Secure list decoding and its application to bit-string commitment

TL;DR

This paper introduces secure list decoding, a novel concept that enhances bit-string commitment by ensuring receiver uncertainty and sender's inability to estimate other list elements, with a derived capacity region.

Contribution

It proposes the concept of secure list decoding, derives its capacity region, and demonstrates its application to bit-string commitment with general probability spaces.

Findings

Defined secure list decoding with new security conditions

Derived the capacity region for secure list decoding

Showed how to combine hash functions with secure list decoding for bit-string commitment

Abstract

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.