We further study the keyless authentication problem in a noisy model in our previous work, where no secret setup is available for sender Alice and receiver Bob while there is discrete memoryless channel (DMC) W1 from Alice to Bob and a two-way noiseless but insecure channel between them. We propose a construction such that the message length over DMC W1 does not depend on the size of the source space. If the source space is S and the number of channel W1 uses is n, then our protocol only has a round complexity of log* |S| - log* n + 4. In addition, we show that the round complexity of any secure protocol in our model is lower bounded by log* |S| - log* n - 5. We also obtain a lower bound on the success probability when the message size on DMC W1 is given. Finally, we derive the capacity for a noninteractive authentication protocol under general DMCs, which extends the result under Binary Symmetric Channels in our previous work.
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.
Keyless authentication is considered in an adversarial point-to-point channel. Namely, a legitimate transmitter and receiver aim to communicate over a noisy channel that may or may not also contain an active adversary, capable of transmitting an arbitrary signal into the channel. If the adversary is not present, then the receiver must successfully decode the message with high probability; if it is present, then the receiver must either decode the message or detect the adversary's presence. Thus, whenever the receiver decodes, it can be certain that the decoded message is authentic. The exact authentication capacity is characterized for discrete-memoryless adversary channels, where the adversary is assumed to know the code but not the message. The authentication capacity is shown to be either zero or equal to the no-adversary capacity, depending on whether the channel satisfies a condition termed overwritability.
We consider the problem of keyless message authentication over noisy channels in the presence of an active adversary. Different from the existing models, in our model, the legitimate users do not have any pre-shared key for authentication. Instead, we use the noisy channel connecting the legitimate users for authentication. The main idea is to utilize the noisy channel connecting the legitimate users to distinguish a legitimate message from a fake message, by generating an output at the receiver that is difficult for the adversary to replicate through its noisy channel. By interpreting the message authentication as a hypothesis testing problem, we investigate the authentication exponent and the authenticated channel capacity of the noisy channel. In the authentication exponent problem, for a given message rate, we investigate the speed at which the optimal successful attack probability can be driven to zero. We fully characterize the authentication exponent for the zero-rate message case and provide both an upper bound and a lower bound on the exponent for the non-zero message rate case. In the authenticated capacity problem, we study the largest data transmission rate under which the attacker's optimal successful attack probability can still be made arbitrarily small. We establish an all or nothing result. In particular, we show that the authenticated channel capacity is the same as the classic channel capacity if a simulatability condition is not satisfied, while the authenticated capacity will be zero if this condition is satisfied. We also provide efficient algorithms to check this condition. We further show that our results are robust to modeling uncertainties about the eavesdropper's channels.
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, we investigate multi-message authentication to combat adversaries with infinite computational capacity. An authentication framework over a wiretap channel
(W1,W2) 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
(W1,W2) 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
Xn by leveraging an existing strongly secure channel coding with exponentially small (in code length
n) average probability of error; finally, Alice sends
Xn over
(W1,W2) 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.