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DIEHARD battery of statistical tests by George Marsaglia

 

 
The DIEHARD battery and documentation can be downloaded from http://stat.fsu.edu/~geo/diehard.html
Descriptions of the 15 tests included in the battery can be also seen as a text-file here

Each of the 15 tests was applied on ten 11Mb files containing data-streams generated by the VMPC Stream Cipher for 10 different keys.

The resulting P-values have been analysed by computing their average (A) (for the 10 tested files), their standard deviation (D), the expected standard deviation of the measured average (DA=0,0912), the expected standard deviation of the measured standard deviation (DD=0,0418) and by testing by how many standard deviations (DA and DD) the measured average (A) and the measured standard deviation (D) differ from their expected values of EA=0.50 and ED=sqrt(1/12)=0,288675), according to formulas rA = (A-EA)/DA and rD = (D-ED)/DD).

[The parameters rA and rD can be interpreted as if A and D were normally distributed, i.e. the probability that rA or rD is higher than 1 or lower than -1 is about 0,32; higher than 2 or lower than -2: about 0,045 and higher than 3 or lower than -3: about 0,0026 - in a single observation. (Obviously in the tables below - because of the fact that 240 variables are tested - probability that one of them will be "suspiciously unlikely" is growing. E.g. an event occurring with probability 0,002 in a single observation has a chance close to 0,4 to occur in a set of 240 observations]

BIRTHDAY SPACINGS TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,59440,34731,041,40
0,59720,23981,07-1,17
0,44040,2597-0,65-0,69
0,44700,2710-0,58-0,42
0,48890,2957-0,120,17
0,62050,25601,32-0,78
0,44860,2863-0,56-0,06
0,54780,26160,52-0,65
0,47800,2766-0,24-0,29
0,59460,25121,04-0,90
OVERLAPPING 5-PERMUTATION TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,39980,3196-1,100,74
0,48660,3393-0,151,21
BINARY RANK TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,55170,21600,57-1,74
0,47090,1694-0,32-2,85
0,51020,22140,11-1,61
0,47380,2447-0,29-1,05
0,35440,3297-1,600,98
0,63510,24881,48-0,95
0,53870,22650,42-1,49
0,44930,3253-0,560,88
0,43450,3461-0,721,37
0,58730,32820,960,95
0,55290,30770,580,45
0,50270,31830,030,71
0,45450,3009-0,500,29
0,55160,29400,570,13
0,62210,28371,34-0,12
0,54630,35340,511,55
0,66130,20441,77-2,02
0,46170,3539-0,421,56
0,35160,1805-1,63-2,59
0,47720,2740-0,25-0,35
0,50800,35520,091,59
0,49320,3906-0,072,44
0,60360,29461,140,14
0,54640,27570,51-0,31
0,47700,3263-0,250,90
0,44180,3427-0,641,29
0,55890,26160,65-0,65
0,57500,28620,82-0,06
BITSTREAM TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,55170,21400,57-1,79
0,58270,25590,91-0,78
0,52850,20310,31-2,05
0,52890,24900,32-0,95
0,57180,34070,791,25
0,49010,2294-0,11-1,42
0,52830,27280,31-0,38
0,47720,2207-0,25-1,63
0,48210,2581-0,20-0,73
0,62660,29001,390,03
0,29480,2153-2,25-1,76
0,52080,36850,231,91
0,52380,28580,26-0,07
0,63670,30021,500,27
0,53270,30910,360,49
0,44820,2425-0,57-1,11
0,42080,2196-0,87-1,65
0,50240,26350,03-0,60
0,46870,3608-0,341,73
0,46060,3055-0,430,40
OPSO TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,67190,25421,88-0,83
0,30880,2653-2,10-0,56
0,56120,23300,67-1,33
0,43620,2200-0,70-1,64
0,42510,2473-0,82-0,99
0,49480,2706-0,06-0,43
0,59450,24581,04-1,03
0,36300,2581-1,50-0,73
0,38510,2894-1,260,02
0,41160,2355-0,97-1,27
0,35120,2186-1,63-1,68
0,65940,31711,750,68
0,45880,3472-0,451,40
0,66560,27481,82-0,33
0,54290,28400,47-0,11
0,45240,2423-0,52-1,11
0,52850,25160,31-0,89
0,45710,2452-0,47-1,04
0,33860,3138-1,770,60
0,51250,23230,14-1,35
0,57190,31610,790,66
0,58010,32860,880,95
0,41470,1980-0,94-2,17
OQSO TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,57840,26870,86-0,48
0,45540,2813-0,49-0,18
0,44740,2710-0,58-0,42
0,28640,2804-2,34-0,20
0,41370,2496-0,95-0,94
0,25500,1929-2,69-2,29
0,67320,27061,90-0,43
0,38050,3142-1,310,61
0,45980,2356-0,44-1,27
0,40730,2286-1,02-1,44
0,57180,30690,790,44
0,48680,2806-0,14-0,19
0,30440,2861-2,14-0,06
0,51060,32030,120,76
0,54300,30020,470,27
0,60150,26591,11-0,55
0,47970,2877-0,22-0,02
0,49120,2330-0,10-1,33
0,52590,28100,28-0,18
0,51960,23300,21-1,33
0,40910,3567-1,001,63
0,47790,3109-0,240,53
0,37950,1746-1,32-2,73
0,35030,2207-1,64-1,63
0,54990,33350,551,07
0,55430,26500,60-0,57
0,53110,17060,34-2,82
0,53040,23600,33-1,26
DNA TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,56590,31300,720,58
0,31210,2310-2,06-1,38
0,39500,2610-1,15-0,66
0,38360,3317-1,281,03
0,54990,33870,551,20
0,46510,2842-0,38-0,11
0,50250,35730,031,64
0,47510,2843-0,27-0,11
0,51570,28270,17-0,14
0,51390,34770,151,41
0,65860,30711,740,44
0,43200,2507-0,75-0,91
0,53880,24330,43-1,09
0,34320,3095-1,720,50
0,35080,3297-1,640,98
0,50250,33640,031,14
0,48360,3004-0,180,28
0,52850,33150,311,02
0,50920,29350,100,12
0,50110,30880,010,48
0,50130,36420,011,81
0,69350,25272,12-0,86
0,29880,2290-2,21-1,43
0,42770,2832-0,79-0,13
0,47380,2866-0,29-0,05
0,32660,2609-1,90-0,66
0,36340,2323-1,50-1,35
0,45320,3513-0,511,50
0,47420,2128-0,28-1,81
0,62840,29861,410,24
0,45880,3805-0,452,20
COUNT-THE-1's TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,49040,2491-0,11-0,95
0,40340,2524-1,06-0,87
0,38650,3354-1,241,12
0,42400,2688-0,83-0,47
0,62240,34631,341,38
0,36970,3048-1,430,39
0,55170,30200,570,32
0,59230,30021,010,27
0,70220,19642,22-2,21
0,46540,3920-0,382,47
0,43750,2782-0,69-0,25
0,47000,2410-0,33-1,14
0,66240,28411,78-0,11
0,55410,30950,590,50
0,34590,3248-1,690,86
0,57740,33160,851,03
0,60220,33841,121,19
0,46210,2749-0,42-0,33
0,48450,3383-0,171,19
0,61230,32651,230,90
0,66320,20871,79-1,91
0,43420,2746-0,72-0,34
0,59680,28411,06-0,11
0,45160,1955-0,53-2,23
0,78300,18583,10-2,46
0,43570,3358-0,701,13
0,61790,27931,29-0,22
PARKING LOT TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,57610,28240,83-0,15
0,53850,29610,420,18
0,49130,2847-0,10-0,10
0,42180,2666-0,86-0,53
0,40730,3185-1,020,71
0,37180,2654-1,41-0,56
0,57660,23610,84-1,26
0,46290,3281-0,410,94
0,55530,22480,61-1,53
0,41340,3054-0,950,40
0,50800,32030,090,76
MINIMUM DISTANCE TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,57990,28640,88-0,06
0,58240,29400,900,13
0,43050,2562-0,76-0,78
0,70600,22522,26-1,52
0,46060,2177-0,43-1,70
0,58750,31350,960,59
0,52510,29170,270,07
0,51700,24630,19-1,01
0,32550,1932-1,91-2,28
0,72470,27592,46-0,30
0,35890,3305-1,551,00
0,65160,22891,66-1,43
0,40800,2291-1,01-1,42
0,73780,20762,61-1,94
0,41370,1863-0,95-2,45
0,54650,30980,510,51
0,46670,3692-0,371,93
0,46370,3099-0,400,51
0,48660,2418-0,15-1,12
0,61140,27721,22-0,27
0,43010,2726-0,77-0,39
3DSPHERES TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,37580,2750-1,36-0,33
0,59390,19801,03-2,17
0,44710,3174-0,580,69
0,56770,28170,74-0,17
0,37650,2640-1,35-0,59
0,51500,22090,16-1,62
0,44170,2901-0,640,03
0,53690,24950,40-0,94
0,49850,2389-0,02-1,19
0,48470,2969-0,170,20
0,62470,35541,371,60
0,25210,2272-2,72-1,47
0,47170,2660-0,31-0,54
0,54160,27560,46-0,31
0,50060,36850,011,91
0,41770,2378-0,90-1,22
0,45150,3577-0,531,65
0,39100,2996-1,200,26
0,37950,2816-1,32-0,17
0,69060,22152,09-1,61
0,36590,2426-1,47-1,10
SQEEZE TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,43920,2572-0,67-0,75
OVERLAPPING SUMS TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,27710,2769-2,44-0,28
0,48280,2486-0,19-0,96
0,56850,29770,750,22
0,56730,29470,740,14
0,52140,35190,231,51
0,56450,31210,710,56
0,47370,3198-0,290,74
0,37200,3086-1,400,48
0,44940,2361-0,55-1,26
0,62970,28431,42-0,10
0,65260,19581,67-2,22
RUNS TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,42140,2388-0,86-1,19
0,46710,2569-0,36-0,76
0,40440,2026-1,05-2,06
0,41120,3063-0,970,42
CRAPS TEST
Average (A) Std. Dev. (D) rA=(A-EA)/DA rD=(D-ED)/DD
0,53740,29770,410,22
0,53480,23300,38-1,33

None of the measured relative deviations rA and rD showed an unexpectedly high value, which indicates that the performed statistical tests found no bias in the output generated by the VMPC Stream Cipher.


by Bartosz Zoltak




Copyright © 1999-2016 Bartosz Zoltak
Supported by OHTON EXPO Okna Wroc³aw