Peter Hauck

Fitting classes and products of totally permutable groups

The second and third authors have been supported by Proyecto PB 97-0674-C02-02 of DGESIC, Ministerio de Educacion y Cultura, Spain.

Investigating the openPGP web of trust

We present results of a thorough analysis of the OpenPGP Web of Trust. We conducted our analysis on a recent data set with a focus on determining properties like usefulness and robustness. To this end, we analyzed graph topology, identified the strongly connected components and derived properties like verifiability of keys, signature chain lengths and redundant signature paths for nodes. Contrary to earlier works, our analysis revealed the Web of Trust to be only similar to a scale-free network, with different properties regarding the hub structure and its influence on overall connectivity. We also analyzed the community structure of the Web of Trust and mapped it to social relationships. Finally, we present statistics which cryptographic algorithms are in use and give recommendations.

Injectors and Radicals in Products of Totally Permutable Groups

Abstract Two subgroups H and K of a group G are said to be totally permutable if every subgroup of H permutes with every subgroup of K. In this paper the behaviour of radicals and injectors associated to Fitting classes in a product of pairwise totally permutable finite groups is studied.

Efficient Majority-Logic Decoding of Short-Length Reed-Muller Codes at Information Positions

Short-length Reed—Muller codes under majority-logic decoding are of particular importance for efficient hardware implementations in real-time and embedded systems. This paper significantly improves Chens two-step majority-logic decoding method for binary Reed—Muller codes RM(r,m), r ≤ m/2, if — systematic encoding assumed — only errors at information positions are to be corrected. Some general results on the minimal number of majority gates are presented that are particularly good for short codes. Specifically, with its importance in applications as a 3-error-correcting, self-dual code, the smallest non-trivial example, RM(2,5) of dimension 16 and length 32, is investigated in detail. Further, the decoding complexity of our procedure is compared with that of Chens decoding algorithm for various Reed—Muller codes up to length 2^{10}.

On 2-generated subgroups and products of groups

Abstract For a non-empty class of groups ℱ, two subgroups A and B of a finite group G are said to be ℱ-connected if 〈a, b〉 ∈ ℱ for all a ∈ A and b ∈ B. This paper is a study of ℱ-connection for saturated formations ℱ ⊆ (where denotes the class of all finite groups with nilpotent commutator subgroup). The class of all finite supersoluble groups constitutes an example of such a saturated formation. It is shown for example that in a finite soluble group G = AB the subgroups A and B are -connected if and only if [A, B] ⩽ F(G), where F(G) denotes the Fitting subgroup of G. Also ℱ-connected finite soluble products for any saturated formation ℱ with ℱ ⊆ are characterized.

Trust-Rated Authentication for Domain-Structured Distributed Systems

We present an authentication scheme and new protocol for domain-based scenarios with inter-domain authentication. Our protocol is primarily intended for domain-structured Peer-to-Peer systems but is applicable for any domain scenario where clients from different domains wish to authenticate to each other. To this end, we make use of Trusted Third Parties in the form of Domain Authentication Servers in each domain. These act on behalf of their clients, resulting in a four-party protocol. If there is a secure channel between the Domain Authentication Servers, our protocol can provide secure authentication. To address the case where domains do not have a secure channel between them, we extend our scheme with the concept of trust-rating. Domain Authentication Servers signal security-relevant information to their clients (pre-existing secure channel or not, trust, ...). The clients evaluate this information to decide if it fits the security requirements of their application.

An Improved Majority-Logic Decoder Offering Massively Parallel Decoding for Real-Time Control in Embedded Systems

We propose an easy-to-implement hard-decision majority-logic decoding algorithm for Reed-Muller codes RM(r,m) with m ≥ 3, m/2 ≥ r ≥ 1. The presented algorithm outperforms the best known majority-logic decoding algorithms and offers highly parallel decoding. The result is of special importance for safety- and time-critical applications in embedded systems. A simple combinational circuit can perform the proposed decoding. In particular, we show how our decoder for the three-error-correcting code RM(2, 5) of dimension 16 and length 32 can be realized on hardware level.

Subgroups of a Direct Product of Groups that Satisfy the Strong Frattini Argument

We give criteria to characterize subgroups of a direct product of finite solvable groups that satisfy the strong Frattini argument.

Maximal supersoluble subgroups of symmetric groups

SummaryAll maximal supersoluble subgroups of symmetric groups are classified.

Cover-avoidance and Frattini argument

The results presented here develop further aspects of the theory of Fitting functors in finite (solvable) groups. These ideas evolved in investigating whether a Fitting functor with the cover-avoidance property necessarily satisfies the Frattini argument. Our results might be seen as an indication for a positive answer.