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arXiv:1708.02888

Multi-message Authentication over Noisy Channel with Secure Channel Codes

Dajiang Chen, Ning Zhang, Nan Cheng, Kuan Zhang, Kan Yang, Zhiguang Qin, Xuemin Shen

Published Aug 9, 2017• 2 citations
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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.

DOI
10.48550/arxiv.1708.02888

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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.
Message authentication is an interactive procedure that allows a legitimate sender Alice to send and authenticate a message M to a legitimate receiver Bob. To prevent the attacks from an adversary Eve, Alice and Bob usually share a secret key K. In this paper, we study a novel authentication framework as follows. Firstly, Alice sends a message M to Bob over a noiseless channel; Secondly, Alice generates an authentication tag with the message M and secret key K; Thirdly, Alice encodes the tag into a codeword Xn; Finally, Alice transmits the codeword Xn to Bob over a wiretap channel. This paper defines an authentication channel capacity under a fixed tag rate, and show that it equals to H(X|Z). Specifically, we prove that the authentication protocol proposed in Ref. [15] is capacity-achievable under our authentication model.
In this paper, a novel message authentication model using the same key over wiretap channel is proposed to achieveinformation-theoretic security. Specifically, in the proposed model, there is a discrete memoryless channelW1:X→Ybetween transmitter Alice and receiver Bob, while an attacker Oscar is connected with Alice via discrete memoryless channelW2:X→Z. Alice encodes messageMto codeword (S,Xn), using an encoding function with secret keyK. Then,Sis sent to Bob over a one-way noiseless channel (fully controlled by Oscar), andXnis sent over the wiretap channel, sayX→(Y,Z). Building on this model, a new message authentication scheme is proposed. The scheme incorporates a secure channel coding, which uses random coding techniques to detect man-in-the-middle (MITM) attacks. The authentication channel capacity is studied in a specific channel model whenW2is not less noisy thanW1. We theoretically demonstrate that the authentication channel capacity is much larger than the secrecy capacity, since Bob does not need to recover information transmitted over the noisy channel.
An approximate message authentication scheme is a primitive that allows a sender Alice to send a source state to a receiver Bob such that the latter is assured of its authenticity, where the source state is considered as authentic if it only undergoes a minor change. Here, the authors propose an efficient scheme for this problem and prove its security under a rigorous model. Our scheme only needs a lightweight computation cost and hence is very efficient. As the authentication message is transmitted over a noisy channel, we also value the channel efficiency (i.e. the coding rate). For a fixed coding method, this is determined by the admissible decoding bit error probability . A larger admits a shorter codeword length and hence a larger coding rate. It turns out that the can be set to be a significantly large constant (determined by the legal distortion level for the source state). Compared with existing schemes, the advantage in is evident.
We study a keyless authentication problem in a new noisy model, where there is a discrete memoryless channel (DMC) W1from sender Alice to receiver Bob and a DMC W2from adversary Oscar to Bob. In addition, there is an insecure noiseless channel between Alice and Bob. Under this model, we characterize the condition under which an authentication from Alice to Bob is possible. We also construct a secure authentication protocol that has an authentication rate approaching infinity. Finally, we prove that the authentication capacity of a noninteractive authentication over binary symmetric channels is exactly 1. This is an interesting result as Shannon capacity of channel W1is strictly less than 1 while the noiseless channel is completely unreliable.
This work establishes that the physical layer can be used to perform information-theoretic authentication in additive white Gaussian noise (AWGN) channels, as long as the adversary is not omniscient. The model considered consists of an encoder, decoder, and adversary, where the adversary knows the message given to the encoder, has a non-causal noisy observation of the encoder’s transmission and may use unlimited transmission power, while the decoder observes a noisy version of the sum of the encoder and adversary’s outputs. A method to modify a generic existing channel code to enable authentication is presented. This method relies on injecting message-dependent noise into the transmission and accepting the transmission as authentic only if the correct noise levels for the decoded message are observed. One drawback to this method is that the encoder must still transmit a low-power signal in the case where there is no message to send. It is shown that this modification costs an asymptotically negligible amount of the coding rate, while still enabling authentication as long as the adversary’s observation is not noiseless. Also notable is that this modification is not (asymptotically) a function of the statistical characterization of the adversary’s channel and no secret key is required. We believe these features will pave the way for a robust practical implementation. Using these results, the channel-authenticated capacity is calculated and shown to be equal to the non-adversarial channel capacity. As our results will show, information-theoretic authentication in AWGN channels is possible without the need for the legitimate party to have a model-based advantage over the adversary. While this modular scheme is designed for use in the given channel model, it is applicable to a wide range of settings.