Secrecy gain, flatness factor, and secrecy-goodness of even unimodular lattices

Nested lattices Ae ⊂ Ab have previously been studied for coding in the Gaussian wiretap channel and two design criteria, namely, the secrecy gain and flatness factor, have been proposed to study how the coarse lattice Ae should be chosen so as to maximally conceal the message against the eavesdropper. In this paper, we study the connection between these two criteria and show the secrecy-goodness of even unimodular lattices, which means exponentially vanishing flatness factor as the dimension grows.

[1]  Cong Ling,et al.  Semantically Secure Lattice Codes for the Gaussian Wiretap Channel , 2012, IEEE Transactions on Information Theory.

[2]  A. J. Scholl.  INTRODUCTION TO ELLIPTIC CURVES AND MODULAR FORMS (Graduate Texts in Mathematics, 97) , 1986 .

[3]  Shlomo Shamai,et al.  Information Theoretic Security , 2009, Found. Trends Commun. Inf. Theory.

[4]  Tsung-Ching Lin,et al.  On the minimum weights of binary extended quadratic residue codes , 2009, 2009 11th International Conference on Advanced Communication Technology.

[5]  Frédérique Oggier,et al.  Coding for Wiretap Channels , 2013 .

[6]  J. Barros,et al.  LDPC codes for the Gaussian wiretap channel , 2009 .

[7]  Gou Hosoya,et al.  国際会議参加報告:2014 IEEE International Symposium on Information Theory , 2014 .

[8]  N. Koblitz.  Introduction to Elliptic Curves and Modular Forms , 1984 .

[9]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[10]  Jean-Pierre Serre.  A Course in Arithmetic , 1973 .

[11]  Cong Ling,et al.  Lattice codes achieving strong secrecy over the mod-Λ Gaussian Channel , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[12]  Frédérique E. Oggier,et al.  Gaussian wiretap lattice codes from binary self-dual codes , 2012, 2012 IEEE Information Theory Workshop.

[13]  Matthieu R. Bloch,et al.  Physical-Layer Security: From Information Theory to Security Engineering , 2011 .

[14]  Frédérique E. Oggier,et al.  2- and 3-Modular lattice wiretap codes in small dimensions , 2013, Applicable Algebra in Engineering, Communication and Computing.

[15]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[16]  Martin E. Hellman,et al.  The Gaussian wire-tap channel , 1978, IEEE Trans. Inf. Theory.

[17]  Jean-Claude Belfiore,et al.  Lattice Codes for the Wiretap Gaussian Channel: Construction and Analysis , 2011, IEEE Transactions on Information Theory.

[18]  Wolfgang Ebeling,et al.  Lattices and Codes: A Course Partially Based on Lectures by Friedrich Hirzebruch , 1994 .

[19]  Byung-Jae Kwak,et al.  LDPC Codes for the Gaussian Wiretap Channel , 2009, IEEE Transactions on Information Forensics and Security.

[20]  Frédérique E. Oggier,et al.  Secrecy gain: A wiretap lattice code design , 2010, 2010 International Symposium On Information Theory & Its Applications.

[21]  Frédérique E. Oggier,et al.  A Classification of Unimodular Lattice Wiretap Codes in Small Dimensions , 2013, IEEE Transactions on Information Theory.