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In this paper, the authors study cyclic shift symmetric wiretap channels in which the channels between Alice and Bob and Alice and Eve are both cyclic shift symmetric. They characterize the rate-equivocation region by determining the optimal selection of rate splitting U and channel prefixing V for these channels. They show that optimal U and V are determined via cyclic shifts of the solution of an auxiliary optimization problem that involves only one auxiliary random variable. They find the cardinality bound on the necessary auxiliary variable and formulate the problem as a constrained optimization problem. They determine the optimality conditions for the binary-input cyclic shift symmetric wiretap channels.
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