Conditional disclosure of secrets (CDS) is the problem of disclosing as efficiently as possible, one secret from Alice and Bob to Carol if and only if the inputs at Alice and Bob satisfy some function $f$. The information theoretic capacity of CDS is the maximum number of bits of the secret that can be securely disclosed per bit of total communication. All CDS instances, where the capacity is the highest and is equal to $1/2$, are recently characterized through a noise and signal alignment approach and are described using a graph representation of the function $f$. In this work, we go beyond the best case scenarios and further develop the alignment approach to characterize the linear capacity of a class of CDS instances to be $(\rho-1)/(2\rho)$, where $\rho$ is a covering parameter of the graph representation of $f$.

中文翻译：

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论有条件泄密的线性容量

有条件的秘密公开 (CDS) 是尽可能有效地公开从 Alice 和 Bob 到 Carol 的秘密的问题，当且仅当 Alice 和 Bob 的输入满足某个函数 $f$ 时。CDS 的信息理论容量是总通信中每比特可以安全披露的秘密的最大比特数。所有 CDS 实例，其中容量最高且等于 $1/2$，最近通过噪声和信号对齐方法进行表征，并使用函数 $f$ 的图形表示进行描述。在这项工作中，我们超越了最佳情况，并进一步开发了对齐方法来将一类 CDS 实例的线性容量表征为 $(\rho-1)/(2\rho)$，其中 $\rho$是 $f$ 图形表示的覆盖参数。