimension n , 16 ≤ n ≤ 23, are computed, covering the four extremal odd unimodular lattices and all the 111 nonextremal unimodular lattices (both odd and even), providing thus a classification of the best wiretap lattice codes coming from unimodular lattices in dimension n , 8