Stefan Maubach

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Papers by Stefan Maubach

A new formulation of the Jacobian Conjecture in characteristic $p$

Colloquium Mathematicum, 2016

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Polynomial automorphisms over finite fields: Mimicking non-tame and tame maps by the Derksen group

If $F$ is a polynomial automorphism over a finite field $\F_q$ in dimension $n$, then it induces ... more If $F$ is a polynomial automorphism over a finite field $\F_q$ in dimension $n$, then it induces a bijection $\pi_{q^r}(F)$ of $(\F_{q^r})^n$ for every $r\in \N^*$. We say that $F$ can be `mimicked' by elements of a certain group of automorphisms $\mathcal{G}$ if there are $g_r\in \mathcal{G}$ such that $\pi_{q^r}(g_r)=\pi_{q^r}(F)$. We show that the Nagata automorphism (and any other automorphism in three variables fixing one variable) can be mimicked by tame automorphisms. This on the one hand removes the hope of showing that such an automorphism is non-tame by studying one bijection it induces, but on the other hand indicates that the bijections of tame automorphisms coincide with bijections of all automorphisms. In section 5 we show that the whole tame group $\TA_n(\F_q)$ in turn can be mimicked by the Derksen subgroup $\DA_n(\F_q)$, which is the subgroup generated by affine maps and one particular element. It is known that if a field $k$ has characteristic zero, then $\TA_n(k)=\DA_n(k)$, which is not expected to be true for characteristic $p$. In section 6 we consider the subgroups $\GLIN_n(k)$ and $\GTAM_n(k)$ of the polynomial automorphism group (which are candidates to equal the entire automorphism group). We show that $\GLIN_n(\F_q)=\GTAM_n(\F_q)$ if $q\not = 2$, and $\GLIN_n(\F_2)\subsetneq \GTAM_n(\F_2)$.

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Some open questions on polynomial automorphisms and related topics

Acta Mathematica Vietnamica, 2007

Abstract. This is a collection∗ of open questions presented at the Open Ses-sion of the Internati... more

Computing preimages of points and curves under polynomial maps

by Stefan Maubach and Michiel de Bondt

Eprint Arxiv 1005 0288, May 3, 2010

In this paper, we give two algorithms to compute preimages of curves under polynomial endomorphis... more In this paper, we give two algorithms to compute preimages of curves under polynomial endomorphisms. In particular, this gives an efficient way of computing preimages of points. Furthermore, we explain the abstract setting under which one can iteratively compute the inverse of a polynomial automorphism.

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Improved rfid tag

Rigid Rings and Makar-Limanov Techniques

Http Dx Doi Org 10 1080 00927872 2012 695832, Aug 25, 2013

A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic ... more A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic geometry, a rigid coordinate ring corresponds to an algebraic affine variety which does not allow any nontrivial algebraic G a -action. Even though it is thought that "generic" rings are rigid, it is far from trivial to show that a ring is rigid. In this paper we provide several examples of rigid rings and we outline two general strategies to help determine if a ring is rigid, which we call "parametrization techniques" and "filtration techniques". We provide many little tools and lemmas which may be useful in other situations. Also, we point out some pitfalls to beware when using these techniques. Finally, we give some reasonably simple hypersurfaces for which the question of rigidity remains unsettled. * Funded by Veni-grant of council for the physical sciences, Netherlands Organisation for scientific research (NWO).

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$Research paper thumbnail of Classification of Maximal Subalgebras of $ textbf{k}[t, t^{-1}, y]$$

Classification of Maximal Subalgebras of $ textbf{k}[t, t^{-1}, y]$

by Immanuel Stampfli and Stefan Maubach

Let $\textbf{k}$ be an algebraically closed field. We classify all maximal $\textbf{k}$-subalgebr... more Let $\textbf{k}$ be an algebraically closed field. We classify all maximal $\textbf{k}$-subalgebras of $\textbf{k}[t, t^{-1}, y]$. To the authors' knowledge, this is the first such classification result for an algebra of dimension $> 1$. In the course of this study, we classify also all maximal $\textbf{k}$-subalgebras of $\textbf{k}[t, y]$ that contain a coordinate of $\textbf{k}[t, y]$. Furthermore, we give examples of maximal $\textbf{k}$-subalgebras of $\textbf{k}[t, y]$ that do not contain a coordinate.

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Information-theoretic analysis of coating PUFs

Abstract: Physical Uncloneable Functions (PUFs) can be used as a cost-eective means tostore crypt... more Abstract: Physical Uncloneable Functions (PUFs) can be used as a cost-eective means tostore cryptographic key material in an uncloneable way. In coating PUFs, keys are generatedfrom capacitance measurements of a coating containing many randomly distributed particleswith dierent dielectric constants.

Polynomial endomorphisms over finite fields: experimental results

Polymer Chemistry, Mar 17, 2011

Given a finite field $\F_q$ and $n\in \N^*$, one could try to compute all polynomial endomorphism... more Given a finite field $\F_q$ and $n\in \N^*$, one could try to compute all polynomial endomorphisms $\F_q^n\lp \F_q^n$ up to a certain degree with a specific property. We consider the case $n=3$. If the degree is low (like 2,3, or 4) and the finite field is small ($q\leq 7$) then some of the computations are still feasible. In this article we study the following properties of endomorphisms: being a bijection of $\F_q^n\lp \F_q^n$, being a polynomial automorphism, being a {\em Mock automorphism}, and being a locally finite polynomial automorphism. In the resulting tables, we point out a few interesting objects, and pose some interesting conjectures which surfaced through our computations.

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Polynomial maps that are roots of power series

Eprint Arxiv 0706 0788, Jun 6, 2007

We introduce a class of polynomial maps that we call polynomial roots of powerseries, and show th... more We introduce a class of polynomial maps that we call polynomial roots of powerseries, and show that automorphisms with this property generate the automorphism group in any dimension. In particular we determine generically which polynomial maps that preserve the origin are roots of powerseries. We study the one-dimensional case in greater depth.

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Information-theoretic analysis of capacitive physical unclonable functions

Journal of Applied Physics, Jul 15, 2006

Physical unclonable functions (PUFs) can be used as a cost-effective means to store cryptographic... more Physical unclonable functions (PUFs) can be used as a cost-effective means to store cryptographic key material in an unclonable way. In coating PUFs, keys are generated from capacitance measurements of a coating containing many randomly distributed particles with different dielectric constants. We introduce a physical model of coating PUFs by simplifying the capacitance sensors to a parallel plate geometry. We estimate the amount of information that can be extracted from the coating. We show that the inherent entropy is proportional to √n (logn)3/2, where n is the number of particles that fit between the capacitor plates in a straight line. However, measurement noise may severely reduce the amount of information that can actually be extracted in practice. In the noisy regime the number of extractable bits is, in fact, a decreasing function of n. We derive an optimal value for n as a function of the noise amplitude, the PUF geometry, and the dielectric constants.

Polynomial maps which are roots of power series

Math Z, 2008

Secure storage system and method for secure storing

by Richard Brinkman, Stefan Maubach, and Suse Engbers

Opt Express, 2007

(12) INTERNATIONAL APPLICATION PUBLISHED UNDER THE PATENT COOPERATION TREATY (PCT) (19) World Int... more

Method and system for authentication of a low-resource prover

by Stefan Maubach and Claudine Conrado

Method, Apparatus and System for Verifying Authenticity of an Object

Transponder System for Transmitting Key-Encrypted Information and Associated Keys

Derivations Having Divergence Zero on

In this paper it is proved that for any Q-algebra R any locally nilpotentR-derivation D on R[X; Y... more In this paper it is proved that for any Q-algebra R any locally nilpotentR-derivation D on R[X; Y ] having divergence zero and 1 2 (D(X); D(Y )) (i)has a slice, and (ii) AD= R[P ] for some P . Furthermore it is shown that anysurjective R-derivation on R[X; Y ] having divergence zero is locally nilpotent.Connections with the Jacobian

Keller Maps of Low Degree over Finite Fields

Springer Proceedings in Mathematics & Statistics, 2014

ALGSICS — Combining Physics and Cryptography to Enhance Security and Privacy in RFID Systems

by Stefan Maubach and Claudine Conrado

Lecture Notes in Computer Science, 2007

RFID-tags can be seen as a new generation of bar codes with added functionality. They are becomin... more RFID-tags can be seen as a new generation of bar codes with added functionality. They are becoming very popular tools for identification of products in various applications such as supply-chain management. The widespread deployment of RFID technology will depend to a large extent on its acceptance by the general public. Thus, developing privacy and security technologies specifically suited to the constrained environment of RFID tags continues to be a key problem. In this paper, we introduce several new mechanisms that are cheap to implement or integrate into RFID tags and that at the same time enhance the security of the tags and the privacy of the individual carrying the tags. These new mechanisms are based on physical principles alone or on their combination with cryptographic methods. We also review previous works that use physical principles to provide security and privacy in RFID systems.

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RFID Security: Cryptography and Physics Perspectives

by Stefan Maubach and Claudine Conrado

RFID Security, 2008

Abstract In this chapter, we provide an overview of mechanisms that are cheap to implement or int... more

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