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We propose a new concept of secure list decoding, which is related tobit-string commitment. While the conventional list decoding requires that thelist contains the transmitted message, secure list decoding requires thefollowing additional security conditions to work as a modification ofbit-string commitment. The first additional security condition is thereceiver's uncertainty for the transmitted message, which is stronger than theimpossibility of the correct decoding, even though the transmitted message iscontained in the list. The other additional security condition is theimpossibility for the sender to estimate another element of the decoded listexcept for the transmitted message. The first condition is evaluated by theequivocation rate. The asymptotic property is evaluated by three parameters,the rates of the message and list sizes, and the equivocation rate. We derivethe capacity region of this problem. We show that the combination of hashfunction and secure list decoding yields the conventional bit-stringcommitment. Our results hold even when the input and output systems are generalprobability spaces including continuous systems. When the input system is ageneral probability space, we formulate the abilities of the honest sender andthe dishonest sender in a different way.

Secure list decoding and its application to bit-string commitment