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open IN, $infile or die "Can't open input file: $!";

my %set;
my $substit = "";
...
        while $set{$randchar}++;
    $substit .= $randchar;
}

my @alpha = split //, "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

my @crypt = @alpha;
fisher_yates_shuffle(\@crypt);

my $substit = join '', @crypt;

sub fisher_yates_shuffle {
    my $array = shift;
...
    }
    return join '', @$array;
}

Benchmark: timing 5000 iterations of orig, f_yates, hash...
      orig: 33 secs (23.60 usr  0.00 sys = 23.60 cpu)
   f_yates:  5 secs ( 2.88 usr  0.00 sys =  2.88 cpu)
      hash: 13 secs ( 5.68 usr  0.00 sys =  5.68 cpu)