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Joachim Rosenthal

Publications and source records attributed to Joachim Rosenthal.

At least 37 records · Page 2Linked to original sources
arXiv2020

Construction of Rate (n-1)/n Non-Binary LDPC Convolutional Codes via Difference Triangle Sets

This paper provides a construction of non-binary LDPC convolutional codes, which generalizes the work of Robinson and Bernstein. The sets of integers forming an $(n-1,w)$-difference triangle set are used as supports of the columns of rate $(n-1)/n$ convolutional codes. If the field size is large enough, the Tanner graph associated to the sliding parity-check matrix of the code is free from $4$ and $6$-cycles not satisfying the full rank condition. This is important for improving the performance of a code and avoiding the presence of low-weight codewords and absorbing sets. The parameters of the convolutional code are shown to be determined by the parameters of the underlying difference triangle set. In particular, the free distance of the code is related to $w$ and the degree of the code is linked to the "scope" of the difference triangle set. Hence, the problem of finding families of difference triangle set with minimum scope is equivalent to find convolutional codes with small degree.

cs.IT↗
arXiv2020

Convolutional Codes

The article provides a survey on convolutional codes stressing the connections to module theory and systems theory. Constructions of codes with maximal possible distance and distance profile are provided. The article will appear as book chapter in "A Concise Encyclopedia of Coding Theory" to be published by CRC Press.

cs.IT↗
arXiv2019

Encryption Scheme Based on Expanded Reed-Solomon Codes

We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its shortened expanded code over the base field. Considering shortened expanded codes provides a safeguard against distinguisher attacks based on the Schur product. Moreover, without using a cyclic or a quasi-cyclic structure we obtain a key size reduction of nearly $45 \%$ compared to the classic McEliece cryptosystem proposed by Bernstein et al.

cs.CR↗
arXiv2018

Generalization of the Ball-Collision Algorithm

In this paper we generalize the Ball-Collision Algorithm by Bernstein, Lange, Peters from the binary field to a general finite field. We also provide a complexity analysis and compare the asymptotic complexity to other generalized information set decoding algorithms.

cs.IT↗
arXiv2018

Design and Implementation of a Digital Signature Scheme Based on Low-density Generator Matrix Codes

In this paper we consider a post-quantum digital signature scheme based on low-density generator matrix codes and propose efficient algorithmic solutions for its implementation. We also review all known attacks against this scheme and derive closed-form estimates of their complexity when running over both classical and quantum computers. Based on these estimates, we propose new parametrization for the considered system to achieve given pre-quantum and post-quantum security levels. Finally, we provide and discuss performance benchmarks obtained through a suitably developed and publicly available reference implementation of the considered system.

cs.CR↗
arXiv2017

A decoding algorithm for Twisted Gabidulin codes

In this work, we modify the decoding algorithm for subspace codes by Koetter and Kschischang to get a decoding algorithm for (generalized) twisted Gabidulin codes. The decoding algorithm we present applies to cases where the code is linear over the base field $\mathbb{F}_q$ but not linear over $\mathbb{F}_{q^n}$.

cs.IT↗
arXiv2017

Variations of the McEliece Cryptosystem

Two variations of the McEliece cryptosystem are presented. The first one is based on a relaxation of the column permutation in the classical McEliece scrambling process. This is done in such a way that the Hamming weight of the error, added in the encryption process, can be controlled so that efficient decryption remains possible. The second variation is based on the use of spatially coupled moderate-density parity-check codes as secret codes. These codes are known for their excellent error-correction performance and allow for a relatively low key size in the cryptosystem. For both variants the security with respect to known attacks is discussed.

cs.IT↗
arXiv2017

Fuzzy Authentication using Rank Distance

Fuzzy authentication allows authentication based on the fuzzy matching of two objects, for example based on the similarity of two strings in the Hamming metric, or on the similiarity of two sets in the set difference metric. Aim of this paper is to show other models and algorithms of secure fuzzy authentication, which can be performed using the rank metric. A few schemes are presented which can then be applied in different scenarios and applications.

cs.IT↗
arXiv2016

Group key management based on semigroup actions

In this work we provide a suite of protocols for group key management based on general semigroup actions. Construction of the key is made in a distributed and collaborative way. Examples are provided that may in some cases enhance the security level and communication overheads of previous existing protocols. Security against passive attacks is considered and depends on the hardness of the semigroup action problem in any particular scenario.

cs.IT↗
arXiv2016

On the Genericity of Maximum Rank Distance and Gabidulin Codes

We consider linear rank-metric codes in $\mathbb F_{q^m}^n$. We show that the properties of being MRD (maximum rank distance) and non-Gabidulin are generic over the algebraic closure of the underlying field, which implies that over a large extension field a randomly chosen generator matrix generates an MRD and a non-Gabidulin code with high probability. Moreover, we give upper bounds on the respective probabilities in dependence on the extension degree $m$.

cs.IT↗
arXiv2015

An Active Attack on a Multiparty Key Exchange Protocol

The multiparty key exchange introduced in Steiner et al.\@ and presented in more general form by the authors is known to be secure against passive attacks. In this paper, an active attack is presented assuming malicious control of the communications of the last two users for the duration of only the key exchange.

cs.IT↗
arXiv2015

Subspace Fuzzy Vault

Fuzzy vault is a scheme providing secure authentication based on fuzzy matching of sets. A major application is the use of biometric features for authentication, whereby unencrypted storage of these features is not an option because of security concerns. While there is still ongoing research around the practical implementation of such schemes, we propose and analyze here an alternative construction based on subspace codes. This offers some advantages in terms of security, as an eventual discovery of the key does not provide an obvious access to the features. Crucial for an efficient implementation are the computational complexity and the choice of good code parameters. The parameters depend on the particular application, e.g. the biometric feature to be stored and the rate one wants to allow for false acceptance. The developed theory is closely linked to constructions of subspace codes studied in the area of random network coding.

cs.IT↗
arXiv2015

Managing key multicasting through orthogonal systems

In this paper we propose a new protocol to manage multicast key distribution. The protocol is based on the use of orthogonal systems in vector spaces. The main advantage in comparison to other existing multicast key management protocols is that the length and the number of the messages which have to be sent are considerably smaller. This makes the protocol especially attractive when the number of legitimate receivers is large.

cs.CR↗
arXiv2014

Linear spanning sets for matrix spaces

Necessary and sufficient conditions are given on matrices $A$, $B$ and $S$, having entries in some field $\mathbb F$ and suitable dimensions, such that the linear span of the terms $A^iSB^j$ over $\mathbb F$ is equal to the whole matrix space. This result is then used to determine the cardinality of subsets of $\mathbb F[A]S\mathbb F[B]$ when $\mathbb F$ is a finite field.

math.RA↗
arXiv2014

Enhanced public key security for the McEliece cryptosystem

This paper studies a variant of the McEliece cryptosystem able to ensure that the code used as the public key is no longer permutation-equivalent to the secret code. This increases the security level of the public key, thus opening the way for reconsidering the adoption of classical families of codes, like Reed-Solomon codes, that have been longly excluded from the McEliece cryptosystem for security reasons. It is well known that codes of these classes are able to yield a reduction in the key size or, equivalently, an increased level of security against information set decoding; so, these are the main advantages of the proposed solution. We also describe possible vulnerabilities and attacks related to the considered system, and show what design choices are best suited to avoid them.

cs.IT↗