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IEEE Transactions on Information Forensics and Security

Wiretap Channels With One-Time State Information: Strong Secrecy

Te Sun Han, Hiroyuki Endo, Masahide Sasaki

Published Aug 28, 2017• 4 citations
Publisher

Abstract

The coding problem for wiretap channels with causal state information available at the encoder is studied. In particular, we address the wiretap channel only with one-time state information (instead of the usual causal state information up to present) in the sense that the one-time encoder uses only the current state information Sk at each time k to establish the secrecy capacity formula under the δ-strong secrecy criterion. The coding problem for wiretap channels with one-time channel state information available at the encoder under cost constraints is also studied and lower bounds on the “δ-strong” secrecy capacity given cost are also demonstrated.

DOI
10.1109/tifs.2017.2746008

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The coding problem for wiretap channels with causal state information available at the encoder is studied. In particular, we address the wiretap channel only with one-time state information (instead of the usual causal state information up to present) in the sense that the one-time encoder uses only the current state information Sk at each time k to establish the secrecy capacity formula under the δ-strong secrecy criterion. The coding problem for wiretap channels with one-time channel state information available at the encoder under cost constraints is also studied and lower bounds on the “δ-strong” secrecy capacity given cost are also demonstrated.
The coding problem for wiretap channels with causal channel state information available at the encoder and/or the decoder is studied under the strong secrecy criterion. This problem consists of two aspects: one is due to wiretap channel coding and the other is due to one-time pad cipher based on the secret key agreement between Alice and Bob using the channel state information. These two aspects are closely related to each other and give rise to an intriguing tradeoff between exploiting the state to boost secret-message rates versus extracting cryptographic key to improve secrecy capabilities. This issue has yet to be understood how to optimally reconcile the two. We newly devised the “iterative” forward-backward coding scheme, combining wiretap channel coding and secret-key-agreement-based one-time pad cipher. We then established reasonable lower bounds of the secrecy capacity for wiretap channels with causal channel state information available only at the encoder (Theorem 1), which can be easily extended to general cases with various kinds of correlated channel state information at the encoder (Alice), decoder (Bob), and wiretapper (Eve). In particular, for degraded wiretap channels, we give the secret-message (secret-key) capacity bounds (Theorems 2, 4, and 5).
A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key, which is used to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and decoder is established and is shown to coincide with the lower bound for several classes of wiretap channels with state.
A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key, which is used to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and decoder is established and is shown to coincide with the lower bound for several classes of wiretap channels with state.
A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and the decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and the decoder is established and is shown to coincide with the aforementioned lower bound for several classes of wiretap channels with state.
In this paper, the wiretap channel with side information studied in [2] is revisited for the case in which the side information is available only at the encoder and in a strictly causal manner. We derive a lower bound on the secrecy capacity of the channel based on a coding scheme which consists of block Markov encoding and key generation using the strictly causal state information available at the encoder. In order to provide the secrecy of messages, at the end of each block a description of the state sequence obtained by the encoder is used to generate the key which encrypts the whole or part of the message to be transmitted in the next block. Moreover, for the decoder to be able to decrypt the messages, the description of the sate sequence of each block is sent in common with the message of that block. Also, an upper bound on the secrecy capacity is developed which assumes that the state is noncausally known at the encoder and we prove that it would coincide the lower bound for a special case and results in the secrecy capacity.
We derive a lower bound on the secrecy capacity of the compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. and thus establishing a full coding theorem in this case. We achieve this with a quite strong secrecy criterion and with a decoder that is robust against the effect of randomisation in the encoding. This relieves us from the need of decoding the randomisation parameter which is in general not possible within this model. Moreover we prove a lower bound and a multi-letter converse to the secrecy capacity of the compound wiretap channel without channel state information.