A Commitment Scheme with Output Locality-3 Fit for the IoT Device

Low output locality is a property of functions, in which every output bit depends on a small number of input bits. In IoT devices with only a fragile CPU, it is important for many IoT devices to cooperate to execute a single function. In such IoT’s collaborative work, a feature of low output locality is very useful. This is why it is desirable to reconstruct cryptographic primitives with low output locality. However, until now, commitment with a constant low output locality has been constructed by using strong randomness extractors from a nonconstant-output-locality collision-resistant hash function. In this paper, we construct a commitment scheme with output locality-3 from a constant-output-locality collision-resistant hash function for the first time. We prove the computational hiding property of our commitment by the decisional M , δ -bSVP assumption and prove the computational binding property by the M , δ -bSVP assumption, respectively. Furthermore, we prove that the M , δ -bSVP assumption can be reduced to the decisional M , δ -bSVP assumption. We also give a parameter suggestion for our commitment scheme with the 128 bit security.