OKlibrary  0.2.1.6
general.hpp
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00001 // Matthew Gwynne, 20.5.2011 (Swansea)
00002 /* Copyright 2011, 2012 Oliver Kullmann
00003 This file is part of the OKlibrary. OKlibrary is free software; you can redistribute
00004 it and/or modify it under the terms of the GNU General Public License as published by
00005 the Free Software Foundation and included in this library; either version 3 of the
00006 License, or any later version. */
00007 Statistics | tail -n 1 | awk " { print \$0 \" ${r} ${s}\"}";
00260   done;
00261 done) > MinisatStatistics
00262      \endverbatim
00263      yields:
00264      \verbatim
00265 shell> oklib --R
00266 E = read.table("MinisatStatistics", header=TRUE)
00267 EM = aggregate(E, by=list(r=E$r), FUN=mean)
00268 options(width=1000)
00269 EM
00270     r    rn     rc           t sat       cfs       dec    rts           r1    mem  ptime  stime        cfl  r    s
00271 1   1  2208  35032   0.1255304   1    644.65   9691.15   4.95     235999.5  10.20 0.0100 0.0300   253616.5  1 10.5
00272 2   2  4368  70000  64.0761374   1  86527.00 358122.40 232.90   82250162.0 146.60 0.0265 0.0700 27228151.5  2 10.5
00273 3   3  6528 104968  73.9325735   1  88100.35 391819.80 241.75  135857271.9 172.30 0.0370 0.1000 26539443.9  3 10.5
00274 4   4  8688 139936  69.7975275   1  76521.80 352603.30 214.65  165313324.8 148.70 0.0505 0.1400 22521359.4  4 10.5
00275 5   5 10848 174904 111.6020595   1  94419.95 430595.80 258.60  256887896.2 195.65 0.0615 0.1800 29326373.7  5 10.5
00276 6   6 13008 209872  74.4716495   1  69564.10 322544.65 204.10  246501658.7 144.85 0.0755 0.2165 19653209.9  6 10.5
00277 7   7 15168 244840  86.8148835   1  77963.80 355796.45 218.90  307490488.7 144.65 0.0885 0.2515 20624755.8  7 10.5
00278 8   8 17328 279808  85.5460900   1  68567.25 310390.85 196.45  357318016.1 136.40 0.1040 0.2900 19237972.4  8 10.5
00279 9   9 19488 314776  77.5300305   1  56471.85 290625.55 163.40  304380006.9 120.85 0.1145 0.3300 16053735.8  9 10.5
00280 10 10 21648 349744 162.2898200   1  88746.25 383298.85 247.80  614681215.0 175.95 0.1280 0.3695 24495250.8 10 10.5
00281 11 11 23808 384712 109.8185080   1  66805.35 295058.50 189.30  503117849.8 123.65 0.1420 0.4085 16640849.0 11 10.5
00282 12 12 25968 419680 109.7141555   1  65693.95 322263.30 192.65  469419385.0 141.95 0.1540 0.4465 18375349.1 12 10.5
00283 13 13 28128 454648 140.8818745   1  74352.10 343013.50 208.05  640736722.1 154.05 0.1660 0.4820 19538114.8 13 10.5
00284 14 14 30288 489616 206.5174700   1  96008.70 475130.45 268.45  814417288.8 221.90 0.1810 0.5215 30333239.5 14 10.5
00285 15 15 32448 524584 231.8048250   1 104810.30 524007.50 283.30  906787661.5 220.10 0.1945 0.5600 31768033.0 15 10.5
00286 16 16 34608 559552  96.1146805   1  44588.15 216541.40 135.20  500882406.6 109.35 0.2055 0.5995 11904817.9 16 10.5
00287 17 17 36768 594520 164.6938600   1  63736.70 275718.50 188.05  850615926.1 142.20 0.2180 0.6385 15086412.6 17 10.5
00288 18 18 38928 629488 210.0075000   1  83165.30 367437.35 233.00  996504673.4 188.20 0.2310 0.6760 23392940.8 18 10.5
00289 19 19 41088 664456 231.9556625   1  82912.30 426112.30 231.20 1038048860.1 193.05 0.2440 0.7130 23248806.1 19 10.5
00290 20 20 43248 699424 178.1621050   1  60341.95 287746.10 177.75  856706437.9 145.75 0.2575 0.7515 15743186.0 20 10.5
00291      \endverbatim
00292      </li>
00293     </ul>
00294    </li>
00295   </ul>
00296 
00297 
00298   \todo The 1-base box translation (bi-directional Mixcolumns)
00299   <ul>
00300    <li> The Sboxes and multiplications boxes are translated using the
00301    1-base translation, discussed in "The 1-base box translation"
00302    in
00303    plans/KeyDiscovery/016/2_1_8/Translations.hpp
00304    where statistics are also provided. </li>
00305    <li> There are currently active investigations attempting to find the
00306    minimum-size 1-base representations for each of the boxes, discussed in
00307     <ul>
00308      <li> AdvancedEncryptionStandard/plans/Representations/Sbox_8.hpp.
00309      </li>
00310      <li> AdvancedEncryptionStandard/plans/Representations/Mul_2_8.hpp.
00311      </li>
00312      <li> AdvancedEncryptionStandard/plans/Representations/Mul_3_8.hpp.
00313      </li>
00314     </ul>
00315    </li>
00316    <li> Over 20 rounds, with 20 random plaintext-ciphertext-pairs per round:
00317     <ul>
00318      <li> For instructions on generating the 1-bases, see
00319      "The 1-base box translation" in
00320      AdvancedEncryptionStandard/plans/KeyDiscovery/016/2_1_8/Translations.hpp.
00321      </li>
00322      <li> Generating the instances (in Maxima):
00323      \verbatim
00324 oklib_monitor : true$
00325 set_hm(ss_sbox_rbase_cnfs,8,read_fcl_f("AES_Sbox_base.cnf"))$
00326 set_hm(ss_field_rbase_cnfs,[8,2],read_fcl_f("AES_byte_field_mul_2_base.cnf"))$
00327 set_hm(ss_field_rbase_cnfs,[8,3],read_fcl_f("AES_byte_field_mul_3_base.cnf"))$
00328 for rounds : 1 thru 20 do
00329   output_ss_fcl_std(rounds, num_columns : 1, num_rows : 2, exp : 8, final_round_b : false, box_tran : aes_rbase_box, mc_tran : aes_mc_bidirectional)$
00330      \endverbatim
00331      </li>
00332      <li> Generating 20 random assignments for the plaintext and ciphertext,
00333      leaving the key unknown:
00334      \verbatim
00335 maxima> for seed : 1 thru 20 do output_ss_random_pc_pair(seed,rounds,num_columns,num_rows,exp,final_round_b);
00336      \endverbatim
00337      </li>
00338      <li> Running minisat-2.2.0:
00339      \verbatim
00340 shell> col=1; row=2; e=8;
00341 for r in $(seq 1 20); do
00342   for k in $(seq 1 20); do
00343       echo "Key ${k} Round ${r}";
00344       AppendDimacs-O3-DNDEBUG ssaes_r${r}_c${col}_rw${row}_e${e}_f0.cnf ssaes_pcpair_r${r}_c${col}_rw${row}_e${e}_f0_s${k}.cnf > r${r}_k${k}.cnf;
00345       minisat-2.2.0 r${r}_k${k}.cnf > minisat_r${r}_k${k}.result 2>&1;
00346   done;
00347 done
00348 shell> ExtractMinisat header-only | awk ' { print $0 " r k" }' > minisat_results;
00349 for r in $(seq 1 20); do
00350   for k in $(seq 1 20); do
00351     cat minisat_r${r}_k${k}.result | ExtractMinisat data-only | awk " { print \$0 \"  $r  $k\" }";
00352   done;
00353 done >> minisat_results;
00354      \endverbatim
00355      yields:
00356      \verbatim
00357 shell> oklib --R
00358 E = read.table("minisat_results", header=TRUE)
00359 EM = aggregate(E, by=list(r=E$r), FUN=mean)
00360 options(width=1000)
00361 EM
00362  r   rn     rc        t       cfs       dec    rts          r1  ptime  stime       cfl
00363  1  192  18272   0.5285    378.40    407.10   3.55    17333.15 0.0110 0.5115    2898.3
00364  2  336  36480   9.6240  38637.05  41081.25 125.30  3096961.95 0.0205 0.9600  635664.8
00365  3  480  54688  15.2920  37360.50  39724.25 118.35  5821360.20 0.0350 1.4000  569780.4
00366  4  624  72896  24.8370  45409.70  49792.90 138.35  8149119.90 0.0445 1.8700  817007.7
00367  5  768  91104  30.2230  40354.70  44488.95 130.10  9966599.80 0.0570 2.3100  644105.6
00368  6  912 109312  46.9385  56145.40  62684.00 170.25 14110385.50 0.0640 2.7595  888331.9
00369  7 1056 127520  46.7475  53666.90  61842.45 166.15 13175222.50 0.0785 3.1975  853229.2
00370  8 1200 145728 102.3470  84242.95  96100.55 239.45 24387576.30 0.0915 3.6640 1316421.4
00371  9 1344 163936 117.9040  87504.90 101635.25 251.80 27133294.20 0.1015 4.1090 1399346.6
00372 10 1488 182144 143.2785  97662.45 114138.40 273.80 30732365.70 0.1130 4.5550 1627517.4
00373 11 1632 200352 100.5410  82608.05 100458.20 239.20 21793714.35 0.1245 4.9960 1477655.9
00374 12 1776 218560 162.2785 112890.40 135246.05 309.75 33442510.10 0.1345 5.4655 2002968.6
00375 13 1920 236768 219.8780 128707.95 154327.85 350.65 44485694.45 0.1510 5.9085 2238872.5
00376 14 2064 254976 277.6545 149758.45 179119.00 397.55 54358522.10 0.1570 6.3560 2664466.5
00377 15 2208 273184 278.9755 154428.90 186527.30 408.50 54256192.65 0.1710 6.7920 2824605.1
00378 16 2352 291392 244.3250 144208.05 177472.55 386.45 48356482.55 0.1835 7.2620 2758481.2
00379 17 2496 309600 283.3340 163903.60 202336.40 422.85 54694309.85 0.1970 7.7045 3221092.9
00380 18 2640 327808 350.5680 180847.40 222289.35 461.60 66776355.60 0.2075 8.1530 3461162.0
00381 19 2784 346016 350.7520 182180.55 226259.50 453.00 66744064.25 0.2190 8.5940 3528544.8
00382 20 2928 364224 365.6620 194371.05 242715.75 491.40 69723963.15 0.2275 9.0660 3904121.5
00383      \endverbatim
00384      </li>
00385      <li> Consider:
00386      \verbatim
00387 R> plot(E$cfs)
00388 R> plot(E$t)
00389      \endverbatim
00390      The minisat-2.2.0 times and number of conflicts appear to be linear in
00391      the number of rounds! </li>
00392     </ul>
00393    </li>
00394   </ul>
00395 
00396 
00397   \todo The 1-base box translation (forward Mixcolumns)
00398   <ul>
00399    <li> The Sboxes and multiplications boxes are translated using the
00400    1-base translation, discussed in "The 1-base box translation"
00401    in
00402    plans/KeyDiscovery/016/2_1_8/Translations.hpp
00403    where statistics are also provided. </li>
00404    <li> There are currently active investigations attempting to find the
00405    minimum-size 1-base representations for each of the boxes, discussed in
00406     <ul>
00407      <li> AdvancedEncryptionStandard/plans/Representations/Sbox_8.hpp.
00408      </li>
00409      <li> AdvancedEncryptionStandard/plans/Representations/Mul_2_8.hpp.
00410      </li>
00411      <li> AdvancedEncryptionStandard/plans/Representations/Mul_3_8.hpp.
00412      </li>
00413     </ul>
00414    </li>
00415    <li> Over 20 rounds, with 20 random plaintext-ciphertext-pairs per round:
00416     <ul>
00417      <li> For instructions on generating the 1-bases, see
00418      "The 1-base box translation" in
00419      AdvancedEncryptionStandard/plans/KeyDiscovery/016/2_1_8/Translations.hpp.
00420      </li>
00421      <li> Generating the instances (in Maxima):
00422      \verbatim
00423 oklib_monitor : true$
00424 set_hm(ss_sbox_rbase_cnfs,8,read_fcl_f("AES_Sbox_base.cnf"))$
00425 set_hm(ss_field_rbase_cnfs,[8,2],read_fcl_f("AES_byte_field_mul_2_base.cnf"))$
00426 set_hm(ss_field_rbase_cnfs,[8,3],read_fcl_f("AES_byte_field_mul_3_base.cnf"))$
00427 for rounds : 1 thru 20 do
00428   output_ss_fcl_std(rounds, num_columns : 1, num_rows : 2, exp : 8, final_round_b : false, box_tran : aes_rbase_box, mc_tran : aes_mc_forward)$
00429      \endverbatim
00430      </li>
00431      <li> Generating 20 random assignments for the plaintext and ciphertext,
00432      leaving the key unknown:
00433      \verbatim
00434 maxima> for seed : 1 thru 20 do output_ss_random_pc_pair(seed,rounds,num_columns,num_rows,exp,final_round_b);
00435      \endverbatim
00436      </li>
00437      <li> Running minisat-2.2.0:
00438      \verbatim
00439 shell> col=1; row=2; e=8;
00440 for r in $(seq 1 20); do
00441   for k in $(seq 1 20); do
00442       echo "Key ${k} Round ${r}";
00443       AppendDimacs-O3-DNDEBUG ssaes_r${r}_c${col}_rw${row}_e${e}_f0.cnf ssaes_pcpair_r${r}_c${col}_rw${row}_e${e}_f0_s${k}.cnf > r${r}_k${k}.cnf;
00444       RunMinisat r${r}_k${k}.cnf > minisat_r${r}_k${k}.result;
00445   done;
00446 done
00447 shell> (ExtractMinisat header-only |  awk " { print \$0 \" r s\"}"; for r in $(seq 1 14); do for s in $(seq 1 20); do
00448     cat ExperimentMinisat_r${r}_k${s}cnf_*/Statistics | tail -n 1 | awk " { print \$0 \" ${r} ${s}\"}";
00449   done;
00450 done) > MinisatStatistics
00451      \endverbatim
00452      yields:
00453      \verbatim
00454 shell> oklib --R
00455 E = read.table("MinisatStatistics", header=TRUE)
00456 EM = aggregate(E, by=list(r=E$r), FUN=mean)
00457 options(width=1000)
00458 EM
00459     r   rn     rc           t sat       cfs       dec    rts          r1    mem  ptime  stime        cfl  r    s
00460 1   1  160  18004   0.6104567   1    278.60    305.30   3.00     9502.55  10.00 0.0100 0.5715     2015.8  1 10.5
00461 2   2  272  35944   8.9246420   1  37719.35  40382.70 123.15  2395809.40  13.10 0.0200 1.0800   573597.6  2 10.5
00462 3   3  384  53884  20.3741645   1  49536.50  53650.70 151.00  4138695.80  18.20 0.0305 1.6505   893056.8  3 10.5
00463 4   4  496  71824  26.8702695   1  49324.45  54105.20 155.00  6267386.90  19.10 0.0420 2.2700   779387.8  4 10.5
00464 5   5  608  89764  48.4103280   1  66860.00  75028.60 200.15 10155973.95  24.25 0.0515 2.8300  1082937.0  5 10.5
00465 6   6  720 107704  54.6627350   1  72134.60  83645.05 211.75  9333295.85  28.45 0.0600 3.4280  1474549.5  6 10.5
00466 7   7  832 125644  95.2220900   1  97380.15 113763.75 273.70 13989496.15  36.35 0.0700 4.0065  2128524.5  7 10.5
00467 8   8  944 143584 169.6973800   1 137002.75 159436.75 370.60 21666151.85  46.00 0.0835 4.6245  3171608.2  8 10.5
00468 9   9 1056 161524 184.8194600   1 158382.95 186715.00 424.10 22857452.65  53.45 0.0935 5.1810  4099751.6  9 10.5
00469 10 10 1168 179464 278.7595500   1 191001.85 224453.70 491.90 32373182.55  60.80 0.1045 5.7885  4913826.3 10 10.5
00470 11 11 1280 197404 304.0785450   1 220656.75 260736.75 544.35 34632592.30  69.65 0.1155 6.3510  6007968.4 11 10.5
00471 12 12 1392 215344 532.7778000   1 305831.90 359501.80 726.90 51302185.20  91.25 0.1235 6.9750  8549126.3 12 10.5
00472 13 13 1504 233284 610.2921000   1 331344.35 390579.65 794.00 57882032.30 103.25 0.1340 7.5305  9413721.1 13 10.5
00473 14 14 1616 251224 827.0625000   1 391152.20 461206.55 925.45 73394383.65 123.95 0.1355 8.1310 11263617.3 14 10.5
00474      \endverbatim
00475      </li>
00476     </ul>
00477    </li>
00478   </ul>
00479 
00480 
00481   \todo The "minimum" box translation (bidirectional MixColumns)
00482   <ul>
00483    <li> The Sboxes and multiplications boxes are translated using the
00484    "minimum" translations, discussed in 'The "minimum" box translation'
00485    in
00486    plans/KeyDiscovery/016/2_1_8/Translations.hpp
00487    where statistics are also provided. </li>
00488    <li> There are currently active investigations attempting to find the
00489    minimum representations for each of the boxes, discussed in
00490     <ul>
00491      <li> AdvancedEncryptionStandard/plans/Representations/Sbox_8.hpp.
00492      </li>
00493      <li> AdvancedEncryptionStandard/plans/Representations/Mul_2_8.hpp.
00494      </li>
00495      <li> AdvancedEncryptionStandard/plans/Representations/Mul_3_8.hpp.
00496      </li>
00497     </ul>
00498    </li>
00499    <li> Over 20 rounds, with 20 random plaintext-ciphertext-pairs per round:
00500     <ul>
00501      <li> For instructions on generating the 1-bases, see
00502      'The "minimum" box translation' in
00503      plans/KeyDiscovery/016/2_1_8/Translations.hpp.
00504      </li>
00505      <li> Generating the instances (in Maxima):
00506      \verbatim
00507 oklib_monitor : true$
00508 for rounds : 1 thru 20 do
00509   output_ss_fcl_std(rounds, num_columns : 1, num_rows : 2, exp : 8, final_round_b : false, box_tran : aes_small_box, mc_tran : aes_mc_bidirectional)$
00510      \endverbatim
00511      </li>
00512      <li> Generating 20 random assignments for the plaintext and ciphertext,
00513      leaving the key unknown:
00514      \verbatim
00515 maxima> for seed : 1 thru 20 do output_ss_random_pc_pair(seed,rounds,num_columns,num_rows,exp,final_round_b);
00516      \endverbatim
00517      </li>
00518      <li> Running minisat-2.2.0:
00519      \verbatim
00520 shell> col=1; row=2; e=8;
00521 for r in $(seq 1 20); do
00522   for k in $(seq 1 20); do
00523       echo "Key ${k} Round ${r}";
00524       AppendDimacs-O3-DNDEBUG ssaes_r${r}_c${col}_rw${row}_e${e}_f0.cnf ssaes_pcpair_r${r}_c${col}_rw${row}_e${e}_f0_s${k}.cnf > r${r}_k${k}.cnf;
00525       minisat-2.2.0 r${r}_k${k}.cnf > minisat_r${r}_k${k}.result 2>&1;
00526   done;
00527 done
00528 shell> ExtractMinisat header-only | awk ' { print $0 " r k" }' > minisat_results;
00529 for r in $(seq 1 7); do
00530   for k in $(seq 1 20); do
00531     cat minisat_r${r}_k${k}.result | ExtractMinisat data-only | awk " { print \$0 \"  $r  $k\" }";
00532   done;
00533 done >> minisat_results;
00534      \endverbatim
00535      yields:
00536      \verbatim
00537 shell> oklib --R
00538 E = read.table("minisat_results", header=TRUE)
00539 EM = aggregate(E, by=list(r=E$r), FUN=mean)
00540 options(width=1000)
00541 EM
00542 r   rn    rc         t sat         cfs          dec       rts         r1    mem ptime  stime          cfl
00543 1  192  1672    0.0000   1      2172.9      2519.45     12.85      30390  19.00 0.000 0.0000      20832.6
00544 2  336  3280    6.5950   1    409431.4    500513.75    890.90   10805115   8.00 0.000 0.0100    5935048.8
00545 3  480  4888   41.2035   1   2037583.0   2750387.90   3644.10   57608122  10.30 0.003 0.0110   31753123.5
00546 4  624  6496  175.4085   1   7296806.1   9758815.50  11511.35  211049076  19.80 0.007 0.0200  121938539.2
00547 5  768  8104 1283.3405   1  34959474.8  45516313.85  47351.05 1298488466  46.30 0.010 0.0200  653104802.5
00548 6  912  9712 2271.9195   1  49611107.0  64456781.95  64882.05 2092377044  62.45 0.010 0.0215  995531156.5
00549 7 1056 11320 8378.2225   1 136949749.2 176287970.80 164861.05 6692014820 116.10 0.010 0.0300 2934315940.0
00550      \endverbatim
00551      </li>
00552      <li> Consider:
00553      \verbatim
00554 R> plot(E$cfs)
00555 R> plot(E$t)
00556      \endverbatim
00557      The minisat-2.2.0 times and number of conflicts grow much more quickly in
00558      the number of rounds than the 1-base and canonical translations. Is this
00559      exponential growth? </li>
00560      <li> We need data for more rounds. </li>
00561     </ul>
00562    </li>
00563   </ul>
00564 
00565 
00566   \todo The "minimum" box translation (forward MixColumns)
00567   <ul>
00568    <li> The Sboxes and multiplications boxes are translated using the
00569    "minimum" translations, discussed in 'The "minimum" box translation'
00570    in
00571    plans/KeyDiscovery/016/2_1_8/Translations.hpp
00572    where statistics are also provided. </li>
00573    <li> There are currently active investigations attempting to find the
00574    minimum representations for each of the boxes, discussed in
00575     <ul>
00576      <li> AdvancedEncryptionStandard/plans/Representations/Sbox_8.hpp.
00577      </li>
00578      <li> AdvancedEncryptionStandard/plans/Representations/Mul_2_8.hpp.
00579      </li>
00580      <li> AdvancedEncryptionStandard/plans/Representations/Mul_3_8.hpp.
00581      </li>
00582     </ul>
00583    </li>
00584    <li> Over 20 rounds, with 20 random plaintext-ciphertext-pairs per round:
00585     <ul>
00586      <li> For instructions on generating the 1-bases, see
00587      'The "minimum" box translation' in
00588      plans/KeyDiscovery/016/2_1_8/Translations.hpp.
00589      </li>
00590      <li> Generating the instances (in Maxima):
00591      \verbatim
00592 oklib_monitor : true$
00593 for rounds : 1 thru 20 do
00594   output_ss_fcl_std(rounds, num_columns : 1, num_rows : 2, exp : 8, final_round_b : false, box_tran : aes_small_box, mc_tran : aes_mc_forward)$
00595      \endverbatim
00596      </li>
00597      <li> Generating 20 random assignments for the plaintext and ciphertext,
00598      leaving the key unknown:
00599      \verbatim
00600 maxima> for seed : 1 thru 20 do output_ss_random_pc_pair(seed,rounds,num_columns,num_rows,exp,final_round_b);
00601      \endverbatim
00602      </li>
00603      <li> Running minisat-2.2.0:
00604      \verbatim
00605 shell> col=1; row=2; e=8;
00606 for r in $(seq 1 20); do
00607   for k in $(seq 1 20); do
00608       echo "Key ${k} Round ${r}";
00609       AppendDimacs-O3-DNDEBUG ssaes_r${r}_c${col}_rw${row}_e${e}_f0.cnf ssaes_pcpair_r${r}_c${col}_rw${row}_e${e}_f0_s${k}.cnf > r${r}_k${k}.cnf;
00610       RunMinisat r${r}_k${k}.cnf > minisat_r${r}_k${k}.result;
00611   done;
00612 done
00613 shell> (ExtractMinisat header-only |  awk " { print \$0 \" r s\"}"; for r in $(seq 1 5); do for s in $(seq 1 20); do
00614     cat ExperimentMinisat_r${r}_k${s}cnf_*/Statistics | tail -n 1 | awk " { print \$0 \" ${r} ${s}\"}";
00615   done;
00616 done) > MinisatStatistics
00617      \endverbatim
00618      yields:
00619      \verbatim
00620 shell> oklib --R
00621 E = read.table("MinisatStatistics", header=TRUE)
00622 EM = aggregate(E, by=list(r=E$r), FUN=mean)
00623 options(width=1000)
00624 EM
00625   r  rn   rc            t sat         cfs        dec      rts          r1   mem ptime  stime         cfl r    s
00626 1 1 160 1496    0.0168469   1     1671.55     1955.4    10.55     17546.3  8.00 0.000 0.0015     16260.5 1 10.5
00627 2 2 272 2928    3.3017000   1   276785.50   355639.2   646.90   4699452.3  8.00 0.000 0.0100   4027811.0 2 10.5
00628 3 3 384 4360   55.2569310   1  3187885.95  4332512.0  5499.50  61522320.7 11.00 0.000 0.0100  50931502.5 3 10.5
00629 4 4 496 5792  400.6832950   1 17425518.15 23077513.3 25184.75 374642468.1 25.35 0.000 0.0200 299792639.6 4 10.5
00630 5 5 608 7224 1215.0958650   1 40428074.70 53320878.9 54069.10 995483497.0 45.35 0.002 0.0200 752860909.4 5 10.5
00631      \endverbatim
00632      </li>
00633      <li> We need data for more rounds. </li>
00634     </ul>
00635    </li>
00636   </ul>
00637 
00638 */