Towards Optimum Counterforensics of Multiple Significant Digits Using Majorisation-Minimisation

Optimum counterforensics of the first significant digits entails a forger minimally modifying a forgery in such a way that its first significant digits follow some preselected authentic distribution, e.g., Benford’s law. A solution to this problem based on the simplex algorithm was put forward by Comesa Optimum counterforensics of the first significant digits entails a forger minimally modifying a forgery in such a way that its first significant digits follow some preselected authentic distribution, e.g., Benford’s law. A solution to this problem based on the simplex algorithm was put forward by Comesana and Perez-Gonzalez. However their approach requires scaling up the dimensionality of the original problem. As simplex has exponential worst-case complexity, simplex implementations can struggle to cope with medium to large scale problems. These computational issues get compounded by upscaling the problem dimensionality. Furthermore, Benford’s law applies beyond the first significant digit, but no counterforensics method to date offers a solution to handle an arbitrary number of significant digits. As the use of simplex would only aggravate the computational issues in this case, we propose a more scalable approach to counterforensics of multiple significant digits informed by the Majorisation-Minimisation optimisation philosophy.