In [34]:
%matplotlib inline
from compare_bmp import compare_images
from PIL import Image, ImageFilter
from matplotlib.pyplot import imshow
import numpy as np
import sys
import textwrap
We'll start with this image:
In [35]:
# let's get our message set up
message = list('this is a message')
# convert to binary representation
message = ['{:07b}'.format(ord(x)) for x in message]
print(message)
# split the binary into
message = [[bit for bit in x] for x in message]
print(message)
# flatten it and convert to integers
message = [int(bit) for sublist in message for bit in sublist]
print(message)
originalMessage = message
['1110100', '1101000', '1101001', '1110011', '0100000', '1101001', '1110011', '0100000', '1100001', '0100000', '1101101', '1100101', '1110011', '1110011', '1100001', '1100111', '1100101']
[['1', '1', '1', '0', '1', '0', '0'], ['1', '1', '0', '1', '0', '0', '0'], ['1', '1', '0', '1', '0', '0', '1'], ['1', '1', '1', '0', '0', '1', '1'], ['0', '1', '0', '0', '0', '0', '0'], ['1', '1', '0', '1', '0', '0', '1'], ['1', '1', '1', '0', '0', '1', '1'], ['0', '1', '0', '0', '0', '0', '0'], ['1', '1', '0', '0', '0', '0', '1'], ['0', '1', '0', '0', '0', '0', '0'], ['1', '1', '0', '1', '1', '0', '1'], ['1', '1', '0', '0', '1', '0', '1'], ['1', '1', '1', '0', '0', '1', '1'], ['1', '1', '1', '0', '0', '1', '1'], ['1', '1', '0', '0', '0', '0', '1'], ['1', '1', '0', '0', '1', '1', '1'], ['1', '1', '0', '0', '1', '0', '1']]
[1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1]
In [36]:
# hamming (7,4)
# able to detect/correct for single-bit error
# cut up message to 4 bit sections to encode
def cut(msg, encode):
# check how to cut message:
# if encode = 1, cut into 4s
# if encode = 0, cut into 7s
if encode == 1:
# check if divisible by 4, if not add buffer 0s to front
if len(msg) % 4 != 0:
left = 4 - (len(msg) % 4)
msg = left * '0' + msg
# slice message into 4 bit chunks
chunks = textwrap.wrap(msg, 4)
# run hamming for each chunk
retval = []
for group in chunks:
# create list of the values for matrix multiplication
val = []
for ch in str(group):
val.append(int(ch))
retval.append(hamming(np.mat(val)))
return retval
if encode == 0:
# slice message into 7 bit chunks
chunks = textwrap.wrap(msg, 7)
# run decode for each chunk
retval = []
for goup in chunks:
retbal.append(decode(msg))
return retval
def hamming(sub_msg):
# create parity bits using transition matrix
transition = np.mat('0,1,1,1,0,0,0;1,0,1,0,1,0,0;1,1,0,0,0,1,0;1,1,1,0,0,0,1')
result = sub_msg * transition
# mod 2 the matrix multiplication
return mod(result)
def decode(msg):
# organize msg into 1-column matrix
val = []
for ch in str(msg):
val.append([int(ch)])
msg = np.mat(val)
# decoding matrix
transition = np.mat('1,0,0,0,1,1,1;0,1,0,1,0,1,1;0,0,1,1,1,0,1')
result = transition * msg
# mod 2 the matrix multiplication
return mod(result)
def mod(msg):
# reshape matrix to list
msg = list(np.array(msg).reshape(-1,))
# mod 2 matrices b/c binary
for i in range(len(msg)):
if msg[i] % 2 == 1:
msg[i] = 1
elif msg[i] % 2 == 0:
msg[i] = 0
return msg
#print(msg)
if len(sys.argv) <= 2:
print('Wrong inputs. Example: hamming_code.py 1011 1')
else:
hammingMsg = cut(''.join([str(bit) for bit in message]), 1)
# first arg is message, second is either 1 or 0 - 1 means encoding, 0 means decoding
message = [int(bit) for sublist in hammingMsg for bit in sublist]
#print(message)
In [37]:
# first, open the original image and hide a message in it
imgpath = 'images/original/image.bmp'
img = Image.open(imgpath)
# we'll use simple repetition as a very rudimentary ECC to try to maintain integrity
# each bit of the message will be repeated 6 times - the two LSBs of the R,G, and B values of one pixel
#imgArray = np.copy(np.asarray(img))[:1]
imgArray = list(np.asarray(img))
def set_bit(val, bitNo, bit):
""" given a value, which bit in the value to set, and the actual bit (0 or 1) to set, return the new value """
mask = 1 << bitNo
val &= ~mask
if bit:
val |= mask
return val
msgIndex = 0
newImg = []
for row in imgArray:
newRow = []
for pixel in row:
newPixel = []
for val in pixel:
# iterate through RGB values, one at a time
#print(bin(r))
if msgIndex >= len(message):
setTo = 0
else:
setTo = message[msgIndex]
val = set_bit(val, 0, setTo)
val = set_bit(val, 1, setTo)
val = set_bit(val, 2, setTo)
# check to make sure that the last 3 bits are the same thing - should not be mixed
"""if not '{:08b}'.format(val)[5:] == '000' and not '{:08b}'.format(val)[5:] == '111':
print('{:08b}'.format(val)[5:])
raise ValueError('stuff broke')"""
newPixel.append(val)
msgIndex += 1
newRow.append(newPixel)
newImg.append(newRow)
arr = np.array(newImg, np.uint8)
im = Image.fromarray(arr)
im.save("image_steg.bmp")
How does the image look now?
Awesome! Doesn't look like anything's wrong.
In [38]:
# now let's blur the image to destroy some data
blurredpath = 'image_blurred.bmp'
img = Image.open("image_steg.bmp")
blurred = img.copy().filter(ImageFilter.BLUR)
blurred.save(blurredpath)
And here it is now that we've blurred it:
In [39]:
# last, open the image and apply our ECC strategy to see if the message made it through
blurredImg = Image.open(blurredpath)
imgArray = list(np.asarray(blurredImg))
origMessage = message[:20]
print(origMessage)
message = []
for val in imgArray[0][:20]:
print([bin(x) for x in val])
for row in imgArray:
for pixel in row:
count = {"0": 0, "1": 0}
for val in pixel:
# iterate through RGB values of the pixel, one at a time
# convert the R, G, or B value to a byte string
byte = '{:08b}'.format(val)
# then, for each of the last n bits...
for i in [-1, -2, -3]:
# try to get an actual 1 or 0 integer from it
try:
bit = int(byte[i])
except:
print(bin(val))
raise
# sum up the bits we've seen
if bit == 0:
count["0"] += 1
elif bit == 1:
count["1"] += 1
else:
print("WAT")
# and once we've seen them all, decide which we should go with
if count["1"] > count["0"]:
message.append(1)
else:
message.append(0)
print(message[:20])
[1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0]
['0b11101111', '0b11101111', '0b11101111']
['0b11101000', '0b11101000', '0b11101000']
['0b11101000', '0b11110000', '0b11101000']
['0b11101000', '0b11110000', '0b11101000']
['0b11101111', '0b11110111', '0b11101111']
['0b11101111', '0b11101111', '0b11101111']
['0b11101111', '0b11101111', '0b11101111']
['0b11101111', '0b11110111', '0b11100111']
['0b11101000', '0b11110000', '0b11101000']
['0b11110111', '0b11110111', '0b11101111']
['0b11110000', '0b11110000', '0b11101000']
['0b11110111', '0b11110111', '0b11101111']
['0b11110000', '0b11110000', '0b11101000']
['0b11110000', '0b11110000', '0b11101000']
['0b11110000', '0b11110000', '0b11101000']
['0b11110000', '0b11110000', '0b11101000']
['0b11110111', '0b11110111', '0b11110111']
['0b11110111', '0b11110111', '0b11110111']
['0b11110111', '0b11110111', '0b11110111']
['0b11110000', '0b11110000', '0b11110000']
[1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0]
In [40]:
from math import floor
# let's see what the message says!
outputMessage = []
originalMessage = list('this is a message')
originalMessage = [ord(x) for x in originalMessage]
for i in range(floor(len(message)/7)):
start = i * 7
# this is gross
char = message[start:start+7]
char = '0b' + ''.join([str(c) for c in char])
#print(char)
outputMessage.append(int(char, 2))
print(originalMessage)
print(outputMessage)
print("ORIGINAL VS. OUTPUT")
print("===================")
print(''.join([chr(c) for c in originalMessage]))
print(''.join([chr(c) for c in outputMessage]))
[116, 104, 105, 115, 32, 105, 115, 32, 97, 32, 109, 101, 115, 115, 97, 103, 101]
[71, 84, 29, 113, 90, 71, 73, 90, 0, 29, 19, 108, 29, 0, 54, 113, 84, 113, 43, 71, 98, 127, 19, 14, 71, 56, 71, 19, 14, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 56, 83, 7, 127, 101, 127, 25, 75, 95, 15, 0, 4, 0, 44, 61, 64, 31, 127, 115, 124, 61, 102, 34, 0, 16, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 64, 62, 63, 12, 0, 6, 4, 15, 1, 124, 0, 96, 31, 127, 0, 60, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 55, 60, 16, 0, 0, 126, 63, 127, 96, 0, 29, 109, 11, 71, 79, 0, 15, 16, 27, 78, 0, 63, 123, 127, 124, 15, 127, 84, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 79, 53, 120, 31, 112, 65, 112, 0, 63, 115, 126, 3, 127, 9, 32, 30, 6, 0, 0, 0, 62, 0, 0, 0, 0, 0, 0, 0, 2, 64, 36, 63, 72, 0, 0, 7, 126, 1, 127, 126, 2, 15, 0, 109, 0, 0, 3, 124, 52, 127, 0, 3, 111, 79, 71, 35, 102, 64, 56, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 64, 0, 0, 28, 47, 125, 126, 56, 14, 0, 0, 1, 68, 126, 64, 63, 83, 124, 16, 32, 0, 0, 7, 96, 0, 0, 0, 0, 0, 0, 0, 40, 0, 32, 8, 0, 15, 127, 127, 0, 127, 112, 31, 117, 64, 15, 121, 24, 31, 67, 126, 39, 96, 0, 3, 127, 115, 127, 91, 98, 127, 3, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 1, 49, 73, 120, 64, 0, 32, 0, 0, 1, 0, 7, 121, 3, 0, 63, 76, 24, 3, 2, 3, 4, 28, 0, 0, 0, 0, 0, 29, 64, 0, 0, 0, 0, 0, 62, 104, 16, 15, 1, 57, 111, 96, 96, 78, 127, 127, 127, 97, 121, 127, 121, 64, 0, 127, 65, 67, 127, 0, 120, 0, 0, 0, 0, 0, 2, 1, 89, 112, 15, 0, 0, 5, 3, 64, 0, 3, 52, 0, 0, 0, 0, 0, 0, 115, 86, 0, 7, 127, 0, 0, 0, 0, 115, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 60, 0, 31, 12, 15, 112, 7, 127, 119, 64, 60, 64, 0, 95, 64, 1, 31, 127, 127, 111, 126, 0, 15, 0, 0, 0, 0, 0, 0, 126, 0, 1, 25, 64, 16, 0, 0, 88, 15, 127, 123, 95, 0, 56, 0, 0, 0, 0, 0, 20, 60, 0, 1, 112, 24, 8, 0, 4, 96, 0, 0, 0, 0, 0, 32, 0, 64, 0, 0, 3, 104, 65, 64, 1, 7, 20, 0, 1, 7, 127, 98, 0, 0, 0, 56, 3, 96, 2, 0, 0, 56, 2, 56, 62, 0, 0, 0, 0, 0, 0, 48, 56, 62, 64, 19, 0, 0, 0, 3, 112, 4, 0, 6, 112, 0, 127, 1, 0, 0, 0, 0, 63, 64, 0, 1, 127, 54, 31, 1, 16, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 15, 0, 28, 0, 16, 125, 76, 0, 11, 120, 110, 7, 112, 127, 127, 0, 16, 0, 127, 120, 16, 0, 3, 115, 0, 0, 0, 0, 0, 0, 4, 10, 0, 31, 127, 55, 64, 0, 0, 31, 127, 63, 127, 31, 127, 112, 15, 106, 32, 0, 0, 0, 56, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 124, 0, 0, 0, 37, 2, 97, 64, 15, 120, 65, 17, 108, 2, 15, 0, 3, 1, 127, 126, 15, 64, 0, 0, 111, 124, 48, 0, 0, 0, 0, 0, 0, 0, 1, 96, 0, 0, 31, 40, 124, 0, 0, 13, 127, 1, 126, 96, 7, 95, 6, 127, 127, 127, 126, 7, 0, 0, 0, 4, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 102, 127, 127, 112, 127, 96, 2, 32, 3, 127, 120, 64, 49, 8, 31, 0, 48, 0, 0, 3, 126, 0, 0, 3, 114, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 15, 124, 7, 127, 127, 64, 0, 0, 3, 67, 127, 124, 29, 67, 95, 96, 0, 0, 31, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 121, 112, 0, 0, 15, 31, 67, 31, 115, 0, 30, 5, 99, 79, 31, 112, 0, 0, 0, 0, 3, 127, 127, 127, 64, 32, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63, 62, 48, 0, 22, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 56, 17, 30, 30, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 64, 0, 31, 127, 31, 97, 109, 32, 4, 96, 31, 120, 13, 111, 0, 30, 0, 0, 0, 0, 0, 0, 0, 3, 123, 127, 105, 62, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 2, 14, 119, 126, 16, 0, 0, 14, 15, 127, 119, 127, 64, 1, 60, 31, 115, 95, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 64, 99, 112, 0, 0, 0, 2, 0, 9, 124, 104, 126, 33, 0, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 104, 26, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 96, 0, 30, 17, 113, 0, 0, 0, 64, 14, 49, 67, 127, 120, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 3, 96, 0, 126, 7, 112, 3, 71, 31, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63, 125, 0, 0, 0, 0, 0, 0, 0, 0, 24, 64, 0, 2, 0, 5, 112, 66, 8, 0, 0, 96, 32, 0, 0, 0, 0, 63, 127, 103, 127, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 79, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 104, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 40, 1, 14, 0, 64, 4, 0, 10, 16, 0, 0, 0, 0, 0, 0, 16, 0, 127, 63, 121, 126, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 96, 0, 0, 0, 0, 0, 0, 31, 64, 0, 1, 0, 63, 113, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 64, 0, 0, 0, 0, 0, 0, 0, 1, 112, 16, 7, 68, 1, 96, 120, 8, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 12, 0, 127, 0, 96, 20, 64, 24, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 127, 127, 127, 64, 0, 96, 0, 115, 126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0, 0, 0, 0, 0, 3, 11, 24, 63, 127, 28, 64, 0, 0, 0, 48, 64, 0, 0, 0, 0, 0, 0, 0, 12, 61, 127, 115, 101, 115, 32, 120, 0, 0, 0, 0, 0, 16, 0, 9, 0, 0, 0, 0, 0, 0, 0, 4, 127, 64, 0, 0, 30, 126, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 67, 126, 7, 96, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 12, 61, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 1, 112, 1, 48, 127, 126, 0, 3, 49, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 64, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 0, 63, 64, 63, 3, 0, 0, 0, 111, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 127, 0, 0, 0, 0, 0, 0, 0, 0, 16, 6, 0, 0, 0, 0, 0, 3, 127, 124, 3, 17, 123, 126, 2, 6, 126, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 126, 127, 127, 64, 68, 0, 0, 8, 114, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 6, 0, 0, 0, 0, 0, 0, 0, 96, 14, 0, 0, 0, 0, 0, 3, 33, 30, 0, 32, 0, 52, 127, 15, 23, 103, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 15, 96, 0, 63, 96, 0, 0, 1, 24, 0, 1, 65, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 92, 0, 0, 127, 41, 12, 7, 120, 0, 48, 0, 0, 0, 0, 0, 1, 127, 127, 48, 0, 0, 0, 0, 0, 0, 0, 2, 96, 0, 0, 1, 0, 3, 3, 127, 64, 0, 24, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 96, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 7, 120, 60, 62, 120, 63, 127, 0, 0, 92, 15, 0, 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27, 71, 43, 62, 94, 98, 72, 23, 60, 112, 8, 91, 112, 20, 27, 53, 3, 45, 31, 84, 92, 1, 78, 18, 46, 86, 109, 48, 88, 28, 119, 105, 24, 5, 72, 90, 111, 56, 122, 91, 83, 97, 51, 7, 110, 8, 29, 73, 34, 17, 18, 8, 31, 63, 28, 36, 100, 14, 2, 5, 106, 86, 76, 17, 13, 5, 82, 4, 122, 74, 21, 79, 8, 62, 10, 23, 103, 98, 90, 96, 51, 43, 2, 76, 59, 13, 34, 25, 107, 108, 112, 68, 103, 39, 65, 87, 72, 13, 51, 86, 120, 46, 66, 79, 71, 66, 49, 61, 31, 9, 99, 68, 8, 93, 116, 125, 42, 98, 48, 64, 0, 41, 15, 119, 103, 103, 92, 15, 90, 34, 112, 56, 63, 121, 55, 6, 23, 100, 71, 113, 46, 103, 74, 120, 15, 84, 11, 43, 105, 50, 49, 23, 13, 62, 92, 14, 119, 55, 68, 75, 66, 88, 14, 27, 2, 60, 111, 57, 65, 13, 81, 120, 67, 27, 98, 91, 77, 79, 107, 4, 14, 15, 111, 23, 11, 18, 47, 86, 53, 86, 118, 9, 17, 90, 10, 18, 41, 127, 40, 82, 49, 16, 7, 73, 77, 64, 65, 93, 33, 48, 89, 35, 27, 111, 27, 103, 58, 122, 10, 31, 86, 126, 56, 33, 58, 89, 97, 16, 55, 88, 94, 91, 113, 4, 106, 75, 37, 92, 119, 105, 101, 35, 47, 99, 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ORIGINAL VS. OUTPUT
===================
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Content source: DakotaNelson/discrete-stego
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