Sebastian Berndt

Hard Communication Channels for Steganography.

This paper considers steganography - the concept of hiding the presence of secret messages in legal communications - in the computational setting and its relation to cryptography. Very recently the first (non-polynomial time) steganographic protocol has been shown which, for any communication channel, is provably secure, reliable, and has nearly optimal bandwidth. The security is unconditional, i.e. it does not rely on any unproven complexity-theoretic assumption. This disproves the claim that the existence of one-way functions and access to a communication channel oracle are both necessary and sufficient conditions for the existence of secure steganography in the sense that secure and reliable steganography exists independently of the existence of one-way functions. In this paper, we prove that this equivalence also does not hold in the more realistic setting, where the stegosystem is polynomial time bounded. We prove this by constructing (a) a channel for which secure steganography exists if and only if one-way functions exist and (b) another channel such that secure steganography implies that no one-way functions exist. We therefore show that security-preserving reductions between cryptography and steganography need to be treated very carefully.

Computing Tree Width: From Theory to Practice and Back

While the theoretical aspects concerning the computation of tree width – one of the most important graph parameters – are well understood, it is not clear how it can be computed practically. As tree width has a wide range of applications, e. g. in bioinformatics or artificial intelligence, this lack of understanding hinders the applicability of many important algorithms in the real world. The Parameterized Algorithms and Computational Experiments (PACE) challenge therefore chose the computation of tree width as one of its challenge problems in 2016 and again in 2017. In 2016, Hisao Tamaki (Meiji University) presented a new algorithm that outperformed the other approaches (including SAT solvers and branch-and-bound) by far. An implementation of Tamaki’s algorithm allowed Larisch (King-Abdullah University of Science and Engineering) and Salfelder (University of Leeds) to solve over 50% of the test suite of PACE 2017 (containing graphs with over 3500 nodes) in under six seconds (and the remaining 50% in under 30 min). Before PACE 2016, no algorithm was known to compute tree width on graphs with about 100 nodes. As a wide range of parameterized algorithms require the computation of a tree decomposition as a first step, this breakthrough result allows practical implementations of these algorithms for the first time.

Using Structural Properties for Integer Programs.

Integer programs (IPs) are one of the fundamental tools used to solve combinatorial problems in theory and practice. Understanding the structure of solutions of IPs is thus helpful to argue about the existence of solutions with a certain simple structure, leading to significant algorithmic improvements. Typical examples for such structural properties are solutions that use a specific type of variable very often or solutions that only contain few non-zero variables. The last decade has shown the usefulness of this method. In this paper we summarize recent progress for structural properties and their algorithmic implications in the area of approximation algorithms and fixed parameter tractability. Concretely, we show how these structural properties lead to optimal approximation algorithms for the classical Makespan Scheduling scheduling problem and to exact polynomial-time algorithm for the Bin Packing problem with a constant number of different item sizes.

Steganography Based on Pattern Languages

In order to transmit secret messages such that the information exchange itself cannot be detected, steganography needs a channel, a set of strings with some distribution that occur in an ordinary communication. The elements of such a language or concept are called coverdocuments. The question how to design secure stegosystems for natural classes of languages is investigated for pattern languages. We present a randomized modification scheme for strings of a pattern language that can reliably encode arbitrary messages and is almost undetectable.

Provable Secure Universal Steganography of Optimal Rate: Provably Secure Steganography does not Necessarily Imply One-Way Functions

We present the first complexity-theoretic secure steganographic protocol which, for any communication channel, is provably secure, reliable, and has nearly optimal bandwidth. Our system is unconditionally secure, i.e. our proof does not rely on any unproven complexity-theoretic assumption, like e.g. the existence of one-way functions. This disproves the claim that the existence of one-way functions and access to a communication channel oracle are both necessary and sufficient conditions for the existence of secure steganography, in the sense that secure and reliable steganography exists independently of the existence of one-way functions.