"Whose" is the possessive of the relative "which". See Wikipedia: English possessive, in particular:

The following sentences illustrate the uses of whose:

• ...
• As the possessive of relative which (again, normally only as determiner): It is an idea whose time has come (alternatively ...of which the time has come).

See also this discussion on English Stack Exchange, whose(!) answers unanimously support this and link to further sources.

Suggestion: Add Whose as an alias for Which. (Long-term you might want to deprecate Which, but I don't really care about that, I just want to use Whose.)