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@mrmekon
Created February 16, 2012 18:55
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Data whitening (scrambling) with 9-bit LFSR
import sys
import os
import numpy
import random
import string
import matplotlib.pyplot as plt
#data = numpy.random.bytes(10000000)
data = [random.choice(string.printable) for x in xrange(1000000)]
#data = numpy.random.bytes(100)
#data = [5, 10, 15, 20, 100, 150, 200, 255, 0, 128, 177, 212, 200, 78, 79, 44, 57, 92, 7,12,123,211,109,120]
#data = [1,2,3,4, 0x1F, 0xFF, 0xA4]
#data = [0x1F, 0xFF, 0xA4] * 1000
#data = [0x0f, 0x00, 0x01, 0x02]
#data = [chr(x) for x in data]
def reversebits(word, numbits=8):
return sum(1<<(numbits-1-i) for i in range(numbits) if word>>i&1)
def lfsr_generator(count=8):
word = 0x1FF
while True:
yield word
for i in range(count):
bit = (word >> 5) ^ (word >> 0) & 1
outword = ((word >> 1) & 0xFF) | (bit << 8)
word = outword & 0x1FF
def lfsr(word, count=8):
word = word & 0x1FF
for i in range(count):
bit = (word >> 5) ^ (word >> 0) & 1
outword = ((word >> 1) & 0xFF) | (bit << 8)
word = outword & 0x1FF
return word
def testlfsr():
x = 0x1FF
for i in range(10):
print "%d: 0x%.4x\t%s" % (i, x, bin(x))
x = lfsr(x)
def lfsr_list(list, reverse=False, display=False):
xordata = []
xorval = 0x1FF
for x in list:
xorbyte = chr(ord(x) ^ (xorval & 0xFF))
if display:
print "0x%.2X ^ 0x%.2X == 0x%.2X" % (ord(x), xorval&0xFF, ord(xorbyte))
xordata.append(xorbyte)
xorval = lfsr(xorval)
return xordata
def check_restore(list):
print "Restore data"
restored = lfsr_list(list, True)
for idx in xrange(len(data)):
if ord(data[idx]) != ord(restored[idx]):
print "Mismatch on byte %d! 0x%.2x != 0x%.2x" % (idx, ord(data[idx]), ord(restored[idx]))
sys.exit(1)
print "Double XORed list okay."
def drawWhiteningPlots(millions=1, randfunc=random.gauss, *randargs):
if not randargs:
randargs = (0.5,.1)
data = [int(randfunc(*randargs)*255)%256 for i in xrange(int(1000000*millions))]
chrdata = [chr(x) for x in data]
xdata = lfsr_list(chrdata)
xdata = [ord(x) for x in xdata]
plt.subplot(2,1,1)
plt.hist(data, bins=256)
plt.xlabel('Byte')
plt.ylabel('Count')
plt.title("%.1f Million Random Bytes"%millions)
plt.subplot(2,1,2)
plt.hist(xdata, bins=256)
plt.xlabel('Byte')
plt.ylabel('Count')
plt.title("%.1f Million Whitened Bytes"%millions)
def maxBitRuns(list):
maxone = 0
sumone = 0
countone = 0
maxzero = 0
sumzero = 0
countzero = 0
bitcount = 0
lastbit = 0
for idx,char in enumerate(list):
byte = ord(char)
for i in range(7,-1,-1):
bit = byte & (1<<i) != 0
if bit != lastbit:
if (bitcount > 200):
print "WARNING: long bitcount at index %d (%d bits)" % (idx, bitcount)
print "%s" % [bin(ord(x)) for x in list[idx - bitcount/8 - 1:idx+1]]
print "%s" % [hex(ord(x)) for x in list[idx - bitcount/8 - 1:idx+1]]
if lastbit and bitcount > maxone:
maxone = bitcount
elif not lastbit and bitcount > maxzero:
maxzero = bitcount
if lastbit:
sumone += bitcount
countone += 1
else:
sumzero += bitcount
countzero += 1
bitcount = 1
else:
bitcount += 1
lastbit = bit
if lastbit and bitcount > maxone:
maxone = bitcount
elif not lastbit and bitcount > maxzero:
maxzero = bitcount
return (maxzero,maxone, float(sumzero)/countzero, float(sumone)/countone)
if __name__ == "__main__":
print "XOR data"
xordata = lfsr_list(data, display=False)
#check_restore(xordata)
print "Max bit runs in %d bytes" % len(data)
maxbits = maxBitRuns(data)
print "Max: %s" % str(maxbits)
print "Max bit runs in whitened data"
maxbits = maxBitRuns(xordata)
print "Max: %s" % str(maxbits)
plt.figure(1)
drawWhiteningPlots(0.25, random.gauss, 0.1,0.2)
plt.figure(2)
drawWhiteningPlots(0.25, random.expovariate, 1.0/0.5)
plt.figure(3)
drawWhiteningPlots(0.25, random.triangular, 0,1.0)
plt.figure(4)
drawWhiteningPlots(0.25, random.gauss, 0.5, 0.1)
plt.figure(5)
drawWhiteningPlots(0.25, random.lognormvariate, 0.3, 0.2)
plt.show()
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