Steganalysis of Stegostorage Library

The main goal of this research is the detection of the secret messages hidden in JPEG files, which were embedded by StegoStorage library. This tool allows the user to embed any type of information into a folder of images. Sequential, pseudo-random or Hamming code-based embedding into the least significant bit (LSB) of DCT coefficients is possible. It is possible to choose what fraction of capacity of the cover files are filled. The aim of this contribution is to test the statistical LSB embedding model (modified weighted-stego analysis) for all modes of embedding which StegoStorage library offers, and for all cover files’ capacities, respectively. Another goal is to implement a more appropriate type of steganalytic attack for Hamming codes and test it. For this purpose, the RS (Regular/Singular) steganalysis was selected. The detectability of the LSB embedding model of sequential embedding is possible if the cover files are filled to at least one percent of capacity. In the case of pseudo-random embedding, the secret message can be detected if the cover files are filled to at least 10% of their capacity. Hamming codes were undetectable using this type of an attack. In the case of attack by RS steganalysis, another situation arose. When sequential or pseudo-random embeddings were used, the results indicated the detectability was possible if the cover files were filled up at least 5 percent of capacity. The capacity filling of 5 percent corresponds to 2.5 percent of DCT coefficient changes from the original media in the case of sequential embedding. This value, 2.5%, is the threshold for the utilization of Hamming codes, too. Therefore, Hamming codes (7, 4), (15, 11) and (32, 26) indicated the detectability, because they exceeded that limit.

Bayesian Optimization in a Billion Dimensions via Random Embeddings

Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesian optimization have identified its scaling to high-dimensions as one of the holy grails of the field. In this paper, we introduce a novel random embedding idea to attack this problem. The resulting Random EMbedding Bayesian Optimization (REMBO) algorithm is very simple, has important invariance properties, and applies to domains with both categorical and continuous variables. We present a thorough theoretical analysis of REMBO. Empirical results confirm that REMBO can effectively solve problems with billions of dimensions, provided the intrinsic dimensionality is low. They also show that REMBO achieves state-of-the-art performance in optimizing the 47 discrete parameters of a popular mixed integer linear programming solver.

Limit theorems for the number of successes in random binary sequences with random embeddings

The sequence of

Random Walks on Quasirandom Graphs

Let $G$ be a quasirandom graph on $n$ vertices, and let $W$ be a random walk on $G$ of length $\alpha n^2$. Must the set of edges traversed by $W$ form a quasirandom graph? This question was asked by Böttcher, Hladký, Piguet and Taraz. Our aim in this paper is to give a positive answer to this question. We also prove a similar result for random embeddings of trees.