Okay. When reason fails, how's about a little empirical evidence?

#! perl -slw
use strict;
use Math::Random::MT qw[ rand srand ];

$|++;
my @c = ( 'A'..'Z', 'a'..'z', 0..9 );

for my $run  ( 1 .. 1e6 ) {
    my %seen; keys %seen = 1e6;
    printf "\rrun: $run";
    for my $id ( 1 .. 1e6 ) {
        srand( $run + $id );
        my $ID = join '', map $c[ int rand( 62 ) ], 1 .. 25;
        warn "Dup $ID at $run/$id" if exists $seen{ $ID };
        undef $seen{ $ID };
    }
}

__END__

C:\test>"IDrand(62)x25.pl"
run: 254
[download]

That console log is a snapshot. After generating 254 sets of 1 million 25-char keys, with each key being generated at a new seed position, NO DUPS SEEN!

How long will it need to run before you are convinced that the OP is safe to use this?

How long will it need to run before you are convinced that the OP is safe to use this?

Did I ever claim otherwise?

All I've been claiming is that if you're seeding a deterministic random number generator with k bits, you will not be getting more than 2^k sequences, and that I've seen no evidence whatsoever that you can pull more out of thin air.

After generating 254 sets of 1 million 25-char keys, with each key being generated at a new seed position, NO DUPS SEEN!

254 sets of 1 million keys? Call me confused, but:

for my $run  ( 1 .. 1e6 ) {
    ...
    for my $id ( 1 .. 1e6 ) {
        srand ( $run + $id );
        ...
    }
}
[download]

Aren't you generating a million sets of a million keys each? But with only 2 million different keys, as $run + $id ranges from 2 .. 2e6.

But never mind that. I've never questioned that picking a different seed is very likely to give you a different key. My claim is, that if you have only 2³² different seeds you will not get more than 2³² keys this way. You exercise showed that if you pick a million different seeds, you get a million different keys. And you repeated that experiment a million times, each time removing a single seed from the set of a million, and adding another one.

More to your satisfaction?

#! perl -slw
use strict;
use Math::Random::MT qw[ rand srand ];

$|++;
my @c = ( 'A'..'Z', 'a'..'z', 0..9 );

for my $run  ( 1 .. 1e6 ) {
    my %seen; keys %seen = 1e6;
    printf "\rrun: $run";
    for my $id ( 1 .. 1e5 ) {
        srand( $run * $id );
        for( 1 .. 10 ) {
            my $ID = join '', map $c[ int rand( 62 ) ], 1 .. 25;
            warn "Dup $ID at $run/$id" if exists $seen{ $ID };
            undef $seen{ $ID };
        }
    }
}

__END__
C:\test>"IDrand(62)x25.pl"
run: 54
[download]

---

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

The start of some sanity?