If we have two commitment schemes Com1 and Com2, which are possibly defective (in the sense of not satisfying hiding or binding properties), is it possible to construct a commitment scheme which does satisfy those properties?
Specifically, in the following scenarios:
Both Com1 and Com2 satisfy the hiding property, and one of them satisfies the binding property (but you do not know which). In this case, I think that we could construct a commitment scheme by letting Com(m,s) = Com1(m,s)||Com2(m,s), but I am not sure if I am right or not.
Both Com1 and Com2 satisfy the binding property, and one of them satisfies the hiding property (but you do not know which). In this case I do not think we could create a good commitment scheme. Suppose that Com1 is the scheme which does not satisfy the hiding property- we cannot be sure to avoid using Com1 in our construction since we do not know which of the two schemes satisfies the hiding property, and using Com1 in our construction in any way would seem to preclude our construction from satisfying the hiding property as well, unless I am mistaken?
Any help would be greatly appreciated, thank you!