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

The notion of commitment is one of the most important primitives in cryptography. To meet various needs, there have been many kinds of commitment schemes among which non-malleable commitment scheme and selective decommitment scheme are important and in general use. And, the increasing security demands suggest a closer look at the relationship between the two schemes. For the convenience of our proof, a new definition for selective decommitment scheme is proposed, which is named as modified selective decommitment scheme. The security relation is deduced that a non-malleable commitment scheme implies a modified selective decommitment scheme, but the reverse is not true.