Anna-Lena Trautmann

Marco Baldi, Massimo Battaglioni, Franco Chiaraluce et al.

In this paper we introduce a variant of the Syndrome Decoding Problem (SDP), that we call Restricted SDP (R-SDP), in which the entries of the searched vector are defined over a subset of the underlying finite field. We prove the NP-completeness of R-SDP, via a reduction from the classical SDP, and describe algorithms which solve such new problem. We study the properties of random codes under this new decoding perspective, in the fashion of traditional coding theory results, and assess the complexity of solving a random R-SDP instance. As a concrete application, we describe how Zero-Knowledge Identification (ZK-ID) schemes based on SDP can be tweaked to rely on R-SDP, and show that this leads to compact public keys as well as significantly reduced communication costs. Thus, these schemes offer an improved basis for the construction of code-based digital signature schemes derived from identification schemes through the well-know Fiat-Shamir transformation.

Violetta Weger, Karan Khathuria, Anna-Lena Horlemann et al.

In this paper we study the hardness of the syndrome decoding problem over finite rings endowed with the Lee metric. We first prove that the decisional version of the problem is NP-complete, by a reduction from the $3$-dimensional matching problem. Then, we study the complexity of solving the problem, by translating the best known solvers in the Hamming metric over finite fields to the Lee metric over finite rings, as well as proposing some novel solutions. For the analyzed algorithms, we assess the computational complexity in the asymptotic regime and compare it to the corresponding algorithms in the Hamming metric.

Anna-Lena Horlemann-Trautmann, Violetta Weger

We convert Stern's information set decoding (ISD) algorithm to the ring $\mathbb{Z}/4 \mathbb{Z}$ equipped with the Lee metric. Moreover, we set up the general framework for a McEliece and a Niederreiter cryptosystem over this ring. The complexity of the ISD algorithm determines the minimum key size in these cryptosystems for a given security level. We show that using Lee metric codes can drastically decrease the key size, compared to Hamming metric codes. In the end we explain how our results can be generalized to other Galois rings $\mathbb{Z}/p^s\mathbb{Z}$.

Anna-Lena Horlemann-Trautmann, Kyle Marshall, Joachim Rosenthal

We present a new attack against cryptosystems based on the rank metric. Our attack allows us to cryptanalyze two variants of the GPT cryptosystem which were designed to resist the attack of Overbeck.

Kyle Marshall, Davide Schipani, Anna-Lena Trautmann et al.

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.

Felix Fontein, Kyle Marshall, Joachim Rosenthal et al.

Secure storage of noisy data for authentication purposes usually involves the use of error correcting codes. We propose a new model scenario involving burst errors and present for that several constructions.