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

In this paper, we study physical layer message authentication with <italic>perfect security</italic> 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 <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-AU₂ hash functions over binary-input wiretap channel. First, a multi-message authentication scheme for noiseless main channel case is presented by leveraging a novel <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-AU₂ hash function family and the dual of large-girth LDPC codes. Concretely, the sender Alice first generates a message tag <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> with message <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and key <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> by using a lightweight <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-AU₂ hash functions; then Alice encodes <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> to a codeword <inline-formula> <tex-math notation="LaTeX">$X^{n}$ </tex-math></inline-formula> with the dual of large-girth LDPC codes; finally, Alice sends <inline-formula> <tex-math notation="LaTeX">$(M,X^{n})$ </tex-math></inline-formula> to the receiver Bob noiselessly. An adversary Eve has infinite computational capacity, and he can obtain <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and the output <inline-formula> <tex-math notation="LaTeX">$Z^{n}$ </tex-math></inline-formula> of the BEC with input <inline-formula> <tex-math notation="LaTeX">$X^{n}$ </tex-math></inline-formula>. Then, an authentication scheme over binary erasure channel and binary-input wiretapper&#x2019;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 <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>. Furthermore, the simulation results are provided to demonstrate that the proposed schemes can achieve high authentication rate with low time latency.