Cryptography Reference
In-Depth Information
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1 4302211000000000100000000000011908534083343
1 04010030000000000100001000000 8634527510415
3121400000000000000000000000001 2074798658290
3 22101000000000000000000100002 6985303737832
1 31110010010000000000021000000 8812005166391
1 00000000100000000010001110001 7292473383297
1 60020100000000001100010000000 8473728166773
0 21120000010000000110100000000 8251324123939
7 1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 3321518619199
2 0210000010110000000000010001016344515442851
1 0020201200100000000000000010013111148356376
4 1301000100000000000000100100116601326113336
7 10001000000040000000001000000 1456434246950
5 41101100011000000000100000000 404027629520
3 1100000020000000000100003000013065668932751
0 51010010000010000011000000010 7525531865225
5 30110001000000000000000011010 4001162293292
0 20001020311000000000000000000 3842569352563
0 80310010000000000000100010000 964914952665
10 2040010000010000000010000000017035585297150
1 0001000121000002000010000000014458766030584
0 2012000000030000000000000000114476141439409
7 8002000010000000010000000000011647353909720
2 30211001000001001000000000100 9788123357331
1 0040001000000000001000100101011629589763307
3 0000000210010000000000000010213159446123783
4 60100211000000000000001000000 182566550689
1 10001201000020002000000000000 3247086793907
5 2310100000000000000300000000015800049899526
2 02101200000000001000001000100 9854413260328
8 01200000100000000100000010100 4381398209006
0 50001110000000000000010000110 1390250884705
5 1000101300010000000000000001015629049208190
0 01001110100100000000001000001 6147525811383
1 0200010000100200100000000000116120430259376
2 10010000101000010010100000001 5390342243078
0 64002100000000000000000000001 290365350528
1 0023000000000010000000010100011847489523301
1 5210001000000000000002000001015363122732369
7 1000030000001001000000000000116451950295874
Discrete logs of the factor base primes:
[7426253006290, 4492127725870, 11192451597521, 17081013481576, 15896098548408,
8053973676115, 14246651143093, 4166997212594, 8724619318636,4 469420019618,
5773327701243, 11127950744169, 7948673165404, 8646993757009, 1650773234392,
12735188425689, 10375910229785, 7580738887351, 8423060253370, 12616673387636,
4883524291858, 16066730563529, 15730446834125, 6016972182391, 10817894383613,
15892873589102, 2696216508825, 9069388948579, 14060808948759, 1891579519393]
These data may be interpreted as follows. The rows of the matrix contain the
relations that will serve to compute the discrete logarithms of the 30 primes in the
factor base. For example, the third row just means that:
g
2074798658290
mod
p
2
3
3
12
7
4
=
·
·
·
·
5
113
We may use Maple's
ifactor
to check that this is indeed the case:
> ifactor(Power(g, 2074798658290) mod p);
(2)ˆ3 (3)ˆ12 (5) (7)ˆ4 (113)
