RockYou 2021 - Password leak

Background

Check if your password has been leaked https://cybernews.com/password-leak-check/

rockyou2021.txt - A Short Summary https://chris.partridge.tech/2021/rockyou2021.txt-a-short-summary/

This is what Mr. Partridge concludes in his analysis:

kys234 explicitly removed any non-ASCII characters, and limited password length to 20 characters. This makes for a very clean list, in stark contrast to other password breaches or dictionaries which are often very messy or unformatted, and can take time to clean before being usable.

Note: On many password leaks, there are passwords longer than 20 characters.

Analysis

Password lenghts in the leaked file

Analyze the file. See how many passwords it contains and how long the passwords are. Running this single-liner in Perl:

perl -ne 'chomp; ++$cnt; $pwlen=length($_); if ($lens{$pwlen}) {++$lens{$pwlen};} else {$lens{$pwlen}=1;} END {printf("Count: %d", $cnt); keys(%lens); while(my($k, $v) = each(%lens)) {printf("Len %d: %d\n", $k, $v);}}' rockyou2021.txt

On my Linux, it took well over 40 minutes, but eventually it will output:

Count: 8459060239
Len 6: 484236159
Len 7: 402518961
Len 8: 1107084124
Len 9: 1315444128
Len 10: 1314988168
Len 11: 1071452326
Len 12: 835365123
Len 13: 613654280
Len 14: 436652069
Len 15: 317146874
Len 16: 215720888
Len 17: 131328063
Len 18: 97950285
Len 19: 65235844
Len 20: 50282947

Plotting the output with R

Plot the gathered password lengths from 6 to 20 characters with R (note the plot range is from 6 to 30 to maintain visual scale):

y <- c(484236159, 402518961, 1107084124, 1315444128, 1314988168, 1071452326, 835365123, 613654280, 436652069, 317146874,
215720888, 131328063, 97950285, 65235844, 50282947)
x <- (6:20)
tab <- data.frame(x, y)

plot(y~x, data=tab, xlim=c(6, 30), xlab="password length", ylab="count passwords")

Creating a model with R

From the shape of the plot, it looks gaussian. Let’s try to model it.

Define some helper functions for gauss and optimization function to return squared sum of differences:

gaussf <- function(x, mu, sigma, k)
{
    mu * exp(-0.5 * (x - sigma)^2 / k^2)
}
optimf <- function(par)
{
  mu <- par[1]
  sigma <- par[2]
  k <- par[3]
  rhat <- gaussf(tab["x"], mu, sigma, k)
  out <- sum((tab["y"] - rhat)^2)
    cat(sprintf("in: mu: %f, sigma: %f, k: %f\n", mu, sigma, k))
    cat(sprintf("out: %f\n", out))
    out
}
plot_f <- function(x)
{
    gaussf(x, gauss_param[1], gauss_param[2], gauss_param[3])
}

Guesstimate start point and scale. This is very tricky, getting this wrong will result in completely useless plots. The values below are obtained by trial-and-error. R-code:

p.init <- c(10000000, 5, 1)
p.scaling <- c(1e-1, 1e-9, 1e-9)

Go optimize the bell-curve:

(res <- optim(p.init, optimf, method="BFGS", control=list(reltol=1e-8, parscale = p.scaling)))

in: mu: 10000000.000000, sigma: 5.000000, k: 1.000000
out: 7668373349352918016.000000
in: mu: 10000000.000100, sigma: 5.000000, k: 1.000000
out: 7668373349352846336.000000
in: mu: 9999999.999900, sigma: 5.000000, k: 1.000000
out: 7668373349352989696.000000
in: mu: 10000000.000000, sigma: 5.000000, k: 1.000000
out: 7668373349352908800.000000
in: mu: 10000000.000000, sigma: 5.000000, k: 1.000000
out: 7668373349352926208.000000
in: mu: 10000000.000000, sigma: 5.000000, k: 1.000000
out: 7668373349352904704.000000
in: mu: 10000000.000000, sigma: 5.000000, k: 1.000000
out: 7668373349352931328.000000
in: mu: 17168000.000000, sigma: 5.008704, k: 1.013312
out: 7662857938085029888.000000
in: mu: 17168000.000100, sigma: 5.008704, k: 1.013312
out: 7662857938084956160.000000
in: mu: 17167999.999900, sigma: 5.008704, k: 1.013312
out: 7662857938085102592.000000
in: mu: 17168000.000000, sigma: 5.008704, k: 1.013312
out: 7662857938085014528.000000
in: mu: 17168000.000000, sigma: 5.008704, k: 1.013312
out: 7662857938085044224.000000
in: mu: 17168000.000000, sigma: 5.008704, k: 1.013312
out: 7662857938085007360.000000
in: mu: 17168000.000000, sigma: 5.008704, k: 1.013312
out: 7662857938085051392.000000
in: mu: 24489600.000000, sigma: 5.023552, k: 1.035328
out: 7656514463012686848.000000
in: mu: 24489600.000100, sigma: 5.023552, k: 1.035328
out: 7656514463012609024.000000
in: mu: 24489599.999900, sigma: 5.023552, k: 1.035328
out: 7656514463012763648.000000
in: mu: 24489600.000000, sigma: 5.023552, k: 1.035328
out: 7656514463012664320.000000
in: mu: 24489600.000000, sigma: 5.023552, k: 1.035328
out: 7656514463012709376.000000
in: mu: 24489600.000000, sigma: 5.023552, k: 1.035328
out: 7656514463012656128.000000
in: mu: 24489600.000000, sigma: 5.023552, k: 1.035328
out: 7656514463012717568.000000
in: mu: 32220800.000000, sigma: 5.046080, k: 1.066048
out: 7648686059164043264.000000
in: mu: 32220800.000100, sigma: 5.046080, k: 1.066048
out: 7648686059163961344.000000
in: mu: 32220799.999900, sigma: 5.046080, k: 1.066048
out: 7648686059164125184.000000
in: mu: 32220800.000000, sigma: 5.046080, k: 1.066048
out: 7648686059164013568.000000
in: mu: 32220800.000000, sigma: 5.046080, k: 1.066048
out: 7648686059164071936.000000
in: mu: 32220800.000000, sigma: 5.046080, k: 1.066048
out: 7648686059164001280.000000
in: mu: 32220800.000000, sigma: 5.046080, k: 1.066048
out: 7648686059164085248.000000
in: mu: 40412800.000000, sigma: 5.075264, k: 1.108032
out: 7638670975604335616.000000
in: mu: 40412800.000100, sigma: 5.075264, k: 1.108032
out: 7638670975604246528.000000
in: mu: 40412799.999900, sigma: 5.075264, k: 1.108032
out: 7638670975604424704.000000
in: mu: 40412800.000000, sigma: 5.075264, k: 1.108032
out: 7638670975604297728.000000
in: mu: 40412800.000000, sigma: 5.075264, k: 1.108032
out: 7638670975604373504.000000
in: mu: 40412800.000000, sigma: 5.075264, k: 1.108032
out: 7638670975604281344.000000
in: mu: 40412800.000000, sigma: 5.075264, k: 1.108032
out: 7638670975604390912.000000
in: mu: 49321600.000000, sigma: 5.113152, k: 1.162816
out: 7625220857507410944.000000
in: mu: 49321600.000100, sigma: 5.113152, k: 1.162816
out: 7625220857507312640.000000
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out: 7625220857507509248.000000
in: mu: 49321600.000000, sigma: 5.113152, k: 1.162816
out: 7625220857507362816.000000
in: mu: 49321600.000000, sigma: 5.113152, k: 1.162816
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in: mu: 49321600.000000, sigma: 5.113152, k: 1.162816
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in: mu: 49321600.000000, sigma: 5.113152, k: 1.162816
out: 7625220857507481600.000000
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out: 7606397305424766976.000000
in: mu: 59152000.000100, sigma: 5.161280, k: 1.233984
out: 7606397305424654336.000000
in: mu: 59151999.999900, sigma: 5.161280, k: 1.233984
out: 7606397305424879616.000000
in: mu: 59152000.000000, sigma: 5.161280, k: 1.233984
out: 7606397305424705536.000000
in: mu: 59152000.000000, sigma: 5.161280, k: 1.233984
out: 7606397305424828416.000000
in: mu: 59152000.000000, sigma: 5.161280, k: 1.233984
out: 7606397305424673792.000000
in: mu: 59152000.000000, sigma: 5.161280, k: 1.233984
out: 7606397305424859136.000000
in: mu: 70416000.000000, sigma: 5.222720, k: 1.326656
out: 7578470348372970496.000000
in: mu: 70416000.000100, sigma: 5.222720, k: 1.326656
out: 7578470348372838400.000000
in: mu: 70415999.999900, sigma: 5.222720, k: 1.326656
out: 7578470348373102592.000000
in: mu: 70416000.000000, sigma: 5.222720, k: 1.326656
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in: mu: 70416000.000000, sigma: 5.222720, k: 1.326656
out: 7578470348373049344.000000
in: mu: 70416000.000000, sigma: 5.222720, k: 1.326656
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in: mu: 70416000.000000, sigma: 5.222720, k: 1.326656
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in: mu: 83625600.000100, sigma: 5.301568, k: 1.448512
out: 7534808111447171072.000000
in: mu: 83625599.999900, sigma: 5.301568, k: 1.448512
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in: mu: 83625600.000000, sigma: 5.301568, k: 1.448512
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in: mu: 83625600.000000, sigma: 5.301568, k: 1.448512
out: 7534808111447434240.000000
in: mu: 83625600.000000, sigma: 5.301568, k: 1.448512
out: 7534808111447168000.000000
in: mu: 83625600.000000, sigma: 5.301568, k: 1.448512
out: 7534808111447493632.000000
in: mu: 99548800.000000, sigma: 5.405504, k: 1.611328
out: 7462459980226269184.000000
in: mu: 99548800.000100, sigma: 5.405504, k: 1.611328
out: 7462459980226067456.000000
in: mu: 99548799.999900, sigma: 5.405504, k: 1.611328
out: 7462459980226470912.000000
in: mu: 99548800.000000, sigma: 5.405504, k: 1.611328
out: 7462459980226128896.000000
in: mu: 99548800.000000, sigma: 5.405504, k: 1.611328
out: 7462459980226409472.000000
in: mu: 99548800.000000, sigma: 5.405504, k: 1.611328
out: 7462459980226049024.000000
in: mu: 99548800.000000, sigma: 5.405504, k: 1.611328
out: 7462459980226489344.000000
in: mu: 119721600.000000, sigma: 5.545792, k: 1.831488
out: 7335682285030593536.000000
in: mu: 119721600.000100, sigma: 5.545792, k: 1.831488
out: 7335682285030330368.000000
in: mu: 119721599.999900, sigma: 5.545792, k: 1.831488
out: 7335682285030857728.000000
in: mu: 119721600.000000, sigma: 5.545792, k: 1.831488
out: 7335682285030401024.000000
in: mu: 119721600.000000, sigma: 5.545792, k: 1.831488
out: 7335682285030787072.000000
in: mu: 119721600.000000, sigma: 5.545792, k: 1.831488
out: 7335682285030299648.000000
in: mu: 119721600.000000, sigma: 5.545792, k: 1.831488
out: 7335682285030888448.000000
in: mu: 146089600.000000, sigma: 5.738816, k: 2.125888
out: 7109687340138514432.000000
in: mu: 146089600.000100, sigma: 5.738816, k: 2.125888
out: 7109687340138159104.000000
in: mu: 146089599.999900, sigma: 5.738816, k: 2.125888
out: 7109687340138871808.000000
in: mu: 146089600.000000, sigma: 5.738816, k: 2.125888
out: 7109687340138252288.000000
in: mu: 146089600.000000, sigma: 5.738816, k: 2.125888
out: 7109687340138778624.000000
in: mu: 146089600.000000, sigma: 5.738816, k: 2.125888
out: 7109687340138131456.000000
in: mu: 146089600.000000, sigma: 5.738816, k: 2.125888
out: 7109687340138899456.000000
in: mu: 181724800.000000, sigma: 6.001984, k: 2.509888
out: 6715789274189170688.000000
in: mu: 181724800.000100, sigma: 6.001984, k: 2.509888
out: 6715789274188691456.000000
in: mu: 181724799.999900, sigma: 6.001984, k: 2.509888
out: 6715789274189648896.000000
in: mu: 181724800.000000, sigma: 6.001984, k: 2.509888
out: 6715789274188824576.000000
in: mu: 181724800.000000, sigma: 6.001984, k: 2.509888
out: 6715789274189514752.000000
in: mu: 181724800.000000, sigma: 6.001984, k: 2.509888
out: 6715789274188703744.000000
in: mu: 181724800.000000, sigma: 6.001984, k: 2.509888
out: 6715789274189635584.000000
in: mu: 229596800.000000, sigma: 6.347072, k: 2.975808
out: 6089944962517897216.000000
in: mu: 229596800.000100, sigma: 6.347072, k: 2.975808
out: 6089944962517286912.000000
in: mu: 229596799.999900, sigma: 6.347072, k: 2.975808
out: 6089944962518508544.000000
in: mu: 229596800.000000, sigma: 6.347072, k: 2.975808
out: 6089944962517478400.000000
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out: 6089944962518316032.000000
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out: 6089944962517384192.000000
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out: 6089944962518411264.000000
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out: 5231986152006437888.000000
in: mu: 290678400.000100, sigma: 6.765888, k: 3.489344
out: 5231986152005723136.000000
in: mu: 290678399.999900, sigma: 6.765888, k: 3.489344
out: 5231986152007153664.000000
in: mu: 290678400.000000, sigma: 6.765888, k: 3.489344
out: 5231986152005979136.000000
in: mu: 290678400.000000, sigma: 6.765888, k: 3.489344
out: 5231986152006896640.000000
in: mu: 290678400.000000, sigma: 6.765888, k: 3.489344
out: 5231986152005934080.000000
in: mu: 290678400.000000, sigma: 6.765888, k: 3.489344
out: 5231986152006942720.000000
in: mu: 362204800.000000, sigma: 7.224640, k: 3.993664
out: 4249761529871484416.000000
in: mu: 362204800.000100, sigma: 7.224640, k: 3.993664
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in: mu: 362204800.000000, sigma: 7.224640, k: 3.993664
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in: mu: 628122750.041916, sigma: 8.870386, k: 5.716777
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out: 1388825653141229312.000000
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$par
[1] 1.260397e+09 9.931107e+00 2.681267e+00

$value
[1] 1.941837e+17

$counts
function gradient 
      55       37 

$convergence
[1] 0

$message
NULL

Now we have parameters for gauss-function, plot it:

plot(y~x, data=tab, xlim=c(6, 30), xlab="password length", ylab="count passwords")
gauss_param = res[[1]]
plot(plot_f, col=2, add=T, xlim=range(tab$x))

Improving the R-model

Password length of 7 characters doesn’t seem to fit well into this model. Skipping lengths 6 and 7, begin analysis from 8 to improve accuracy:

tab <- data.frame(x=tail(x, -2), y=tail(y, -2))
(res <- optim(p.init, optimf, method="BFGS", control=list(reltol=1e-8, parscale = p.scaling)))

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$par
[1] 1.260489e+09 9.193810e+00 3.370517e+00

$value
[1] 3.684495e+16

$counts
function gradient 
      64       60 

$convergence
[1] 0

$message
NULL

Plot the new model (green) with old one (red):

orig_tab = data.frame(x, y)
plot(y~x, data=orig_tab, xlim=c(6, 30), xlab="password length", ylab="count passwords")
gauss_param = res[[1]]
plot(plot_res_f, col="green", add=T, xlim=c(6, 30))

gauss_param = c(1.260397e+09, 9.931107, 2.681267)
plot(plot_f, col=2, add=T, xlim=range(orig_tab$x))

Looking at the fit from password length 9 to 17 looks pretty solid. However, at 18 to 20 characters the model is still off. Sure it looks better now than with previous parameters, but is still off.

Now that there is a plausible model, extrapolate the password lenghts 21 to 30:

cat(sprintf("Len %2d: %d\n", (8:30), as.integer(plot_res_f((8:30)))), sep="")

Len  8: 1183852526
Len  9: 1258407109
Len 10: 1224942990
Len 11: 1091897186
Len 12: 891289463
Len 13: 666234247
Len 14: 456043522
Len 15: 285862234
Len 16: 164088609
Len 17: 86252410
Len 18: 41517882
Len 19: 18300810
Len 20: 7387144
Len 21: 2730574
Len 22: 924277
Len 23: 286498
Len 24: 81322
Len 25: 21138
Len 26: 5031
Len 27: 1096
Len 28: 218
Len 29: 40
Len 30: 6

From the table we can see the password lenght having a drastic impact on frequency.