Optimal Ferrers Diagram Rank-Metric Codes

Optimal rank-metric codes in Ferrers diagrams are considered. Such codes consist of matrices having zeros at certain fixed positions and can be used to construct good codes in the projective space. Four techniques and constructions of Ferrers diagram rank-metric codes are presented, each providing optimal codes for different diagrams and parameters.Comment: to be presented in Algebra, Codes, and Networks, Bordeaux, June 16 - 20, 201

High-rate self-synchronizing codes

Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error-tolerant self-synchronizing codes may be realized as cosets of linear codes. Ideally, difference systems of sets should sacrifice as few bits as possible for a given code length, alphabet size, and error-tolerance capability. However, it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low. In fact, the majority of known optimal difference systems of sets are for exceptionally noisy channels, requiring a substantial amount of bits for synchronization. To address this problem, we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent. Our constructions utilize optimal difference systems of sets as ingredients and, when applied carefully, generate asymptotically optimal ones with higher information rates. We also give direct constructions for optimal difference systems of sets with high information rates and error-tolerance that generate binary and ternary self-synchronizing codes.Comment: 9 pages, no figure, 2 tables. Final accepted version for publication in the IEEE Transactions on Information Theory. Material presented in part at the International Symposium on Information Theory and its Applications, Honolulu, HI USA, October 201

Cryptanalysis of the Fuzzy Vault for Fingerprints: Vulnerabilities and Countermeasures

Das Fuzzy Vault ist ein beliebter Ansatz, um die Minutien eines menschlichen Fingerabdrucks in einer Sicherheitsanwendung geschützt zu speichern. In dieser Arbeit werden verschiedene Implementationen des Fuzzy Vault für Fingerabdrücke in verschiedenen Angriffsszenarien untersucht. Unsere Untersuchungen und Analysen bestätigen deutlich, dass die größte Schwäche von Implementationen des Fingerabdruck Fuzzy Vaults seine hohe Anfälligkeit gegen False-Accept Angriffe ist. Als Gegenmaßnahme könnten mehrere Finger oder sogar mehrere biometrische Merkmale eines Menschen gleichzeitig verwendet werden. Allerdings besitzen traditionelle Fuzzy Vault Konstruktionen eine wesentliche Schwäche: den Korrelationsangriff. Es ist bekannt, dass das Runden von Minutien auf ein starres System, diese Schwäche beheben. Ausgehend davon schlagen wir eine Implementation vor. Würden nun Parameter traditioneller Konstruktionen übernommen, so würden wir einen signifikanten Verlust an Verifikations-Leistung hinnehmen müssen. In einem Training wird daher eine gute Parameterkonfiguration neu bestimmt. Um den Authentifizierungsaufwand praktikabel zu machen, verwenden wir einen randomisierten Dekodierer und zeigen, dass die erreichbaren Raten vergleichbar mit den Raten einer traditionellen Konstruktion sind. Wir folgern, dass das Fuzzy Vault ein denkbarer Ansatz bleibt, um die schwierige Aufgabe ein kryptographisch sicheres biometrisches Kryptosystem in Zukunft zu implementieren.The fuzzy fingerprint vault is a popular approach to protect a fingerprint's minutiae as a building block of a security application. In this thesis simulations of several attack scenarios are conducted against implementations of the fuzzy fingerprint vault from the literature. Our investigations clearly confirm that the weakest link in the fuzzy fingerprint vault is its high vulnerability to false-accept attacks. Therefore, multi-finger or even multi-biometric cryptosystems should be conceived. But there remains a risk that cannot be resolved by using more biometric information of an individual if features are protected using a traditional fuzzy vault construction: The correlation attack remains a weakness of such constructions. It is known that quantizing minutiae to a rigid system while filling the whole space with chaff makes correlation obsolete. Based on this approach, we propose an implementation. If parameters were adopted from a traditional fuzzy fingerprint vault implementation, we would experience a significant loss in authentication performance. Therefore, we perform a training to determine reasonable parameters for our implementation. Furthermore, to make authentication practical, the decoding procedure is proposed to be randomized. By running a performance evaluation on a dataset generally used, we find that achieving resistance against the correlation attack does not have to be at the cost of authentication performance. Finally, we conclude that fuzzy vault remains a possible construction for helping in solving the challenging task of implementing a cryptographically secure multi-biometric cryptosystem in future

MOCZ for Blind Short-Packet Communication: Practical Aspects

We investigate practical aspects of a recently introduced blind (noncoherent) communication scheme, called modulation on conjugate-reciprocal zeros (MOCZ). MOCZ is suitable for a reliable transmission of sporadic and short-packets at ultra-low latency and high spectral efficiency via unknown multipath channels, which are assumed to be static over the receive duration of one packet. The information is modulated on the zeros of the transmitted discrete-time baseband signal’s z− transform. Because of ubiquitous impairments between the transmitter and receiver clocks, a carrier frequency offset occurs after down-conversion to the baseband. This results in a common rotation of the zeros. To identify fractional rotations of the base angle in the zero-pattern, we propose an oversampled direct zero-testing decoder to identify the most likely one. Integer rotations correspond to cyclic shifts of the binary message, which we determine by cyclically permutable codes (CPC). Additionally, the embedding of CPCs into cyclic codes, enables additive error-correction which reduces the bit-error-rate tremendously. Furthermore, we exploit the trident structure in the signal’s autocorrelation for an energy based detector to estimate timing offsets and the effective channel delay spread. We finally demonstrate how this joint data and channel estimation can be largely improved by receive antenna diversity at low SNR

Unconditionally secure authentication for quantum key distribution

This work describes the using of Universal and Strongly Universal classes of hash functions for unconditionally secure message authentication in quantum cryptogra- phy. Different classes are compared and constructions of flexible ε-Almost Strongly Universal classes are described. A new upper bound on the lifetime of a single hash function in one-time padded tags is introduced and optimisation on the final QKD key rate is shown for the QuAKE experiment, a B92 based QKD system. The public channel communication protocol of QuAKE is described, with special stress on the security issue

Coding Theory and Algebraic Combinatorics

This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings, kissing numbers, lattices, and association schemes. In particular, special interest is devoted to the relationship between codes and combinatorial designs. We describe and recapitulate important results in the development of the state of the art. In addition, we give illustrative examples and constructions, and highlight recent advances. Finally, we provide a collection of significant open problems and challenges concerning future research.Comment: 33 pages; handbook chapter, to appear in: "Selected Topics in Information and Coding Theory", ed. by I. Woungang et al., World Scientific, Singapore, 201