安全列表译码及其在位串承诺中的应用
Secure list decoding and its application to bit-string commitment
AI总结：
本文提出安全列表译码概念，给出含消息速率、列表大小速率和疑义率的容量区域，并证明其结合哈希函数可实现传统位串承诺。
摘要：
我们提出了一个与位串承诺相关的安全列表译码新概念。传统列表译码只要求列表包含所传输的消息，而安全列表译码作为位串承诺的一种改进形式，还需要满足以下附加安全条件。第一个附加安全条件是接收方对所传输消息的不确定性；即使所传输消息包含在列表中，该条件也强于无法正确译码。另一个附加安全条件是发送方不可能估计译码列表中除所传输消息之外的另一个元素。第一个条件通过疑义率来评估。其渐近性质由三个参数评估，即消息速率、列表大小速率和疑义率。我们推导了该问题的容量区域。我们表明，哈希函数与安全列表译码的结合可产生传统的位串承诺。即使输入和输出系统是包括连续系统在内的一般概率空间，我们的结果仍然成立。当输入系统为一般概率空间时，我们以不同方式形式化了诚实发送方和不诚实发送方的能力。
英文摘要：
We propose a new concept of secure list decoding, which is related to bit-string commitment. While the conventional list decoding requires that the list contains the transmitted message, secure list decoding requires the following additional security conditions to work as a modification of bit-string commitment. The first additional security condition is the receiver's uncertainty for the transmitted message, which is stronger than the impossibility of the correct decoding, even though the transmitted message is contained in the list. The other additional security condition is the impossibility for the sender to estimate another element of the decoded list except for the transmitted message. The first condition is evaluated by the equivocation rate. The asymptotic property is evaluated by three parameters, the rates of the message and list sizes, and the equivocation rate. We derive the capacity region of this problem. We show that the combination of hash function and secure list decoding yields the conventional bit-string commitment. Our results hold even when the input and output systems are general probability spaces including continuous systems. When the input system is a general probability space, we formulate the abilities of the honest sender and the dishonest sender in a different way.
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