Ooh, another constraint; that helps. :) If false positives aren't an issue perhaps a Bloom filter (see also Bloom::Filter)?

But zipping purely random data this short probably isn't going to be worthwhile (I get the compressed version being around 115% of the input; the more regularity within individual keys the better performance you'll get though so take that as a worst case upper bound).

use IO::Compress::Gzip qw(gzip);
use constant NUM_REPS => 100;

my $num_reps = shift || NUM_REPS();

print "Trying ", $num_reps, " random strings\n";

my %lengths;
for ( 1 .. $num_reps ) {
    my $in
        = join( "", map { chr( int rand(256) ) } 0 .. ( rand(100) + 10
+0 ) );
    gzip \$in => \$out;

    my ( $li, $lo ) = map length, ( $in, $out );

    $lengths{$lo}++;
    $pct = $lo / $li * 100.0;
    $avg += $pct;

    printf "%d\t=>\t%d\t%4.3f%%\n", $li, $lo, $pct if $ENV{SHOW};
}

printf "avg size after compression: %4.3f%%\n", $avg / $num_reps;

if ( $ENV{SHOW_HIST} ) {
    print "Length distribution\n";
    for my $len ( sort { $a <=> $b } keys %lengths ) {
        print "$len\t$lengths{ $len }\n";
    }
}

exit 0;

__END__
$ perl comptest 5000
Trying 5000 random strings
avg size after compression: 115.864%
$ SHOW=1 perl comptest 5
Trying 5 random strings
104     =>      127     122.115%
173     =>      196     113.295%
171     =>      194     113.450%
145     =>      168     115.862%
190     =>      213     112.105%
avg size after compression: 115.366%
[download]