Using jethro/tye's interpretation of your description:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];
use Algorithm::Combinatorics qw[ combinations ];

my @lines = map [ do{ chomp; split ',' } ], <DATA>;
my $w = $#{ $lines[0] };

my @keyFields;

WIDTH: for my $k ( 1 .. $w ) {
    my $iter = combinations( [ 0 .. $w ], $k );
    COMB: while( my $c = $iter->next ) {
        my %uniq;
        for my $a ( @lines ) {
            next COMB if exists $uniq{ join ',', @{ $a }[ @$c ] };
            $uniq{ join ',', @{ $a }[ @$c ] } = 1;
        }
        @keyFields = @$c;
        last WIDTH;
    }
}

print "All lines are unique using a combination of fields:[ @keyFields
+ ]";

__DATA__
2,6,5,2,1,1,7,9,8,6
5,8,5,0,9,3,8,9,0,2
2,3,1,1,5,2,9,7,8,3
0,1,3,7,6,2,4,3,7,5
4,6,2,8,6,4,1,5,4,3
4,6,7,2,0,9,6,5,0,9
5,6,2,4,3,7,1,9,3,5
2,5,7,1,0,0,0,5,8,5
3,8,1,4,9,2,5,8,1,0
5,2,2,2,0,7,2,8,3,1
7,1,2,6,5,4,0,9,2,5
1,6,3,7,3,8,7,0,7,7
0,0,8,9,9,8,3,3,6,0
0,2,5,3,8,4,1,8,9,4
5,6,9,0,6,4,9,5,0,7
9,0,9,3,2,6,3,2,4,6
3,3,0,4,8,5,7,7,2,4
3,1,3,0,0,3,1,7,3,8
0,6,7,0,8,9,4,8,4,8
0,2,0,3,7,4,6,8,4,5
[download]

Output:

c:\test>896650-2
All lines are unique using a combination of fields:[ 3 6 ]
[download]

On a randomly generated dataset of the scale you've suggested, it takes around 30 seconds to complete:

[19:42:44.71] c:\test>head -2 896650.dat
357,67,815,493,516,302,810,899,672,91,542,795,527,429,217,502,811,554,
+345,312,689,336,710,194,778,869,711,413,402,313,960,351,264,511,558,3
+01,184,414,955,528,44,839,786,363,629,599,611,623,488,534,948,140,489
+,474,511,662,217,665,58,930,879,683,764,203,863,384,509,5,612,903,0,3
+82,969,240,130,460,652,474,478,562,7,117,360,688,702,657,329,626,521,
+808,547,477,903,510,913,883,398,201,375,729
675,393,313,605,265,95,415,813,667,95,945,188,2,646,803,534,842,589,29
+9,934,395,429,34,733,684,412,799,463,896,130,896,505,530,669,793,750,
+527,865,514,55,25,659,668,780,892,119,532,163,707,132,85,841,327,314,
+408,284,714,166,344,425,165,998,843,272,612,671,873,772,134,665,331,7
+26,356,522,838,22,875,191,835,965,373,304,885,7,586,908,588,623,764,7
+02,4,656,794,289,18,872,639,495,513,35

[19:54:27.66] c:\test>wc -l 896650.dat
  10000 896650.dat

[19:54:40.64] c:\test>896650-2 896650.dat
All lines are unique using a combination of fields:[ 0 1 2 ]

[19:55:10.04] c:\test>
[download]