Secure fingerprint embedding based on modified GDFT based parametric transform

Fractional Discrete Fourier Transforms (DFT) offer a secret frequency domain in which digital fingerprints can be concealed for traitor tracing. However transforms directly based on DFT have an oscillatory period of 4, which limits the key space to a real number in the interval [0,4]. By introducing a perturbation parameter in the Generalized DFT (GDFT) kernel, it can be converted into an invertible but non-orthogonal transform whose eigenvalues do not all have a modulus of unity. This desynchronizing effect expands the key space considerably. The overall secure fingerprinting system in conjunction with the anti-collusion coding scheme was found to be sensitive to linear and non-linear fusion operations while remaining robust to several basic signal processing attacks.