Multi-message Authentication over Noisy Channel with Polar Codes

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., ε-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. Based on this theorem, we propose and implement an efficient and feasible authentication protocol over binary symmetric wiretap channel (BSWC) by using 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.