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Sven Müelich

Publications and source records attributed to Sven Müelich.

11 recordsLinked to original sources
arXiv2018

Constructing an LDPC Code Containing a Given Vector

The coding problem considered in this work is to construct a linear code $\mathcal{C}$ of given length $n$ and dimension $k<n$ such that a given binary vector $\mathbf{r} \in \mathbb{F}^{n}$ is contained in the code. We study a recent solution of this problem by Müelich and Bossert, which is based on LDPC codes. We address two open questions of this construction. First, we show that under certain assumptions, this code construction is possible with high probability if $\mathbf{r}$ is chosen uniformly at random. Second, we calculate the uncertainty of $\mathbf{r}$ given the constructed code $\mathcal{C}$. We present an application of this problem in the field of Physical Unclonable Functions (PUFs).

cs.IT↗
arXiv2018

Using Convolutional Codes for Key Extraction in SRAM Physical Unclonable Functions

Physical Unclonable Functions (PUFs) exploit variations in the manufacturing process to derive bit sequences from integrated circuits, which can be used as secure cryptographic keys. Instead of storing the keys in an insecure, non-volatile memory, they can be reproduced when needed. Since the reproduced sequences are not stable due to physical reasons, error correction must be applied. Recently, convolutional codes were shown to be suitable for key reproduction in PUFs based on SRAM. This work shows how to further decrease the reconstruction failure probability and PUF implementation size using codes with larger memory length and decoding concepts such as soft-information and list decoding.

cs.IT↗
arXiv2016

Timing Attack Resilient Decoding Algorithms for Physical Unclonable Functions

This paper deals with the application of list decoding of Reed--Solomon codes to a concatenated code for key reproduction using Physical Unclonable Functions. The resulting codes achieve a higher error-correction performance at the same code rate than known schemes in this scenario. We also show that their decoding algorithms can be protected from side-channel attacks on the runtime both by masking techniques and by directly modifying the algorithms to have constant runtime.

cs.IT↗
arXiv2016

A New Error Correction Scheme for Physical Unclonable Functions

Error correction is an indispensable component when Physical Unclonable Functions (PUFs) are used in cryptographic applications. So far, there exist schemes that obtain helper data, which they need within the error correction process. We introduce a new scheme, which only uses an error correcting code without any further helper data. The main idea is to construct for each PUF instance an individual code which contains the initial PUF response as codeword. In this work we use LDPC codes, however other code classes are also possible. Our scheme allows a trade-off between code rate and cryptographic security. In addition, decoding with linear complexity is possible.

cs.CR↗
arXiv2016

Low-Rank Matrix Recovery using Gabidulin Codes in Characteristic Zero

We present a new approach on low-rank matrix recovery (LRMR) based on Gabidulin Codes. Since most applications of LRMR deal with matrices over infinite fields, we use the recently introduced generalization of Gabidulin codes to fields of characterstic zero. We show that LRMR can be reduced to decoding of Gabidulin codes and discuss which field extensions can be used in the code construction.

cs.IT↗
arXiv2016

Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm

We prove that Alekhnovich's algorithm can be used for row reduction of skew polynomial matrices. This yields an $O(\ell^3 n^{(ω+1)/2} \log(n))$ decoding algorithm for $\ell$-Interleaved Gabidulin codes of length $n$, where $ω$ is the matrix multiplication exponent, improving in the exponent of $n$ compared to previous results.

cs.IT↗
arXiv2016

An Alternative Decoding Method for Gabidulin Codes in Characteristic Zero

Gabidulin codes, originally defined over finite fields, are an important class of rank metric codes with various applications. Recently, their definition was generalized to certain fields of characteristic zero and a Welch--Berlekamp like algorithm with complexity $O(n^3)$ was given. We propose a new application of Gabidulin codes over infinite fields: low-rank matrix recovery. Also, an alternative decoding approach is presented based on a Gao type key equation, reducing the complexity to at least $O(n^2)$. This method immediately connects the decoding problem to well-studied problems, which have been investigated in terms of coefficient growth and numerical stability.

cs.IT↗
arXiv2015

Code-Based Cryptosystems Using Generalized Concatenated Codes

The security of public-key cryptosystems is mostly based on number theoretic problems like factorization and the discrete logarithm. There exists an algorithm which solves these problems in polynomial time using a quantum computer. Hence, these cryptosystems will be broken as soon as quantum computers emerge. Code-based cryptography is an alternative which resists quantum computers since its security is based on an NP-complete problem, namely decoding of random linear codes. The McEliece cryptosystem is the most prominent scheme to realize code-based cryptography. Many codeclasses were proposed for the McEliece cryptosystem, but most of them are broken by now. Sendrier suggested to use ordinary concatenated codes, however, he also presented an attack on such codes. This work investigates generalized concatenated codes to be used in the McEliece cryptosystem. We examine the application of Sendrier's attack on generalized concatenated codes and present alternative methods for both partly finding the code structure and recovering the plaintext from a cryptogram. Further, we discuss modifications of the cryptosystem making it resistant against these attacks.

cs.IT↗
arXiv2015

On Error Correction for Physical Unclonable Functions

Physical Unclonable Functions evaluate manufacturing variations to generate secure cryptographic keys for embedded systems without secure key storage. It is explained how methods from coding theory are applied in order to ensure reliable key reproduction. We show how better results can be obtained using code classes and decoding principles not used for this scenario before. These methods are exemplified by specific code constructions which improve existing codes with respect to error probability, decoding complexity and codeword length.

cs.IT↗
arXiv2014

Error Correction for Physical Unclonable Functions Using Generalized Concatenated Codes

Physical Unclonable Functions can be used for secure key generation in cryptographic applications. It is explained how methods from coding theory must be applied in order to ensure reliable key regeneration. Based on previous work, we show ways how to obtain better results with respect to error probability and codeword length. Also, an example based on Generalized Concatenated codes is given, which improves upon used coding schemes for PUFs.

cs.IT↗