Fast Witness Extraction Using a Decision Oracle

The gist of many (NP-)hard combinatorial problems is to decide whether a universe of $n$ elements contains a witness consisting of $k$ elements that match some prescribed pattern. For some of these problems there are known advanced algebra-based FPT algorithms which solve the decision problem but do not return the witness. We investigate techniques for turning such a YES/NO-decision oracle into an algorithm for extracting a single witness, with an objective to obtain practical scalability for large values of $n$. By relying on techniques from combinatorial group testing, we demonstrate that a witness may be extracted with $O(k\log n)$ queries to either a deterministic or a randomized set inclusion oracle with one-sided probability of error. Furthermore, we demonstrate through implementation and experiments that the algebra-based FPT algorithms are practical, in particular in the setting of the $k$-path problem. Also discussed are engineering issues such as optimizing finite field arithmetic.Comment: Journal version, 16 pages. Extended abstract presented at ESA'1

Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof

In recent work, we formalized the theory of optimal-size sorting networks with the goal of extracting a verified checker for the large-scale computer-generated proof that 25 comparisons are optimal when sorting 9 inputs, which required more than a decade of CPU time and produced 27 GB of proof witnesses. The checker uses an untrusted oracle based on these witnesses and is able to verify the smaller case of 8 inputs within a couple of days, but it did not scale to the full proof for 9 inputs. In this paper, we describe several non-trivial optimizations of the algorithm in the checker, obtained by appropriately changing the formalization and capitalizing on the symbiosis with an adequate implementation of the oracle. We provide experimental evidence of orders of magnitude improvements to both runtime and memory footprint for 8 inputs, and actually manage to check the full proof for 9 inputs.Comment: IMADA-preprint-c

Formalizing group blind signatures and practical constructions without random oracles

Group blind signatures combine anonymity properties of both group signatures and blind signatures and offer privacy for both the message to be signed and the signer. The primitive has been introduced with only informal definitions for its required security properties. In this paper, we offer two main contributions: first, we provide foundations for the primitive and present formal security definitions. In the process, we identify and address some subtle issues which were not considered by previous constructions and (informal) security definitions. Our second main contribution is a generic construction that yields practical schemes with a round-optimal signing protocol and constant-size signatures. Our constructions permit dynamic and concurrent enrollment of new members and satisfy strong security requirements. To the best of our knowledge, our schemes are the first provably secure constructions in the standard model. In addition, we introduce some new building blocks which may be of independent interest. © 2013 Springer-Verlag

Privacy enhancing technologies : protocol verification, implementation and specification

In this thesis, we present novel methods for verifying, implementing and specifying protocols. In particular, we focus properties modeling data protection and the protection of privacy. In the first part of the thesis, the author introduces protocol verification and presents a model for verification that encompasses so-called Zero-Knowledge (ZK) proofs. These ZK proofs are a cryptographic primitive that is particularly suited for hiding information and hence serves the protection of privacy. The here presented model gives a list of criteria which allows the transfer of verification results from the model to the implementation if the criteria are met by the implementation. In particular, the criteria are less demanding than the ones of previous work regarding ZK proofs. The second part of the thesis contributes to the area of protocol implementations. Hereby, ZK proofs are used in order to improve multi-party computations. The third and last part of the thesis explains a novel approach for specifying data protection policies. Instead of relying on policies, this approach relies on actual legislation. The advantage of relying on legislation is that often a fair balancing is introduced which is typically not contained in regulations or policies.In dieser Arbeit werden neue Methoden zur Verifikation, Implementierung und Spezifikation im von Protokollen vorgestellt. Ein besonderer Fokus liegt dabei auf Datenschutz-Eigenschaften und dem Schutz der Privatsph¨are. Im ersten Teil dieser Arbeit geht der Author auf die Protokoll- Verifikation ein und stellt ein Modell zur Verifikation vor, dass sogenannte Zero-Knowledge (ZK) Beweise enth¨alt. Diese ZK Beweise sind ein kryptographisches primitiv, dass insbesondere zum Verstecken von Informationen geeignet ist und somit zum Schutz der Privatsph¨are dient. Das hier vorgestellte Modell gibt eine Liste von Kriterien, welche eine Implementierung der genutzten kryptographischen Primitive erf¨ullen muss, damit die verifikationen im Modell sich auf Implementierungen ¨ubertragen lassen. In Bezug auf ZK Beweise sind diese Kriterien sch¨acher als die vorangegangener Arbeiten. Der zweite Teil der Arbeit wendet sich der Implementierung von Protokollen zu. Hierbei werden dann ZK Beweise verwendet um sichere Mehrparteienberechnungen zu verbessern. Im dritten und letzten Teil der Arbeit wird eine neuartige Art der Spezifikation von Datenschutz-Richtlinien erl¨autert. Diese geht nicht von Richtlinien aus, sondern von der Rechtsprechung. Der Vorteil ist, dass in der Rechtsprechung konkrete Abw¨agungen getroffen werden, die Gesetze und Richtlinien nicht enthalten