We present an implementation that turns out to be most efficient in practice to compute singular moduli within a fixed floating point precision. First, we show how to efficiently determine the Fourier coefficients of the modular function j and related functions γ2, f2, and η. Comparing several alternative methods for computing singular moduli, we show that in practice the computation via the η-...

Consider an i.i.d. sequence of random variables whose distribution f lies in one of a nested family of models (Mq)q∈N, Mq ⊂ Mq+1. The smallest index q such that Mq⋆ contains f is called the model order. We establish strong consistency of the penalized likelihood order estimator in a general setting with penalties of order η(q) log log n, where η(q) is a dimensional quantity. Moreover, such pena...

This paper gives an overview of cryptographically strong mass application invisibility in digital communication. It summarizes principles and methodology, clariies terminology, and deenes some new concepts. A new algorithm for hiding bit selection in digital images is proposed and an experimental implementation of the algorithm is described. Finally, the paper closes with a discussion of the im...