Cryptography-Digest Digest #17, Volume #12 Tue, 13 Jun 00 07:13:01 EDT
Contents:
PRNG test results ("cranky cransky")
Re: Large S-Boxes (tomstd)
----------------------------------------------------------------------------
From: "cranky cransky" <[EMAIL PROTECTED]>
Crossposted-To: sci.crypt.random-numbers
Subject: PRNG test results
Date: Tue, 13 Jun 2000 20:36:55 +1000
128 bit internal state remember...
don't read this if you're sick of newbies. you have been warned. im sorry.
i tested the generator from state to state, for bit changes
and achieved a value of 62.5 / 128 bits changed, after 3 iterations.
63.85 after 10, 63.995 after 100
and it approaches 64, as iterations -> infinity. so on average 1/2 the bits
change every iteration.
also ent reports, 50.0% chi-square deviation, and 0.03 error for Monte-Carlo
circumscribed ( ? the right word ) square test results...
has anyone one got any interpretations?
here are my die hard results for my mixing generator:
BIRTHDAY SPACINGS TEST, M= 512 N=2**24 LAMBDA= 2.0000
a using bits 1 to 24 p-value= .096074
a using bits 2 to 25 p-value= .138751
a using bits 3 to 26 p-value= .274324
a using bits 4 to 27 p-value= .618054
a using bits 5 to 28 p-value= .741029
a using bits 6 to 29 p-value= .612722
a using bits 7 to 30 p-value= .747140
a using bits 8 to 31 p-value= .746571
a using bits 9 to 32 p-value= .645953
The 9 p-values were
.096074 .138751 .274324 .618054 .741029
.612722 .747140 .746571 .645953
A KSTEST for the 9 p-values yields .439138
============================================================================
----
OPERM5 test for file a
chisquare for 99 degrees of freedom= 98.402; p-value= .501914
OPERM5 test for file a
chisquare for 99 degrees of freedom= 93.605; p-value= .365709
============================================================================
----
Binary rank test for a
Rank test for 31x31 binary matrices:
rows from leftmost 31 bits of each 32-bit integer
rank observed expected (o-e)^2/e sum
28 221 211.4 .434279 .434
29 5176 5134.0 .343423 .778
30 23047 23103.0 .135967 .914
31 11556 11551.5 .001734 .915
chisquare= .915 for 3 d. of f.; p-value= .347634
Binary rank test for a
Rank test for 32x32 binary matrices:
rows from leftmost 32 bits of each 32-bit integer
rank observed expected (o-e)^2/e sum
29 200 211.4 .616651 .617
30 5219 5134.0 1.406942 2.024
31 23100 23103.0 .000402 2.024
32 11481 11551.5 .430566 2.455
chisquare= 2.455 for 3 d. of f.; p-value= .575033
============================================================================
----
b-rank test for bits 1 to 8 p=1-exp(-SUM/2)= .71552
b-rank test for bits 2 to 9 p=1-exp(-SUM/2)= .20860
b-rank test for bits 3 to 10 p=1-exp(-SUM/2)= .35722
b-rank test for bits 4 to 11 p=1-exp(-SUM/2)= .79014
b-rank test for bits 5 to 12 p=1-exp(-SUM/2)= .65635
b-rank test for bits 6 to 13 p=1-exp(-SUM/2)= .47969
b-rank test for bits 7 to 14 p=1-exp(-SUM/2)= .18395
b-rank test for bits 8 to 15 p=1-exp(-SUM/2)= .38562
b-rank test for bits 9 to 16 p=1-exp(-SUM/2)= .30904
b-rank test for bits 10 to 17 p=1-exp(-SUM/2)= .89149
b-rank test for bits 11 to 18 p=1-exp(-SUM/2)= .83502
b-rank test for bits 12 to 19 p=1-exp(-SUM/2)= .47975
b-rank test for bits 13 to 20 p=1-exp(-SUM/2)= .20266
b-rank test for bits 14 to 21 p=1-exp(-SUM/2)= .59868
b-rank test for bits 15 to 22 p=1-exp(-SUM/2)= .70232
b-rank test for bits 16 to 23 p=1-exp(-SUM/2)= .43527
b-rank test for bits 17 to 24 p=1-exp(-SUM/2)= .05534
b-rank test for bits 18 to 25 p=1-exp(-SUM/2)= .75849
b-rank test for bits 19 to 26 p=1-exp(-SUM/2)= .72609
b-rank test for bits 20 to 27 p=1-exp(-SUM/2)= .70366
b-rank test for bits 21 to 28 p=1-exp(-SUM/2)= .06324
b-rank test for bits 22 to 29 p=1-exp(-SUM/2)= .20644
b-rank test for bits 23 to 30 p=1-exp(-SUM/2)= .79215
b-rank test for bits 24 to 31 p=1-exp(-SUM/2)= .57362
b-rank test for bits 25 to 32 p=1-exp(-SUM/2)= .78805
TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices
These should be 25 uniform [0,1] random variables:
.715517 .208600 .357224 .790140 .656354
.479686 .183955 .385623 .309043 .891488
.835019 .479745 .202656 .598676 .702316
.435270 .055340 .758488 .726092 .703659
.063244 .206435 .792154 .573615 .788049
brank test summary for a
The KS test for those 25 supposed UNI's yields
KS p-value= .411341
============================================================================
----
No. missing words should average 141909. with sigma=428.
tst no 1: 142348 missing words, 1.02 sigmas from mean, p-value= .84730
tst no 2: 142016 missing words, .25 sigmas from mean, p-value= .59841
tst no 3: 141105 missing words, -1.88 sigmas from mean, p-value= .03010
tst no 4: 142258 missing words, .81 sigmas from mean, p-value= .79236
tst no 5: 142547 missing words, 1.49 sigmas from mean, p-value= .93187
tst no 6: 142309 missing words, .93 sigmas from mean, p-value= .82480
tst no 7: 141713 missing words, -.46 sigmas from mean, p-value= .32322
tst no 8: 142180 missing words, .63 sigmas from mean, p-value= .73644
tst no 9: 141591 missing words, -.74 sigmas from mean, p-value= .22851
tst no 10: 141720 missing words, -.44 sigmas from mean, p-value= .32912
tst no 11: 142245 missing words, .78 sigmas from mean, p-value= .78356
tst no 12: 140723 missing words, -2.77 sigmas from mean, p-value= .00279
tst no 13: 141703 missing words, -.48 sigmas from mean, p-value= .31488
tst no 14: 142116 missing words, .48 sigmas from mean, p-value= .68541
tst no 15: 141754 missing words, -.36 sigmas from mean, p-value= .35833
tst no 16: 142123 missing words, .50 sigmas from mean, p-value= .69119
tst no 17: 141738 missing words, -.40 sigmas from mean, p-value= .34447
tst no 18: 141461 missing words, -1.05 sigmas from mean, p-value= .14744
tst no 19: 141796 missing words, -.26 sigmas from mean, p-value= .39559
tst no 20: 140990 missing words, -2.15 sigmas from mean, p-value= .01586
============================================================================
----
OPSO for a using bits 23 to 32 141803 -.367 .3569
OPSO for a using bits 22 to 31 142472 1.940 .9738
OPSO for a using bits 21 to 30 142222 1.078 .8595
OPSO for a using bits 20 to 29 142038 .444 .6714
OPSO for a using bits 19 to 28 142132 .768 .7787
OPSO for a using bits 18 to 27 141746 -.563 .2866
OPSO for a using bits 17 to 26 142027 .406 .6575
OPSO for a using bits 16 to 25 141827 -.284 .3882
OPSO for a using bits 15 to 24 142589 2.344 .9905
OPSO for a using bits 14 to 23 141301 -2.098 .0180
OPSO for a using bits 13 to 22 141826 -.287 .3869
OPSO for a using bits 12 to 21 141980 .244 .5963
OPSO for a using bits 11 to 20 141640 -.929 .1765
OPSO for a using bits 10 to 19 142055 .502 .6923
OPSO for a using bits 9 to 18 142082 .595 .7242
OPSO for a using bits 8 to 17 142055 .502 .6923
OPSO for a using bits 7 to 16 142067 .544 .7067
OPSO for a using bits 6 to 15 141835 -.256 .3989
OPSO for a using bits 5 to 14 141790 -.411 .3404
OPSO for a using bits 4 to 13 141326 -2.011 .0221
OPSO for a using bits 3 to 12 141585 -1.118 .1317
OPSO for a using bits 2 to 11 141903 -.022 .4913
OPSO for a using bits 1 to 10 141841 -.236 .4069
OQSO for a using bits 28 to 32 142054 .490 .6881
OQSO for a using bits 27 to 31 142025 .392 .6525
OQSO for a using bits 26 to 30 141761 -.503 .3075
OQSO for a using bits 25 to 29 141889 -.069 .4725
OQSO for a using bits 24 to 28 141609 -1.018 .1543
OQSO for a using bits 23 to 27 141803 -.360 .3593
OQSO for a using bits 22 to 26 141926 .057 .5225
OQSO for a using bits 21 to 25 141873 -.123 .4510
OQSO for a using bits 20 to 24 142167 .873 .8088
OQSO for a using bits 19 to 23 141817 -.313 .3771
OQSO for a using bits 18 to 22 142031 .412 .6600
OQSO for a using bits 17 to 21 142117 .704 .7593
OQSO for a using bits 16 to 20 142140 .782 .7829
OQSO for a using bits 15 to 19 141712 -.669 .2518
OQSO for a using bits 14 to 18 142230 1.087 .8615
OQSO for a using bits 13 to 17 142058 .504 .6929
OQSO for a using bits 12 to 16 141919 .033 .5131
OQSO for a using bits 11 to 15 142323 1.402 .9196
OQSO for a using bits 10 to 14 141595 -1.066 .1433
OQSO for a using bits 9 to 13 141664 -.832 .2028
OQSO for a using bits 8 to 12 141570 -1.150 .1250
OQSO for a using bits 7 to 11 141907 -.008 .4969
OQSO for a using bits 6 to 10 141531 -1.282 .0998
OQSO for a using bits 5 to 9 141849 -.205 .4190
OQSO for a using bits 4 to 8 141814 -.323 .3733
OQSO for a using bits 3 to 7 141619 -.984 .1625
OQSO for a using bits 2 to 6 142162 .857 .8041
OQSO for a using bits 1 to 5 141686 -.757 .2245
DNA for a using bits 31 to 32 142171 .772 .7799
DNA for a using bits 30 to 31 142053 .424 .6641
DNA for a using bits 29 to 30 141841 -.202 .4201
DNA for a using bits 28 to 29 142067 .465 .6791
DNA for a using bits 27 to 28 141978 .203 .5803
DNA for a using bits 26 to 27 142020 .326 .6280
DNA for a using bits 25 to 26 141827 -.243 .4041
DNA for a using bits 24 to 25 141916 .020 .5079
DNA for a using bits 23 to 24 142292 1.129 .8705
DNA for a using bits 22 to 23 142038 .380 .6479
DNA for a using bits 21 to 22 141778 -.387 .3492
DNA for a using bits 20 to 21 142099 .560 .7121
DNA for a using bits 19 to 20 142175 .784 .7834
DNA for a using bits 18 to 19 142615 2.082 .9813
DNA for a using bits 17 to 18 141401 -1.499 .0669
DNA for a using bits 16 to 17 141969 .176 .5699
DNA for a using bits 15 to 16 142202 .863 .8060
DNA for a using bits 14 to 15 141956 .138 .5548
DNA for a using bits 13 to 14 141288 -1.833 .0334
DNA for a using bits 12 to 13 141449 -1.358 .0872
DNA for a using bits 11 to 12 141873 -.107 .4573
DNA for a using bits 10 to 11 141625 -.839 .2008
DNA for a using bits 9 to 10 141387 -1.541 .0617
DNA for a using bits 8 to 9 141776 -.393 .3470
DNA for a using bits 7 to 8 141108 -2.364 .0090
DNA for a using bits 6 to 7 141898 -.033 .4867
DNA for a using bits 5 to 6 142012 .303 .6190
DNA for a using bits 4 to 5 141834 -.222 .4121
DNA for a using bits 3 to 4 142194 .840 .7995
DNA for a using bits 2 to 3 141782 -.376 .3536
DNA for a using bits 1 to 2 141629 -.827 .2041
============================================================================
----
Test results for a
Chi-square with 5^5-5^4=2500 d.of f. for sample size:2560000
chisquare equiv normal p-value
Results fo COUNT-THE-1's in successive bytes:
byte stream for a 2419.82 -1.134 .128429
byte stream for a 2668.49 2.383 .991410
============================================================================
----
Chi-square with 5^5-5^4=2500 d.of f. for sample size: 256000
chisquare equiv normal p value
Results for COUNT-THE-1's in specified bytes:
bits 1 to 8 2486.62 -.189 .424949
bits 2 to 9 2497.14 -.040 .483895
bits 3 to 10 2477.56 -.317 .375507
bits 4 to 11 2503.03 .043 .517068
bits 5 to 12 2577.91 1.102 .864732
bits 6 to 13 2287.41 -3.006 .001322
bits 7 to 14 2498.20 -.025 .489872
bits 8 to 15 2430.71 -.980 .163565
bits 9 to 16 2564.33 .910 .818530
bits 10 to 17 2410.21 -1.270 .102081
bits 11 to 18 2503.11 .044 .517551
bits 12 to 19 2582.16 1.162 .877378
bits 13 to 20 2520.80 .294 .615694
bits 14 to 21 2542.14 .596 .724414
bits 15 to 22 2562.62 .886 .812080
bits 16 to 23 2491.75 -.117 .453565
bits 17 to 24 2471.74 -.400 .344716
bits 18 to 25 2525.80 .365 .642391
bits 19 to 26 2497.21 -.039 .484291
bits 20 to 27 2470.00 -.424 .335706
bits 21 to 28 2503.36 .048 .518958
bits 22 to 29 2548.15 .681 .752055
bits 23 to 30 2488.52 -.162 .435539
bits 24 to 31 2489.87 -.143 .443063
bits 25 to 32 2443.91 -.793 .213802
============================================================================
----
CDPARK: result of ten tests on file a
Of 12,000 tries, the average no. of successes
should be 3523 with sigma=21.9
Successes: 3498 z-score: -1.142 p-value: .126820
Successes: 3522 z-score: -.046 p-value: .481790
Successes: 3508 z-score: -.685 p-value: .246694
Successes: 3499 z-score: -1.096 p-value: .136563
Successes: 3528 z-score: .228 p-value: .590298
Successes: 3512 z-score: -.502 p-value: .307734
Successes: 3547 z-score: 1.096 p-value: .863437
Successes: 3525 z-score: .091 p-value: .536382
Successes: 3516 z-score: -.320 p-value: .374623
Successes: 3532 z-score: .411 p-value: .659449
square size avg. no. parked sample sigma
100. 3518.700 14.474
KSTEST for the above 10: p= .377724
============================================================================
----
This is the MINIMUM DISTANCE test
for random integers in the file a
Sample no. d^2 avg equiv uni
5 .2729 .4394 .239903
10 3.6319 .9742 .974014
15 .5458 .8310 .422198
20 4.0257 .9543 .982507
25 1.3426 .8827 .740603
30 .0359 .9011 .035459
35 1.2518 1.0712 .715801
40 1.4977 1.0286 .778025
45 .4207 .9807 .344806
50 1.0011 1.0055 .634360
55 1.3298 1.0342 .737219
60 1.4951 1.0664 .777445
65 .1947 1.0580 .177745
70 1.9788 1.0670 .863137
75 .5228 1.0710 .408693
80 .9438 1.0806 .612681
85 1.6990 1.0942 .818682
90 .2448 1.1093 .218123
95 1.0323 1.0834 .645652
100 1.1281 1.1296 .678178
MINIMUM DISTANCE TEST for a
Result of KS test on 20 transformed mindist^2's:
p-value= .630550
============================================================================
----
The 3DSPHERES test for file a
sample no: 1 r^3= 73.635 p-value= .91409
sample no: 2 r^3= 31.529 p-value= .65040
sample no: 3 r^3= 127.073 p-value= .98553
sample no: 4 r^3= 40.726 p-value= .74271
sample no: 5 r^3= 7.530 p-value= .22198
sample no: 6 r^3= 11.079 p-value= .30878
sample no: 7 r^3= 35.291 p-value= .69161
sample no: 8 r^3= 101.186 p-value= .96571
sample no: 9 r^3= 45.655 p-value= .78169
sample no: 10 r^3= 16.377 p-value= .42068
sample no: 11 r^3= 45.164 p-value= .77809
sample no: 12 r^3= 51.810 p-value= .82219
sample no: 13 r^3= 4.150 p-value= .12919
sample no: 14 r^3= 98.380 p-value= .96235
sample no: 15 r^3= 22.110 p-value= .52146
sample no: 16 r^3= 10.920 p-value= .30511
sample no: 17 r^3= 13.169 p-value= .35530
sample no: 18 r^3= 11.385 p-value= .31579
sample no: 19 r^3= 128.724 p-value= .98631
sample no: 20 r^3= 25.736 p-value= .57594
3DSPHERES test for file a p-value= .934257
============================================================================
----
RESULTS OF SQUEEZE TEST FOR a
Table of standardized frequency counts
( (obs-exp)/sqrt(exp) )^2
for j taking values <=6,7,8,...,47,>=48:
-.1 .9 .3 -.8 .2 -2.0
.7 1.2 .3 -.9 .1 1.5
-.8 1.3 1.1 .2 -1.5 .0
-.7 -.8 -.5 .2 -.2 .6
.4 -.1 -.2 -.3 1.4 .2
.1 -.8 -2.6 .9 .6 -1.4
.5 .2 2.5 1.0 .1 -1.0
-.1
Chi-square with 42 degrees of freedom: 40.180
z-score= -.199 p-value= .448757
______________________________________________________________
============================================================================
----
Test no. 1 p-value .285011
Test no. 2 p-value .162071
Test no. 3 p-value .536086
Test no. 4 p-value .512949
Test no. 5 p-value .315339
Test no. 6 p-value .292698
Test no. 7 p-value .939511
Test no. 8 p-value .231423
Test no. 9 p-value .679435
Test no. 10 p-value .188505
Results of the OSUM test for a
KSTEST on the above 10 p-values: .642910
============================================================================
----
The RUNS test for file a
Up and down runs in a sample of 10000
_________________________________________________
Run test for a :
runs up; ks test for 10 p's: .182704
runs down; ks test for 10 p's: .827895
Run test for a :
runs up; ks test for 10 p's: .522536
runs down; ks test for 10 p's: .783609
============================================================================
----
Results of craps test for a
No. of wins: Observed Expected
98650 98585.86
Chisq= 17.63 for 20 degrees of freedom, p= .38846
Throws Observed Expected Chisq Sum
SUMMARY FOR a
p-value for no. of wins: .612896
p-value for throws/game: .388460
Test completed. File a
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
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------------------------------
Subject: Re: Large S-Boxes
From: tomstd <[EMAIL PROTECTED]>
Date: Tue, 13 Jun 2000 04:04:33 -0700
Well I intend to write a paper this summer on what I have
learned about sboxes... It may help.
If anyone knows of papers online (other then CAST) please share
em.
Tom
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