Relationship Between a Non-Malleable Commitment Scheme and a Modified Selective Decommitment Scheme

The notion of commitment is one of the most important primitives incryptography. To meet various needs, there have been many kinds ofcommitment schemes among which non-malleable commitment scheme andselective decommitment scheme are important and in general use.And, the increasing security demands suggest a closer look at the relationshipbetween the two schemes. For the convenience of our proof, a newdefinition for selective decommitment scheme is proposed, which is named asmodified selective decommitment scheme. The security relation isdeduced that a non-malleable commitment scheme implies a modifiedselective decommitment scheme, but the reverse is not true.