Thomas Beth

Valuation of Trust in Open Networks

Authentication in open networks usually requires participation of trusted entities. Many protocols allow trust to be obtained by recommendation of other entities whose recommendations are known to be reliable. To consider an entity as being trustworthy, especially if there have been several mediators or contradicting recommendations, it is necessary to have a means of estimating its trustworthiness. In this paper we present a method for the valuation of trustworthiness which can be used to accept or reject an entity as being suitable for sensitive tasks. It constitutes an extension of the work of Yahalom, Klein and Beth ([YKB93]).

Trust relationships in secure systems-a distributed authentication perspective

The notion of trust is fundamental in inter-domain authentication protocols. The goal is to develop an effective formalism for explicit expressions of trust relations between entities involved in authentication protocols. Different relevant types of trust are identified and classified. A formalism for expressing trust relations is presented along with an algorithm for deriving trust relations from recommendations. The advantages of the approach are demonstrated by analyzing and comparing the trust relation requirements of a few known authentication protocols.<<ETX>>

Codes for the quantum erasure channel

The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i.e., arbitrary errors at known positions. We show that four quantum bits are necessary and sufficient to encode one quantum bit and correct one erasure, in contrast to five quantum bits for unknown positions. Moreover, a family of quantum codes for the QEC, the quantum Bose-Chaudhuri-Hocquenghem codes, that can be efficiently decoded is introduced.

On almost perfect nonlinear permutations

In this paper basic properties of APN permutations, which can be used in an iterated secret-key block cipher as a round function to protect it from a differential cryptanalysis, are investigated. Several classes of almost perfect nonlinear permutations and other permutations in GF(2)n with good nonlinearity and high nonlinear order are presented. Included here are also three methods for constructing permutations with good nonlinearity.

On optimal quantum codes

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters 〚n, n - 2d + 2, d〛q exist for all 3≤n≤q and 1≤d≤n/2+1. We also present quantum MDS codes with parameters 〚q2, q2-2d+2, d〛q for 1≤d≤q which additionally give rise to shortened codes 〚q2-s, q2-2d+2-s, d〛q for some s.

The stop-and-go generator

Under the correct assumptions cascading of primitive shift registers leads to interesting results. But from Gollmann’s work it is clear that general results on cascaded arbitrary shift registers cannot be expected.

Identification Tokens - or: Solving the Chess Grandmaster Problem

Fiat and Shamir have proposed to use zero-knowledge interactive proofs to obtain secure identification mechanisms. Real time attacks in which active eavesdroppers relay questions and answers or in which the prover helps deliberately an impersonator have been described [4j. In this paper a solution against such frauds is given and (based on some physical assumptions) it is proved that the solution protects against the real-time attacks.

Efficient zero-knowledged identification scheme for smart cards

In this paper we present a Fiat-Shamir like authentication protocol for the El-Gamal Scheme.

Computing Local Invariants of Qubit Systems

We investigate means to describe the nonlocal properties of quantum systems and to test if two quantum systems are locally equivalent. For this we consider quantum systems that consist of several subsystems, especially multiple quantum bits, i.e., systems consisting of subsystems of dimension 2. We compute invariant polynomials, i.e., polynomial functions of the entries of the density operator that are invariant under local unitary operations. As an example, we consider a system of two quantum bits. We compute the Molien series for the corresponding representation, which gives information about the number of linearly independent invariants. Furthermore, we present a set of polynomials that generate all invariants (at least) up to degree 23. Finally, the use of invariants to check whether two density operators are locally equivalent is demonstrated.

Quantum Reed-Solomon Codes

We introduce a new class of quantum error-correcting codes derived from (classical) Reed-Solomon codes over finite fields of characteristic two. Quantum circuits for encoding and decoding based on the discrete cyclic Fourier transform over finite fields are presented.