tailieunhanh - Lecture Steganography: Naive steganography - Ho Dac Hung

Lecture Steganography: Naive steganography has contents such as LSB embedding and steganography in palette images. Download this lecture to see more. | Naive steganography Ho Dac Hung 1 Contents LSB embedding Steganography in palatte images 2 1. LSB embedding Arguably LSB embedding is the simplest steganographic algorithm. It can be applied to any collection of numerical data represented in digital form. 3 1. LSB embedding Let us assume that 0 1 2 2 1 is a sequence of integers. Depending on the image format and the bit depth chosen for representing the individual values each can be represented using nc bits 1 2 -2 1 4 1. LSB embedding LSB embedding as its name suggests works by replacing the LSBs of - with the message bits - obtaining in the process the stego image -. 5 1. LSB embedding Path Perm n y x m min m n for i 1 to m y Path i x Path i m i x Path i mod 2 6 1. LSB embedding Path Perm n for i 1 to m m i y Path i mod 2 7 1. LSB embedding The amplitude of changes in LSB embedding is 1. because natural images contain a small amount of noise due to various noise sources present during image acquisition the LSB plane of raw never-compressed natural images already looks random. 8 1. LSB embedding 9 1. LSB embedding The data are consistent with the claim that the LSB plane is random. Even though this is not a proof of randomness the argument is convincing enough to make us intuitively believe that any attempts to detect the act of randomly flipping a subset of bits from the LSB plane are doomed to fail. This seemingly intuitive claim is far from truth because LSB embedding in images can be very reliably detected. 10 1. LSB embedding Even if the LSB plane of covers was truly random it may still be possible to detect embedding changes due to flipping LSBs if for example the second LSB plane b i nc 1 and the LSB plane were somehow dependent In the most extreme case of dependence if b i nc 1 b i nc for each i detecting LSB changes would be trivial. All we would have to do is to compare the LSB plane with the second LSB plane. 11 1. LSB embedding The embedding operation of flipping the LSB can be written mathematically