Sven Müelich

Low-Area Reed Decoding in a Generalized Concatenated Code Construction for PUFs

Physical Unclonable Functions (PUFs) enable secure key storage for integrated circuits and FPGAs. PUF responses are noisy such that error correction is required to generate stable cryptographic keys. One popular approach is to use error-correcting codes. We present an area-optimized VLSI implementation of a recent Generalized Concatenated (GC) code construction using Reed-Muller codes. Reed-Muller codes have the advantage that there exist very efficient decoders. Our new Reed decoding implementation makes extensive use of a circular shift register. The functionality is extended so that it can also handle erasure symbols to improve the error correction capability. The overall GC code decoder occupies less than 110 slices and two block RAMs on an entry-level FPGA, and has a key error probability of 1.5 × 10-9. The slice count is reduced by 50% compared to the reference implementation.

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(n3) 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(n2). This method immediately connects the decoding problem to well-studied problems, which have been investigated in terms of coefficient growth and numerical stability.

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.

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 Sendriers 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.

Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm

We prove that Alekhnovichs algorithm can be used for row reduction of skew polynomial matrices. This yields an

On Error Correction for Physical Unclonable Functions

O(\ell^3 n^{(\omega+1)/2} \log(n))

Error Correction for Physical Unclonable Functions Using Generalized Concatenated Codes

decoding algorithm for

A New Error Correction Scheme for Physical Unclonable Functions.

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Timing Attack Resilient Decoding Algorithms for Physical Unclonable Functions

-Interleaved Gabidulin codes of length

Constructing an LDPC Code Containing a Given Vector.

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