1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
|
/*
* Copyright (c) 2014, Yawning Angel <yawning at torproject dot org>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
package obfs4
import (
"container/list"
"fmt"
"math/rand"
"github.com/yawning/obfs4/csrand"
"github.com/yawning/obfs4/drbg"
)
const (
minValues = 1
maxValues = 100
)
// wDist is a weighted distribution.
type wDist struct {
minValue int
maxValue int
values []int
weights []float64
alias []int
prob []float64
}
// newWDist creates a weighted distribution of values ranging from min to max
// based on a HashDrbg initialized with seed.
func newWDist(seed *drbg.Seed, min, max int) (w *wDist) {
w = &wDist{minValue: min, maxValue: max}
if max <= min {
panic(fmt.Sprintf("wDist.Reset(): min >= max (%d, %d)", min, max))
}
w.reset(seed)
return
}
// genValues creates a slice containing a random number of random values
// that when scaled by adding minValue will fall into [min, max].
func (w *wDist) genValues(rng *rand.Rand) {
nValues := (w.maxValue + 1) - w.minValue
values := rng.Perm(nValues)
if nValues < minValues {
nValues = minValues
}
if nValues > maxValues {
nValues = maxValues
}
nValues = rng.Intn(nValues) + 1
w.values = values[:nValues]
}
// genBiasedWeights generates a non-uniform weight list, similar to the
// ScrambleSuit prob_dist module.
func (w *wDist) genBiasedWeights(rng *rand.Rand) {
w.weights = make([]float64, len(w.values))
culmProb := 0.0
for i := range w.values {
p := (1.0 - culmProb) * rng.Float64()
w.weights[i] = p
culmProb += p
}
}
// genUniformWeights generates a uniform weight list.
func (w *wDist) genUniformWeights(rng *rand.Rand) {
w.weights = make([]float64, len(w.values))
for i := range w.weights {
w.weights[i] = rng.Float64()
}
}
// genTables calculates the alias and prob tables used for Vose's Alias method.
// Algorithm taken from http://www.keithschwarz.com/darts-dice-coins/
func (w *wDist) genTables() {
n := len(w.weights)
var sum float64
for _, weight := range w.weights {
sum += weight
}
// Create arrays $Alias$ and $Prob$, each of size $n$.
alias := make([]int, n)
prob := make([]float64, n)
// Create two worklists, $Small$ and $Large$.
small := list.New()
large := list.New()
scaled := make([]float64, n)
for i, weight := range w.weights {
// Multiply each probability by $n$.
p_i := weight * float64(n) / sum
scaled[i] = p_i
// For each scaled probability $p_i$:
if scaled[i] < 1.0 {
// If $p_i < 1$, add $i$ to $Small$.
small.PushBack(i)
} else {
// Otherwise ($p_i \ge 1$), add $i$ to $Large$.
large.PushBack(i)
}
}
// While $Small$ and $Large$ are not empty: ($Large$ might be emptied first)
for small.Len() > 0 && large.Len() > 0 {
// Remove the first element from $Small$; call it $l$.
l := small.Remove(small.Front()).(int)
// Remove the first element from $Large$; call it $g$.
g := large.Remove(large.Front()).(int)
// Set $Prob[l] = p_l$.
prob[l] = scaled[l]
// Set $Alias[l] = g$.
alias[l] = g
// Set $p_g := (p_g + p_l) - 1$. (This is a more numerically stable option.)
scaled[g] = (scaled[g] + scaled[l]) - 1.0
if scaled[g] < 1.0 {
// If $p_g < 1$, add $g$ to $Small$.
small.PushBack(g)
} else {
// Otherwise ($p_g \ge 1$), add $g$ to $Large$.
large.PushBack(g)
}
}
// While $Large$ is not empty:
for large.Len() > 0 {
// Remove the first element from $Large$; call it $g$.
g := large.Remove(large.Front()).(int)
// Set $Prob[g] = 1$.
prob[g] = 1.0
}
// While $Small$ is not empty: This is only possible due to numerical instability.
for small.Len() > 0 {
// Remove the first element from $Small$; call it $l$.
l := small.Remove(small.Front()).(int)
// Set $Prob[l] = 1$.
prob[l] = 1.0
}
w.prob = prob
w.alias = alias
}
// reset generates a new distribution with the same min/max based on a new seed.
func (w *wDist) reset(seed *drbg.Seed) {
// Initialize the deterministic random number generator.
drbg := drbg.NewHashDrbg(seed)
rng := rand.New(drbg)
w.genValues(rng)
//w.genBiasedWeights(rng)
w.genUniformWeights(rng)
w.genTables()
}
// sample generates a random value according to the distribution.
func (w *wDist) sample() int {
var idx int
// Generate a fair die roll from an $n$-sided die; call the side $i$.
i := csrand.Intn(len(w.values))
// Flip a biased coin that comes up heads with probability $Prob[i]$.
if csrand.Float64() <= w.prob[i] {
// If the coin comes up "heads," return $i$.
idx = i
} else {
// Otherwise, return $Alias[i]$.
idx = w.alias[i]
}
return w.minValue + w.values[idx]
}
/* vim :set ts=4 sw=4 sts=4 noet : */
|