Nested Polar Codes for Wiretap and Relay Channels

Abstract

We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding scheme also achieves the capacity of the physically degraded receiver-orthogonal relay channel. We show simulation results for moderate block length for the binary erasure wiretap channel, comparing polar codes and two edge type LDPC codes.© 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.QC 2011011

Wiretap codes for secure multi-party computation

“…While in this paper we have only considered the case of passive eavesdropping, the proposed framework can also be applied in cases where clients tamper with the data given that the effect of such attacks can be modelled in the design of the underlying wiretap codes. This can be achieved by adopting, e.g., polar code designs (see, e.g., [6]- [8]) to the resulting wiretap channel model. However, in contrast to the scheme proposed in this paper, this approach would not provide perfect secrecy for finite block length.…”

“…For k 0 = e B , reliability follows immediately from the MDS (maximumdistance separable) property of the fine code C 0 . Furthermore, from Lemma IV.1 in [6] we know that…”

“…Since our secret sharing scheme is constructed from linear codes it may also be extended to other attacker models where clients tamper with the secret shares of other clients. This can be achieved by adopting, e.g., polar code designs (see, e.g., [6]- [8]) to the resulting wiretap channel model. However, for finite block length, this approach would not be able to guarantee perfect secrecy.…”

Polar codes for bidirectional broadcast channels with common and confidential messages

“…Let W 1 and W 2 be two symmetric binary input memoryless channels, and let W 2 be degraded with respect to W 1 . Denote the polarized channels as defined in (1) The following result for degraded wiretap channels [19] was shown in [13][14][15][16]:…”

“…Polar codes were introduced by Arıkan and were shown to be capacity achieving for a large class of channels in [9,10]. They have been further studied for a large range of multi-user channels in [11][12][13][14][15][16][17].…”