The Wiretap Channel with Feedback: Encryption over the Channel
7002 rpA 81 ]TI.sc[ 1v9522.4070:viXra 1 The Wiretap Channel with Feedback: Encryption over the Channel Lifeng Lai, Hesham El Gamal and H.
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The Wiretap Channel with Feedback:
Encryption over the Channel
Lifeng Lai, Hesham El Gamal and H. Vincent Poor
Abstract
In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap
channel is established. Unlike previous works, where a noiseless public discussion channel is used for
feedback, the feed-forward and feedback signals share the same noisy channel in the present model.
Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting.
More specifically, the discrete memoryless modulo-additive channel with a full-duplex destination node
is considered first, and it is shown that the judicious use of feedback increases the perfect secrecy
capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the
achievability scheme, the feedback signal corresponds to a private key, known only to the destination.
In the half-duplex scheme, a novel feedback technique that always achieves a positive perfect secrecy
rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is
proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the
destination to perform encryption over the channel without revealing its key to the source. Finally, this
Λ
scheme is extended to the continuous real valued modulo- channel where it is shown that the perfect
secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper.
I. INTRODUCTION
The study of secure communication from an information theoretic perspective was pioneered
by Shannon [1]. In Shannon’s model, both the sender and the destination possess a common secret
key K, which is unknown to the wiretapper, and use this key to encrypt and decrypt the message
Lifeng Lai (llai@princeton.edu) was with the Department of Electrical and Computer Engineering at the Ohio State University,
he is now is with the Department of Electrical Engineering at Princeton University. Hesham El Gamal (helgamal@ece.osu.edu) is
with the Department of Electrical and Computer Engineering at the Ohio State University. H. Vincent Poor (poor@princeton.edu)
is with the Department of Electrical Engineering at Princeton University. This research was supported by the National Science
Foundation under Grants ANI-03-38807 and CNS-06-25637.
DRAFT
2
M. Shannon considered a scenario where both the legitimate receiver and the wiretapper have
direct access to the transmitted signal and introduced the perfect secrecy condition I(M; Z) = 0,
implying that the signal Z received by the wiretapper does not provide any additional information
about the source message M. Under this model, he proved the pessimistic result that the
achievability of perfect secrecy requires the entropy of the shared private key K to be at least
equal to the entropy of the message itself (i.e., H(K) ≥ H(M) for perfect secrec
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"excerpt": "##PAGE:1##\n7002\nrpA\n81\n]TI.sc[\n1v9522.4070:viXra\n1\nThe Wiretap Channel with Feedback:\nEncryption over the Channel\nLifeng Lai, Hesham El Gamal and H. Vincent Poor\nAbstract\nIn this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap\nchannel is established. Unlike previous works, where a noiseless public discussion channel is used for\nfeedback, the feed-forward and feedback signals share the same noisy channel in the present model.\nQuite interestingly, this no…"
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