Steganography in digital media

Word origin From Greek Steganos (covered) and graphia (writing) Steganography is sometimes called - Secret writing - Concealed writing - Covert communication - Stealth communication - Data hiding - Electronic invisible ink - The prisoners’ problem

Steganography ~470 B.C. First written evidence by Greek historian Herodotus. Term coined by Johannes Trithemius in 1499. Digital media provide ideal hideout. Steganography in its modern form is only ~15 years old.

Stego software

Stego software

Research Number of IEEE publications containing the keywords steganography or steganalysis.

Steganography The prisoners’ problem, Simmons (1983) Alice Bob 00101…1 encryption key Bob stego key 00101…1 00101…1 Compression Encryption Decryption Decompression Image source Communication is monitored by a warden looking for suspicious artifacts Cover object Stego-object Main requirement: Undetectability (no algorithm can decide about stego and cover objects with success better than random guessing) Warden: passive, active, malicious

Example of a steganographic channel Alice pretends that she wants to sell her sofa at the auction site eBay Secret message Buyer No. 10,000 Buyer No. 1 Buyer No. 2 … … … Secret message

Difference between steganography and cryptography Both are privacy tools involving keys that enable two or more parties communicate privately Crypto makes the message unintelligible to those not possessing the correct keys, but the existence of secret message is obvious (overt) Stego conceals the very presence of message (covert), the communicated object is just a decoy.

Three fundamental types of steganography 1. Steganography by cover selection Sender selects a cover from a large set of available covers so that the required message is communicated. 2. Steganography by cover synthesis Sender creates the cover that communicates the desired message. 3. Steganography by cover modification Sender modifies an existing cover in order to convey the required message.

1. Steganography by cover selection Secret shared codebook A picture in landscape format means “yes”, portrait format means “no” If picture contains an animal, attack tomorrow. Red T-shirt means 0, yellow 1,… Steganography by hashing Apply a pre-agreed message digest function (could depend on a key) to the cover and search for a cover till the digest matches the message. The recipient hashes the image to extract the message. Advantage: The cover is “100% natural” Disadvantage: Low payload, is it really secure?

2. Steganography by cover synthesis Alice creates the cover Mimic functions SpamMimic (www.spammimic.com) encodes a message to resemble spam. Acrostics (linguistic steganography) “Apparently neutral's protest is thoroughly discounted and ignored. Isman hard hit. Blockade issue affects pretext for embargo on byproducts, ejecting suets and vegetable oils”. “Amorosa Visione” by Giovanni Boccaccio (1313–1375) contains three sonnets and poems, such that the initial letters of successive tercets correspond exactly to the sonnets. Cardan’s grille (1501–1576)

3. Steganography by cover modification Assume there are three sets C … set of all cover objects K … set of all keys M … set of all messages that can be communicated A steganographic embedding scheme is a pair of embedding and extraction functions Emb and Ext such that m c Emb Ext s … m k k

The problem of steganography We wish to embed as many bits in the cover object without introducing any statistically detectable artifacts. Statistical undetectability (no one should be able to tell whether an image contains secret message) -- can be formalized using Information Theory

A tip of an iceberg? Dhiren Barot, an Al Qaeda operative filmed reconnaissance video between Broadway and South Street and concealed it by splicing it into a copy of the Bruce Willis movie "Die Hard: With a Vengeance." Barot was sentenced to 40-to-life in Great Britain. NY Times article available from http://www.nytimes.com/2006/11/08/world/europe/08britain.html?th&emc=th (Requires registration) Steganography program S-Tools was used to distribute child porn. This case occurred between 1998 and 2000.  A person working at a government facility was using S-Tools to hide child porn in images and then distributing them through e-mail and postings from his work computer. Steganography was detected by identifying color patterns in the GIF palette. The suspect was confronted the embedded images were retrieved. Source: Neil Johnson, 2006 and N.F. Johnson and S. Jajodia, “Steganalysis of Images Created Using Current Steganography Software,” in D. Aucsmith (ed.): Information Hiding. 2nd International Workshop, LNCS vol.1525, Springer-Verlag Berlin Heidelberg, pp. 273289, 1998.

June 19, 2001

Schwarzenegger’s letter

Considerable interest from Government and law enforcement Major US agencies funding research in steganography – US Air Force and AFOSR – National Institute of Justice (NIJ) – Office of Naval Research (ONR) – National Science Foundation (NSF) – Defense Advanced Research Project Agency (DARPA) Steganalysis is considered part of Computer Forensics Important for protection against malware Tools developed for steganalysis find applications in Digital Forensics in general (e.g., for detection of digital forgeries and integrity and origin verification)

Steganalysis in the wide sense Traditional steganalysis: a steganography system is considered broken, when the mere presence of a hidden message is detected Forensic analysis: detection of the message may not be sufficient; often, other information would be useful identification of the embedding algorithm (LSB, ±1, …) the stego software used (F5 , OutGuess, Steganos, …) the stego key (StegoSuite © by Wetstones, Inc.) the hidden bit-stream the decrypted message

LSB embedding and its analysis

LSB embedding Embedding function Emb (Matlab syntax) c = imread(‘my_decoy_image.bmp’); % Grayscale cover image in BMP format % ‘b’ is a vector of m bits (secret message) k = 1; % Counter for i = 1 : 512 for j = 1 : 512 LSB = mod(c[i, j], 2); if LSB = b[k] | k  m s[i, j] = c[i, j]; else s[i, j] = c[i, j] + b[k] – LSB; end k = k + 1; imwrite(s, ‘stego_image.bmp’, ‘bmp’); % Stego image ‘s’ saved to disk

LSB embedding Extraction function Ext (Matlab syntax) s = imread(‘stego_image.bmp’); % Grayscale stego image in BMP format k = 1; for i = 1 : 512 for j = 1 : 512 if k  m b[k] = mod(s[i, j], 2); k = k + 1; end % b is the extracted secret message

Why is LSB embeddig so popular? General (can be applied to any digital file consisting of numerical data) Extremely simple Fast High capacity (1 bit per pixel, embedding efficiency 2) Does not require any software present on the computer One command line in UNIX Perl script (source: A. Ker, Oxford University): perl -n0777e ’$_=unpack"b*",$_;split/(\s+)/,<STDIN>,5; @_[8]=~s{.}{$&&v254|chop()&v1}ge;print@_’ <input.pgm >output.pgm secrettextfile LSB plane of images resembles random noise  this method was believed to be undetectable.

LSB plane of Lenna LSB bit plane of a never-compressed Lenna image.

Properties of LSB flipping LSBflip(x) = x + 1 – 2(x mod 2) FlipLSB(x) is idempotent, e.g., LSBflip(LSBflip(x)) = x for all x LSB flipping induces a permutation on {0, …, 255} 0  1, 2  3, 4  5, …, 254  255 LSB flipping is “asymmetrical” (e.g., 3 may change to 2 but never to 4) | LSB(x) – x | = 1 for all x (embedding distortion is 1 per pixel)

Effect of LSB embedding on histogram LSB flipping pair 2i, 2i+1 hc [2i] = number of occurrences of the value 2i in the cover image hc [2i+1] = number of occurrences of the value 2i + 1 in the cover image hs [2i+1] hc [2i+1] parts untouched by embedding hc [2i] hs [2i] 2i 2i+1 2i 2i+1 For a fully embedded image: hs [2i] = (hc [2i] + hc [2i+1])/2 hs [2i+1] = (hc [2i] + hc [2i+1])/2

“Twin peaks” in the histogram The peaks can be tested for using a chi-square test By looking at the histogram of pixel pairs, an even more accurate attack can be built (Sample Pairs Analaysis – SPA).

EECE 562 Fundamentals of Steganography Cambridge University Press, November 2009, 460 pages, $68 on Amazon.