my %myhash = (
  key1 => { map {$_ => 1} qw(abd bcd cde def efg) },
  key2 => { map {$_ => 1} qw(abd def} },
  key3 => { map {$_ => 1} qw(efg cde tgh) },
);

##</code><code>##

my @winners = grep $myhash{$_}{efg}, keys %myhash;

##</code><code>##

my %inside_out;
for my $first_key (keys %myhash) {
  for my $second_key (keys %{$myhash{$first_key}}) {
    $inside_out{$second_key}{$first_key} = 1;
  }
}
for my $second_key (keys %inside_out) {
  print "$second_key => ",
    join(", ", sort keys %{$inside_out{$second_key}}), "\n";
}