Bitspotting: Detecting optimal adaptive steganography

We analyze a two-player zero-sum game between a steganographer, Alice, and a steganalyst, Eve. In this game, Alice wants to hide a secret message of length in a binary sequence, and Eve wants to detect whether a secret message is present. The individual positions of all binary sequences are independently distributed, but have different levels of predictability. Using knowledge of this distribution, Alice randomizes over all possible size-subsets of embedding positions. Eve uses an optimal (possibly randomized) decision rule that considers all positions, and incorporates knowledge of both the sequence distribution and Alice's embedding strategy. Our model extends prior work by removing restrictions on Eve's detection power. The earlier work determined where Alice should hide the bits when Eve can only look in one position. Here, we expand Eve's capacity to spot these bits by allowing her to consider all positions. We give defining formulas for each player's best response strategy and minimax strategy; and we present additional structural constraints on the game's equilibria. For the special case of length-two binary sequences, we compute explicit equilibria and provide numerical illustrations.