A novel anti-collusion coding scheme tailored to track linear collusions

Abstract

A set of semi-fragile watermarks W <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fr</sub> = {V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,.., V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> } can be used as building blocks for constructing any digital fingerprint. One such family, is obtained by modulating the sign bits alone of selective DCT-AC coefficients, where, each V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> represents the positions of a disjoint subset of modulated coefficients. We show that a linear collusion of K < n sign fingerprinted images neatly translates into a majority bit vote of K corresponding binary strings and in this binary output, 'I' represents survival of a particular block V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> and '0' its erasure. By design, each block V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> is unperturbed by specific collusion patterns and so by facilitating complementary coverage of each newly added block V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j+1</sub> , a compact anti-collusion code (ACC)for tracking linear collusions can be constructed.