Secret Sharing LDPC Codes for the BPSK-constrained Gaussian Wiretap Channel

Details Secret Sharing LDPC Codes for the BPSK-constrained Gaussian Wiretap Channel Secret Sharing LDPC Codes for the BPSK-constrained Gaussian Wiretap Channel

2010-09-15

arxiv.org/abs/1009.3041v3

Computer Science

Information Theory

submitted to IEEE Trans. on Information Forensics and Security, special issues on using the physical layer for securing the ne

Scientific paper

The problem of secret sharing over the Gaussian wiretap channel is considered. A source and a destination intend to share secret information over a Gaussian channel in the presence of a wiretapper who observes the transmission through another Gaussian channel. Two constraints are imposed on the source-to-destination channel; namely, the source can transmit only binary phase shift keyed (BPSK) symbols, and symbol-by-symbol hard-decision quantization is applied to the received symbols of the destination. An error-free public channel is also available for the source and destination to exchange messages in order to help the secret sharing process. The wiretapper can perfectly observe all messages in the public channel. It is shown that a secret sharing scheme that employs a random ensemble of regular low density parity check (LDPC) codes can achieve the key capacity of the BPSK-constrained Gaussian wiretap channel asymptotically with increasing block length. To accommodate practical constraints of finite block length and limited decoding complexity, fixed irregular LDPC codes are also designed to replace the regular LDPC code ensemble in the proposed secret sharing scheme.

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