Multi-message Authentication over Noisy Channel with Secure Channel Codes

TL;DR

This paper introduces an information-theoretic multi-message authentication framework over noisy channels, combining secure transmission and message authentication, with protocols that achieve high authentication rates and low error rates.

Contribution

It proposes a novel authentication framework over wiretap channels that guarantees information-theoretic security for multiple messages using existing coding techniques.

Findings

Authentication rate can approach infinity as code length increases.

The protocol achieves low time cost and high authentication rate.

Experimental results confirm low error and high efficiency.

Abstract

In this paper, we investigate multi-message authentication to combat adversaries with infinite computational capacity. An authentication framework over a wiretap channel $(W_1,W_2)$ is proposed to achieve information-theoretic security with the same key. The proposed framework bridges the two research areas in physical (PHY) layer security: secure transmission and message authentication. Specifically, the sender Alice first transmits message $M$ to the receiver Bob over $(W_1,W_2)$ with an error correction code; then Alice employs a hash function (i.e., $\varepsilon$-AWU$_2$ hash functions) to generate a message tag $S$ of message $M$ using key $K$, and encodes $S$ to a codeword $X^n$ by leveraging an existing strongly secure channel coding with exponentially small (in code length $n$) average probability of error; finally, Alice sends $X^n$ over $(W_1,W_2)$ to Bob who authenticates the received messages. We develop a theorem regarding the requirements/conditions for the authentication framework to be information-theoretic secure for authenticating a polynomial number of messages in terms of $n$. Based on this theorem, we propose an authentication protocol that can guarantee the security requirements, and prove its authentication rate can approach infinity when $n$ goes to infinity. Furthermore, we design and implement an efficient and feasible authentication protocol over binary symmetric wiretap channel (BSWC) by using \emph{Linear Feedback Shifting Register} based (LFSR-based) hash functions and strong secure polar code. Through extensive experiments, it is demonstrated that the proposed protocol can achieve low time cost, high authentication rate, and low authentication error rate.