Identification via wiretap channels

Abstract

The wiretap channel can be viewed as a probabilistic model for cryptography. The channel has two outputs. One is for the legitimate receiver and the other is for the wiretapper. The goal of communication is to send messages to the legitimate receiver while the wiretapper must be kept ignorant. A wiretap channel is a quintuple (X,W(y|x),V(x|x),Y,Z), where X is the input alphabet, Y is the output alphabet for the legitimate receiver, Z is the output alphabet for the wiretapper, W(y|x) is the channel transition matrix, whose output is available to the legitimate receiver, and V(x|x) is the channel transition matrix, whose output is available to the wiretapper. The channel is assumed to be memoryless. In the classical transmission problem, an (n,M,/spl epsi/)-code for the wiretap channel is defined as a system {(c/sub i/,D/sub i/)|1/spl les/i/spl les/M}, where, for all i,c/sub i//spl isin/X/sup n/ are the codewords and D/sub i//spl sub/y/sup n/ are the disjoint decoding sets. It is required that for any i /spl lambda//sub i/=/sup def/W/sup n/(D/sub i//sup c/|c/sub i/)/spl les//spl epsi/, and if X/sup n/ has uniform distribution over {c/sub i/|/spl les/i/spl les/M}, then 1/nI(X/sup n/;Z/sup n/)/spl les//spl epsi/. The secret capacity of the wiretap channel is defined as the maximum rate of any code which satisfies these conditions. Formally, let M(n,/spl epsi/)=max{M:/spl exist/a(n,M,/spl epsi/) code}, then the secret capacity of the wiretap channel is defined as C/sub s/=max{R:/spl forall//spl epsi/>0,/spl exist/n such that M(n,C)/spl ges//sup nR/. The secret capacity of the wiretap channel can then be determined. The problem of identification via this channel is then formulated.<>