An LDPC Code Based Physical Layer Message Authentication Scheme With Prefect Security

Abstract

In this paper, we study physical layer message authentication with perfect security for wireless networks, regardless of the computational power of adversaries. Specifically, we propose an efficient and feasible authentication scheme based on low-density parity-check (LDPC) codes and ϵ-AU <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> hash functions over binary-input wiretap channel. First, a multimessage authentication scheme for noiseless main channel case is presented by leveraging a novel ϵ-AU <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> hash function family and the dual of large-girth LDPC codes. Concretely, the sender Alice first generates a message tag T with message M and key K by using a lightweight ϵ-AU <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> hash functions; then Alice encodes T to a codeword X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> with the dual of large-girth LDPC codes; finally, Alice sends (M, X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ) to the receiver Bob noiselessly. An adversary Eve has infinite computational capacity, and he can obtain M and the output Z <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> of the BEC with input X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> . Then, an authentication scheme over binary erasure channel and binary-input wiretapper's channel is further developed, which can reduce the noisy main channel case to noiseless main channel case by leveraging public discussion. We theoretically prove that, the proposed schemes are perfect secure if the number of attacks from Eve is upper bounded by a polynomial times in terms of n. Furthermore, the simulation results are provided to demonstrate that the proposed schemes can achieve high authentication rate with low time latency.