my %original = ( a => 1, b => 2, c => 3, d => 4);
my %subset = (e => 2, f => 4);

# Doing a thing if keys are shared (or not, just invert)
for $key (keys %original) {
    if( exists $subset{$key} ) {
        # shared key, do something
        ...
        if( $subset{$key} == $original{$key} ) {
            # shared key and value, do something
            ...
        }
    }
}

# Doing a thing if values are shared
%original_values = reverse( %original )
%subset_values = reverse( %subset )
# now repeat the above loop, except note that if values aren't unique you will get a random key for it which might not match the random one chosen from the other hash and I don't know if that's important to you.

# there are other solutions but I think this one spells it out most clearly.