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klg.passwordEntropy
Raw
README
klg.passwordEntropy
===================
1. Motivation
Provision of password strength checker integrated into user interface can
easily guide users in choosing stronger passwords. It can not substitute
strict password policy but it should make passwords harder to crack on
average without frustrating users (like strict policies do).
Currently there are two kinds of strength checkers in use. Most common ones
simply check whether supplied password adheres to usual guidelines and score
them with length, number of "special" characters, etc. Their main advantage
is simplicity and that they can prune off really bad passwords when properly
calibrated. They are, however, hardly useful for users who do follow all
the guidelines.
Those of another kind assume some information-theoretic model of passwords
and then try to estimate probability of given password being generated by the
source with this model. This is usually reported as log probability in bits
and is called password "entropy" (note that outside this scope term entropy
usually associated with expected value of information contained in message
coming from source but here it is used to denote information content of a
single given message/password).
There exist only few strength checkers of the later kind and most of them
are unnecessarily complicated, require huge amount of data to describe model
and/or don't give satisfying results anyway. They also often make some
unlikely assumptions that result in confusing estimates. It is especially
annoying when appending another character to a password results in lower
strength estimate even though it is not a dictionary password.
This program is of the later kind and tries to be less annoying than others
by providing well motivated upper estimate of password entropy. It will often
give higher values than other of this kind but that is because it gives
correct upper estimate. For the obvious reason we would prefer to have the
lower estimate but it is in general not possible. Other checkers of this kind
often ignore some of the information content making their results possibly
closer to real value but completely unreliable.
Because I aimed for simplicity in design of this strength checker, it will
assign high entropy values to sufficiently long passwords even if those are
simple patterns or dictionary words, therefore it might be sane to couple
its output with simple scoring system that would warn about those.
2. Model
Estimation of information content is closely related to data compression and,
provided that model string given to this estimator is correctly built, values
computed with it are equal to length in bits of output of hypothetical lossless
compressor of the PPM kind with arithmetically coded output. This is a bit
unusual compressor because it uses static precomputed model and therefore can
efficiently code short strings like passwords and it doesn't have to deal with
zero frequency problem (too often).
Model used here consist of conditional probabilities of certain bytes coming
after number of bytes that form a context. Multiple lengths of contexts are
used simultaneously. If there is no match in longer context, a shorter one
is tried. Of course, upon switching to shorter context one has to emit an
escape sequence signifying this. Because a precomputed model is used, it is
not an unexpected event at all and there exist a good estimate of its
probability.
Actual zero frequency problem is encountered only when there is no match in
zero order context, i.e. given byte really never appears in the model.
Therefore when single byte is to be encoded without any context, it is first
determined whether it is a known byte or not with Laplace's rule of succession
then a byte is encoded either using known probabilities or assuming that all
unknown values are equiprobable. This should never happen if model was
carefully generated from representative sample.
3. Technical details
3.1. Formula for entropy estimation
All values used in computation are log probabilities (in bits, i.e. with base
2) of certain events. Password is first converted to UTF-8 (model must also
be computed for UTF-8 byte streams) and then cost of encoding each byte is
calculated and sum for all bytes is returned as an estimate of information
content.
Each n-tuple of bytes (a[1],a[2],...,a[n]) in model is associated with two
probabilities:
1. P(s[0]=a[n] | s[-1]=a[n-1], s[-2]=a[n-2], ...)
Probability that next byte after context (a[1],a[2],...,a[n-1]) is a[n].
2. P((a[1],...,a[n],x) in model) for any x
Probability that there is NO longer match than this tuple.
The second value should not be zero as mentioned earlier because some longer
tuples that have appeared during creation of model might be omitted because
they were too rare to be included. Otherwise some non-zero value must be
chosen (zero would result in infinite entropy), but this should be negligibly
rare.
To calculate probability of given byte b[0] appearing after all the previous
bytes b[-k],...,b[-1] is calculated as follows:
1. If the tuple (b[-k],...,b[-1],b[0]) exist in model, then the first of
mentioned probabilities is returned.
2. Otherwise get the second probability of tuple (b[-k],...,[b-1]) or one
if this tuple also is not in model.
(Note: value of 1, corresponds to zero bits, that is no cost, because lack
of these tuples in model implies that we know that context MUST be shorter).
3. Decrement k, i.e. try to match the shorter context.
Repeat until match is found.
4. Multiply all the probabilities (or equivalently add log probabilities) of
shortening the context and probability of the tuple finally found.
If there is no match longer than two, i.e. single byte without context must
be encoded, additionally amend its probability with the probability of this
byte being known in model calculated from the Laplace's rule of succession.
Initially assume that all known values occurred once.
3.2. Model format
Actual model is separated from the rest of the code to make it easy to update
it. It is encoded in a single alphanumeric string and it is formatted in a way
that allows using it directly to get required values without having to use a
lot of additional memory to create searchable structure. Additional index is
created, however, to facilitate searches in presence of run-length coded
exclusions. Although reasonably concise representation is used, string is not
compressed and it could be easily further compacted. It is encoded using only
"safe" ASCII characters so it can be easily put directly into ECMAScript
source as well as be embedded directly in SGML or XML document without
additional escaping.
Since each byte can take values only in range 0-255, it is easy to enumerate
all (a[1],...,a[n]) tuples using integers in form of sum a[i]*256^(n-i).
Each tuple is then stored in aforementioned string in order starting from
zeroth tuple. Many tuples will intentionally be omitted from the model so
continuous runs of excluded tuples are encoded only with run length. All
excluded tuples are assumed to have infinitesimal probability and that it's
certain that there are no longer matches. If given tuple is included in
model, all of its prefixes also should be included.
Because ECMAScript uses IEEE 754 doubles for its only numeric type, it is
advisable not to use tuples longer than 6 because their indices might not
be representable (all integers are representable up to 2^53).
Each tuple included in model is encoded as two unsigned floating point values
representing two log probabilities associated with it. Each value takes
exactly two characters (so information about each included tuple is encoded
using 4 ASCII characters) each encodes 6 raw bits.
Floating point values used have raw length of 12 bits with 3 bit exponent and
10 bit mantissa (9 explicitly encoded). Exponent bias is 3 and neither NaNs
nor infinity is supported, thus normal values range from 0.25 to 31.96875
(the highest value of exponent is used to encode normal values instead of
Inf and NaN as in IEEE 754). Minimal subnormal value is about 5e-4.
Therefore typical log probabilities of single bytes are encoded with
reasonable precision.
3.3. Generation of model
As mentioned above, model is basically an association between a pair of log
probabilities and tuple of bytes. This is a very simple, yet powerful model
that allows describing many of sources efficiently. The ECMAScript part that
only uses precomputed model is very simple and accuracy of its estimates
depends only on the model string it is given.
There are probably many ways to generate a model and I can not assert that
one I used is better than others possible, but just for reference I provide
tools written in Lua to show working example of generating valid model string.
To use them, a representable dictionary of passwords must be assembled in
format where each line contains one UTF-8 encoded password optionally preceded
by decimal count and *exactly* one space (note that passwords may contain
spaces at beginning). All tuples are extracted from it and counted.
This can be done with contexts.lua followed by sort and merge.lua.
Some kind of pruning must be then applied in order to reduce size of the model.
Pruning is a crucial part of generating model and quality of final product
greatly depends on it. It can be done in many ways and I provide no script
for that. Use awk, grep, sort, head, etc. The easiest way is simple to
ignore existence of all the tuples that have count below some threshold (see
the limit parameter of splitmakedata.lua script).
Two probabilities mentioned earlier are calculated from counts as:
(1) P(ab|a) = count(ab) / count(a)
(2) P(no b such that ab in model | a) = (count(a) - sum b: count(ab)) / count(a)
There is no problem when (1) is zero because checker with simply try shorter
matches as described before, but (2) can not be zero. If it is zero, above
formulae are multiplied by a term that comes from Laplace's rule of succession:
(2) P(no b after a) = 1 / (count(a) + 2)
(1) P(ab|a) = count(ab) / count(a) * (count(a) + 1) / (count(a) + 2)
The second change (in (1)) affects all the suffixes of a, not just the a tuple.
It must be made in order to ensure that appropriate probabilities add up to 1.
Those calculations are done by splitmakedata.lua which creates output in
intermediate format cat be assembled into single string by splitmergedata.lua.
Script splitmergedata.lua can consume concatenated output from multiple
sources (e.g. you can use splitmakedata.lua with different count limit for
different tuple lengths or even use different dictionaries). It must however
get all the required data to make a consistent model. If you mess up with
this, either of last two scripts will die on assertion. Otherwise a model
string ready to use with password strength checker is created.
In short, the simplest pipeline is as follows:
$ cat dict | contexts.lua | LC_ALL=C sort -k2 | merge.lua \
| splitmakedata.lua 1 4 1000 | splitmergedata.lua > model.js
4. License
This program is free software. It comes without any warranty, to
the extent permitted by applicable law. You can redistribute it
and/or modify it under the terms of the Do What The Fuck You Want
To Public License, Version 2, as published by Sam Hocevar. See
http://sam.zoy.org/wtfpl/COPYING for more details.
Raw
contexts.lua
#!/usr/bin/env lua
-- contexts.lua [-c] [-length]
-- Read a dictionary, one word in a line (-c preceded by count separated by
-- single space) and count occurrences of all of the substrings (not longer
-- than given value, default 7). Beginning of a word is marked with 0xff
-- byte which should never appear in valid UTF-8 byte stream. Each line of
-- output contains count, single space, and substring (bytes, not characters).
-- Single substring may appear more than once in output because of memory
-- constraints.
-- limit memory usage
local MAXKEYS = 2^20
local maxlen = 7
local parse = function(ln) return 1, ln end
-- configure
for k, v in ipairs(arg) do
if v == "-c" then -- with counts
parse = function(ln)
return ln:match("^ *([0-9.]+) (.+)$")
-- return ln:match("^ *([0-9]+) (.+)$")
end
elseif v:match("^-([0-9]+)$") then
maxlen = tonumber(v:sub(2))
end
end
local data = {}
local n, k = 0, 0
local function outdat()
-- sort to speed up later merges
local t, i = {}, 0
for k, v in pairs(data) do
t[i] = k
i = i + 1
end
table.sort(t)
for j, k in ipairs(t) do
if data[k] >= 1 then
print(string.format("%9d %s", data[k], k))
end
end
end
local function adddat(ctx, cnt)
assert(#ctx <= maxlen)
assert(#ctx > 0)
if data[ctx] then
data[ctx] = data[ctx] + cnt
else
n = n + 1
-- [[
if n > MAXKEYS then
outdat()
data = {}
n = 0
io.stderr:write "\rWarning: Premature output. Merge required. \x1b[K\n"
collectgarbage()
end
--]]
data[ctx] = cnt
end
end
assert(maxlen > 1 and maxlen < 2^53)
for ln in io.lines() do
local count, context = parse(ln)
if context then
if context:sub(#context) == "\r" then
context = context:sub(1,#context-1)
end
context = "\xff" .. context -- prepend start of text marker
count = tonumber(count)
if #context >= 2 then
for i = 1, #context-maxlen+1 do
for j = i, i+maxlen-1 do
adddat(context:sub(i,j), count)
end
end
for i = math.max(1,#context-maxlen+1), #context do
for j = i, #context do
adddat(context:sub(i,j), count)
end
end
end
k = k + 1
if k % 8147 == 0 then
io.stderr:write(string.format("\r%d => %d\x1b[K", k, n))
end
end
end
outdat()
io.stderr:write(string.format("\r%d => %d.\x1b[K\n", k, n))
Raw
demo.html
<!DOCTYPE html>
<meta charset="utf-8">
<title>klg.passwordEntropy demo</title>
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.8.0/jquery.min.js"></script>
<script type="text/ecmascript" src="passwordModel.js"></script>
<script type="text/ecmascript" src="passwordEntropy.js"></script>
<script type="text/ecmascript">
jQuery(function($){
"use strict";
var d2f = function(x) {
var f = Math.round(100*x)%100;
return Math.floor(x) + (f<10?".0":".") + f;
};
var rg = function(x) {
if (x < 0) x = 0; else if (x > 1) x = 1;
var a,b,c,d;
// rat. fun. approx. of red-green geodesic
a = 18.8686; b = 2.21763;
c = 401.943; d = 650.562;
a *= x; b *= x; c *= x; d *= x;
a += 20.3168; b += 30.2787;
c += 19.1898; d -= 675.851;
a *= x; b *= x; c *= x; d *= x;
a += 1.45626; b += 8.00815;
c -= 447.809; d -= 304.904;
a *= x; b *= x; c *= x; d *= x;
b += 0.13718; c -= 251.399;
d -= 94.2593; c *= x; d *= x;
c -= 441.895; d -= 285.105;
c *= x; d *= x;
c += 719.97; d += 719.97;
a /= b; a *= 255; a |= 0;
c /= d; c *= 255; c |= 0;
return "rgb("+c+","+a+",0)";
};
// get a model string and create a strength checker function
var entropy = klg.passwordEntropy(klg.passwordModel);
// create GUI
var ent, bpc, bar, input;
var update;
$("#demo")
.empty()
.append($("<div>Password:</div>"))
.append(input = $(document.createElement("input"))
.css({width:"200px",borderWidth:"1px",padding:0,margin:0})
.prop({type:"password"})
.keyup(update = function() {
var p = $(this).val();
var s = entropy(p);
ent.text(d2f(s));
bpc.text(p ? d2f(s / p.length) : "-");
bar.css({
"width": Math.round(Math.atan(s/96)*400/Math.PI)+"px",
"border-color": rg(s/256)
});
})
.click(update))
.append($(document.createElement("label"))
.append($(document.createElement("input"))
.prop({type:"checkbox",checked:true})
.change(function() {
input.prop("type", this.checked ? "password" : "text")
}))
.append($(document.createTextNode(" hide"))))
.append(bar = $(document.createElement("div"))
.css({width:0,border:"2px solid red",padding:0,margin:0}))
.append($(document.createElement("div"))
.append(ent = $(document.createElement("span"))
.css({display:"inline-block",minWidth:"7ex",textAlign:"right"}))
.append(document.createTextNode(" bits")))
.append($(document.createElement("div"))
.append(bpc = $(document.createElement("span"))
.css({display:"inline-block",minWidth:"7ex",textAlign:"right"}))
.append(document.createTextNode(" bpc")));
ent.text(d2f(0));
bpc.text("-");
bar.css({"border-width":"2px 0"});
});
</script>
<div id="demo">Javascript required</div>
Raw
encode.lua
-- Utilities used to encode (and decode) model data
do
-- Common routines
local bit = bit32 or bit or require "bit"
local bsub, bfind
do
local base = "+/0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
assert(#base == 2^6)
bsub = function(x)
assert(x >= 0 and x < 2^6)
return base:sub(x+1,x+1)
end
bfind = function(x,i)
assert(type(x) == "string")
return base:find(string.sub(x,i,i),1,true)-1
end
end
-- ASCII-encoded unsigned floating point type
-- Exponent length: 3 bits (bias 3, no Inf/NaN, range: -2 to +4)
-- Mantissa: 10 bits (9 explicitly stored)
-- Minimal normal value: 0.25, subnormal: 0.00048828125
-- Maximal value: 31.96875
local flencode, fldecode
do
flencode = function(x)
assert(x == x)
assert(x >= 0)
local e, s
if x > (1+(1-2^-9))*2^4 then -- ~Inf
e, s = 4, 2^9-1
else
e = math.floor(math.log(x)/math.log(2))
if e < -11 then
-- zero
e, s = -3, 0
elseif e < -2 then
-- subnormal
e, s = -3, math.floor(x * 2^11 + 0.5)
else
-- normal
s = math.floor((x / 2^e - 1) * 2^9 + 0.5)
end
if s >= 512 then
-- fix conversion round-offs
s, e = 0, e+1
end
end
return bsub(bit.lshift(bit.band(e+3, 0x7), 3) +
bit.band(bit.rshift(s, 6), 0x7)) ..
bsub(bit.band(s, 0x3f)), e, s
end
fldecode = function(str)
local a, b = bfind(str, 1), bfind(str, 2)
local e, s = bit.rshift(a, 3), bit.lshift(bit.band(a, 0x7), 6) + b
if e == 0 then
if s == 0 then
return 0
else
return s / 2^11
--return math.ldexp(s, -11)
end
else
return 2^(e-3) * (1 + s / 2^9)
--return math.ldexp(1 + math.ldexp(s, -9), e-3)
end
end
end
-- Run length code
-- Runs of 1 to 8 encoded with single byte, longer with multi-byte
-- sequence of arbitrary length (highest bit signifies where does it end)
local rlencode, rldecode
do
local base = "!#%,:;=@_"
rlencode = function(x)
if x < #base then
return base:sub(x,x)
else
x = x - #base
if x == 0 then
return "_" .. bsub(0)
end
local s = ""
s = bsub(x % 32) .. s
x = math.floor(x / 32)
while x > 0 do
x = x - 1
s = bsub(32 + (x % 32)) .. s
x = math.floor(x / 32)
end
return "_" .. s
end
end
rldecode = function(str)
local x = base:find(str:sub(1,1),1,true)
if x == #base then
local k, q = 2
x = 0
while true do
x = x * 32
q = bfind(str, k)
if bit.band(q, 32) == 0 then
return x + q + #base
else
x = x + q - 31
end
k = k + 1
end
end
return x
end
end
return {
rlencode = rlencode,
rldecode = rldecode,
flencode = flencode,
fldecode = fldecode,
flmax = fldecode "ZZ"
}
end
Raw
merge.lua
#!/usr/bin/env lua
-- merge.lua
-- Merge multiple occurrences of the same contexts as output by contexts.lua.
-- Similarly to uniq tool, input must be sorted by context. Don't forget to
-- set LC_ALL=C when sorting with POSIX-compatible sort(1)!
local last = {}
for c in io.lines() do
local cnt, ctx = c:match("^ *([0-9.]+) (.+)$")
if ctx then
-- cnt = tonumber(cnt)
if ctx ~= last.ctx then
if last.ctx then
print(string.format("%9d %s",
last.cnt, last.ctx))
end
last.ctx = ctx
last.cnt = cnt
else
last.cnt = last.cnt + cnt
end
end
end
print(string.format("%9d %s",
last.cnt, last.ctx))
Raw
passwordEntropy.js
(function(klg) {
"use strict";
var Model = (function() {
var FLOAT_SIZE = 2;
var CELL_VALUES = 2;
var CELL_SIZE = CELL_VALUES*FLOAT_SIZE;
var ZERO = [Number.POSITIVE_INFINITY, 0];
// Utility routines required to decode model data
var decoder = (function() {
// ASCII conversion table
var base = function() {
var a = new (typeof Uint8Array != "undefined" ? Uint8Array : Array)(256);
var b = "+/0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";
var c = "!#%,:;=@_";
var i;
for (i = 0; i < a.length; i++) a[i] = -1;
for (i = 0; i < b.length; i++) a[b.charCodeAt(i)] = i;
for (i = 0; i < c.length; i++) a[c.charCodeAt(i)] = i+1;
return a;
} ();
// Decode unsigned s10e3 float
var decfloat = function(str, i) {
if (i !== undefined) this.lastIndex = i;
var s = base[str.charCodeAt(this.lastIndex++) & 0xff];
var e = s >>> 3; s &= 7; s <<= 6;
s |= base[str.charCodeAt(this.lastIndex++) & 0xff];
if (e == 0) {
if (s == 0) return 0;
return s / (1<<11); // subnormal
}
// normal
return (1+s/(1<<9)) * Math.pow(2,e-3);
};
// Decode length of zero run
var decrle = function(str, i) {
if (i !== undefined) this.lastIndex = i;
var x = base[str.charCodeAt(this.lastIndex++)];
if (x < 9)
return x;
x = 0;
while (this.lastIndex < str.length) {
var q = base[str.charCodeAt(this.lastIndex++)];
x *= 32;
if ((q & 0x20) == 0)
return x + q + 9;
x += q - 31;
}
throw "Unexpected end of string";
};
return {
decfloat: decfloat,
decrle: decrle,
lastIndex: 0
};
})();
// Find zero runs and prepare index
var makeIndex = function(data) {
var a = [], b = [];
var k = 0, p = 0;
var re = new RegExp("[!#%,:;=@_]","g");
var rx = re.exec(data);
if (!rx || rx.index)
a.push([0,0], b = [0,0,0]);
if (rx)
do {
var z = [0,0], y = [0,0,0];
k += (rx.index - p) / CELL_SIZE;
z[0] = k;
b[1] = k - 1;
k += decoder.decrle(data, rx.index);
y[0] = k;
z[1] = k - 1;
y[2] = p = decoder.lastIndex;
a.push(z,y);
b = y;
} while ((rx = re.exec(data)) != null);
b[1] = k - 1 + (data.length-p) / CELL_SIZE;
return a;
};
// Get data from model for n-th context
var getData = (function() {
var read = function(data, at) {
var a = new Array(CELL_VALUES);
decoder.lastIndex = at;
for (var i = 0; i < CELL_VALUES; i++)
a[i] = decoder.decfloat(data);
return a;
};
return function(dat, idx, n) {
var i, dn = 0, up = idx.length-1;
if (n < 0 || n > idx[up][1])
return ZERO;
for (;;) {
i = Math.floor((dn+up)/2);
if (n < idx[i][0]) { up = i - 1; continue; }
if (n > idx[i][1]) { dn = i + 1; continue; }
if (i & 1)
return read(dat, idx[i][2] + CELL_SIZE*(n - idx[i][0]));
else
return ZERO;
}
};
})();
// Convert tuple to its index
var t2i = function(a) {
var i, k = 0;
for (i = 0; i < a.length; i++)
k *= 256, k += a[i];
return k;
};
// Model constructor
return function(data) {
var index = makeIndex(data);
this.ZERO = ZERO;
this.CELL_VALUES = CELL_VALUES;
this.get = function(tuple) {
return getData(data, index, t2i(tuple));
};
// known part of alphabet
this.ALPHABET = (function() {
var s = "";
for (var i = 0; i < 256; i++)
if (getData(data,index,i) != ZERO)
s += String.fromCharCode(i);
return s;
})();
// how many bits to waste for encoding of unknown bytes
this.unknownBits = Math.log((this.ALPHABET.length < 224 ? 224 : 256)
- this.ALPHABET.length) / Math.log(2);
// maximal known tuple length
this.length = Math.ceil(Math.log(index[index.length-1][1])/Math.log(256));
this.reset = function() {
this.n = this.ALPHABET.length;
this.k = this.ALPHABET.length;
};
this.reset();
};
})();
var Cache = function() {
var data = {};
var size = 2048;
var k = 0;
var timer;
this.setMinSize = function(length) {
return size = length > size ? length : size;
};
this.set = function(x, y) {
return (data[x] = [k++,y])[1];
};
this.get = function(x) {
if (data[x] === undefined)
return undefined;
data[x][0] = k++;
return data[x][1];
};
this.clean = function() {
var a = [], k = 0;
for (var i in data)
if (data.hasOwnProperty(i))
a[k++] = [data[i][0], i];
if (a.length > size) {
a.sort(function(a,b) { return a[0]-b[0]; });
if (a.length > size)
for (k = 1; k < size-a.length; k++)
delete data[a[k][1]];
}
};
};
// Convert string to array of UTF-8 bytes
var utf8array = function(s) {
var i, k, uc, lo;
var utf8bin = [];
for (i = 0; i < s.length; i++) {
uc = s.charCodeAt(i);
if (uc >= 0xD800 && uc < 0xE000) {
if (uc >= 0xDC00)
throw "Unpaired surrogate at "+i;
lo = s.charCodeAt(++i);
if (lo < 0xDC00 || lo >= 0xE000)
throw "Unpaired surrogate at "+i;
uc = 0x400*(uc-0xD800) + (lo-0xDC00) + 0x10000;
}
if (uc == 0xFFFE || uc == 0xFFFF)
throw "Non-character at "+i;
k = (uc < 0x00000080) ? 0 :
(uc < 0x00000800) ? 1 :
(uc < 0x00010000) ? 2 :
(uc < 0x00200000) ? 3 :
(uc < 0x04000000) ? 4 : 5;
utf8bin.push( [0x00, 0xC0, 0xE0, 0xF0, 0xF8, 0xFC][k] ^ (uc >> 6*k) );
while (k--) utf8bin.push( 0x80 ^ (uc >> 6*k) & 0x3F );
}
return utf8bin;
};
// Find log probability of last byte in context
var endlogp = function(tuple, model) {
var x, s = 0;
while (tuple.length > 1) {
if ((x = model.get(tuple)) !== model.ZERO) {
return s += x[0];
}
// fall back to lower order
s += model.get(tuple.slice(0,tuple.length-1))[1];
tuple = tuple.slice(1);
};
// single byte without context
if ((x = model.get(tuple)) !== model.ZERO) {
s += Math.log( (model.n+2) / (model.k+1) ) / Math.log(2);
s += x[0];
model.k++;
}
else {
s += Math.log( (model.n+2) / (model.n-model.k+1) ) / Math.log(2);
s += model.unknownBits;
}
model.n++;
return s;
};
// Memoize
endlogp = (function(endlogp) {
return function(tuple, model) {
var key = tuple + "\x01" + String((model.n+2)/(model.n-model.k+1));
var x = model.cache.get(key);
if (x !== undefined) {
model.n = x[1];
model.k = x[2];
return x[0];
}
x = endlogp(tuple, model);
model.cache.set(key, [x, model.n, model.k]);
return x;
};
})(endlogp);
// Find log probability of whole string
var entropy = function(bytes, model) {
var s = 0;
model.cache.setMinSize(bytes.length);
bytes.unshift(0xff); // start of string context
for (var i = 2; i <= bytes.length; i++) {
var tuple = bytes.slice(0,i);
if (tuple.length > model.length)
tuple = tuple.slice(tuple.length-model.length, tuple.length);
s += endlogp(tuple, model);
}
setTimeout(function(){ model.cache.clean(); }, 0);
return s;
};
// Crate estimator function from given model
return klg["passwordEntropy"] = function(data) {
var model = new Model(data);
model.cache = new Cache();
return function(password) {
model.reset();
return entropy(utf8array(password), model);
};
};
})(typeof module !== "undefined" && module.exports || window.klg || (window.klg = {}));
Raw
passwordModel.js
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Raw
splitmakedata.lua
#!/usr/bin/env lua
-- splitmakedata.lua min max [limit]
-- Read context counts and calculate conditional probabilities of [2]
-- last byte appearing in context of previous ones, and [3] of longer
-- context not being known (see code for details), for all of the contexts
-- of length between min and max (and with count not lower than limit).
-- Input MUST contain also counts for contexts of min-1 length.
-- Output is an intermediate form that should be given to splitmergedata.lua.
local min = tonumber(arg[1])
local max = tonumber(arg[2])
local limit = tonumber(arg[3])
if not min or not max or max < min then
io.stderr:write("Usage "..arg[0].." min max [limit]\n")
os.exit(-1)
end
min = math.floor(min)
max = math.floor(max)
-- [1] raw count
-- [2] P of last byte in context of all preceding in tuple
-- [3] P that there are no longer matches
local cx = {}
for ln in io.lines() do
local count, context = ln:match("^ *([0-9]+) (.+)$")
if context and #context >= min-1 and #context <= max then
count = tonumber(count)
if limit == nil or count >= limit then
cx[context] = {count, -1, 0}
end
end
end
local function log2p(a,b)
return math.log(b / a) / math.log(2)
end
-- Singletons (absolute probabilities, not conditional)
if min < 2 then
local sum1 = 0
for context, data in pairs(cx) do
if #context == 1 and context ~= "\xff" then
sum1 = sum1 + data[1]
end
end
for context, data in pairs(cx) do
if #context == 1 then
data[2] = log2p(data[1], sum1)
end
end
end
-- Calculate [2] and count suffixes
for context, data in pairs(cx) do
if #context >= min and #context > 1 then
local prefix = context:sub(1,#context-1)
if not cx[prefix] then -- FIXME: DEBUG
io.stderr:write("No prefix «"..prefix.."»\n")
end
assert(cx[prefix])
data[2] = log2p(data[1], cx[prefix][1])
cx[prefix][3] = cx[prefix][3] + data[1]
end
end
-- Ignore singleton tuple of start of string marker
-- (it should be present in longer contexts but never by itself)
cx["\xff"] = nil
-- Prune unused data
for context, data in pairs(cx) do
if #context < min and data[3] == 0 then
cx[context] = nil
end
end
-- Calculate [3] and adjust [2] when needed
for context, data in pairs(cx) do
local nx = data[1] - data[3]
if nx > 0 then
data[3] = log2p(nx, data[1])
else
-- zero-freq., use Laplace's rule of succession
data[3] = log2p(1, data[1]+2)
local fix = log2p(data[1]+1, data[1]+2)
-- adjust suffixes to ensure that P adds up to 1.
for k, v in pairs(cx) do
if #k == #context + 1 and k:sub(1,#context) == context then
v[2] = v[2] + fix
end
end
end
end
local o = require "tupleorder"
local e = require "encode"
-- Output intermediate data
for context, data in pairs(cx) do
local n = o.t2i(context)
if n < 2^53 then
if data[2] == -1 then
data[2] = "--"
else
data[2] = e.flencode(data[2])
end
data[3] = e.flencode(data[3])
print(string.format("%2s%2s %d %s",
data[2], data[3], n, context))
end
end
Raw
splitmergedata.lua
#!/usr/bin/env lua
-- splitmergedata.lua
-- Read concatenated partial models as generated with splitmakedata.lua and
-- merge them producing a model string that can be used with klg.passwordEntropy.
-- Output is a nicely formatted Javascript source.
local e = require "encode"
local cx = {}
for ln in io.lines() do
local p1, p2, n = ln:match("^%s*(..)(..)%s(%d+)")
if n then
local p2f = e.fldecode(p2)
n = tonumber(n)
if cx[n] == nil then
cx[n] = { p1, p2, p2f }
else
if cx[n][1] == "--" then
cx[n][1] = p1
elseif p1 ~= "--" and p1 ~= cx[n][1] then
error "Inconsistent model"
end
if cx[n][3] < p2f then
cx[n][2] = p2
cx[n][3] = p2f
end
end
end
end
local sx = {}
for i, dat in pairs(cx) do
if dat[1] == "--" then
io.stderr:write(string.format(
"Warning: Model incomplete. Unknown probability for tuple %d.\n", i))
else
table.insert(sx, i)
end
end
table.sort(sx)
local last = -1
local str = ""
io.write("// Generated "..os.date().."\n")
io.write("(window.klg || (window.klg = {})).passwordModel =\n")
for _, k in ipairs(sx) do
if k - last > 1 then
str = str .. e.rlencode(k-last-1)
end
str = str .. cx[k][1]
str = str .. cx[k][2]
last = k
if #str > 77 then
io.write('"', str:sub(1, 77), '"+\n')
str = str:sub(78)
end
end
io.write('"', str, '";\n')
Raw
tupleorder.lua
-- Implicit indexes of tuples (number<->string conversion)
do
local function t2i(s)
local i = 0
for k = 1, #s do
i = i * 256 + s:byte(k)
end
return i
end
local function i2t(i)
local a = {0}
if i < 256 then
return string.char(i)
elseif i > 1 then
local k = math.ceil(math.log(i+.5)/math.log(256))
while i > 0 do
a[k] = i % 256
i = math.floor(i / 256)
k = k - 1
end
end
return string.char(unpack(a))
end
return {
t2i = t2i,
i2t = i2t
}
end
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