Stefan Maubach

Information-theoretic analysis of capacitive physical unclonable functions

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.

The commuting derivations conjecture

Abstract This paper proves the Commuting Derivations Conjecture in dimension three: if D 1 and D 2 are two locally nilpotent derivations which are linearly independent and satisfy [ D 1 , D 2 ]=0 then the intersection of the kernels, A D 1 ∩ A D 2 equals C [f] where f is a coordinate. As a consequence, it is shown that p ( X ) Y + Q ( X , Z , T ) is a coordinate if and only if Q ( a , Z , T ) is a coordinate for every zero a of p ( X ). Next to that, it is shown that if the Commuting Derivations Conjecture in dimension n , and the Cancellation Problem and Abhyankar–Sataye Conjecture in dimension n −1, all have an affirmative answer, then we can similarly describe all coordinates of the form p ( X ) Y + q ( X , Z 1 ,…, Z n −1 ). Also, conjectures about possible generalisations of the concept of “coordinate” for elements of general rings are made.

Derivations having divergence zero on R[X,Y]

In this paper it is proved that for any ℚ-algebraR any locally nilpotentR-derivationD onR[X,Y] having divergence zero and 1 ∈ (D(X),D(Y)) (i) has a slice, and (ii)AD=R[P] for someP. Furthermore, it is shown that any surjectiveR-derivation onR[X,Y] having divergence zero is locally nilpotent. Connections with the Jacobian Conjecture are made.

Triangular monomial derivations on k[X1,X2,X3,X4] have kernel generated by at most four elements

Abstract It is shown that any triangular derivation on k [ X 1 , X 2 , X 3 , X 4 ] sending X i to a monomial has kernel generated by at most four elements, hence is finitely generated. An explicit formula for the generators is given.

The Automorphism Group Of

ABSTRACT The automorphism group of is studied, and a sufficient set of generators is given. Motivations for this theorem are given.

An Algorithm to Compute the Kernel of a Derivation up to a Certain Degree

An algorithm is described which computes generators of the kernel of derivations on kX1, . . . , Xn] up to a previously given bound. For w -homogeneous derivations it is shown that if the algorithm computes a generating set for the kernel, then this set is minimal.

Constructing (Almost) Rigid Rings and a UFD Having Infinitely Generated Derksen and Makar-Limanov Invariants

An example is given of a UFD which has infinitely generated Derksen invariant. The ring is “almost rigid” meaning that the Derksen invariant is equal to the Makar-Limanov invariant. Techniques to show that a ring is (almost) rigid are discussed, among which is a generalization of Mason’s abc-theorem.

The special automorphism group of R[t]/(tm)[x1,¿,xn] and coordinates of a subring of R[t][x1,¿,xn]

Let RR be a ring. The Special Automorphism Group SAutRR[x1,…,xn] is the set of all automorphisms with determinant of the Jacobian equal to 1. It is shown that the canonical map of SAutR[t]R[t][x1,…,xn] to SAutRmRm[x1,…,xn] where Rm≔R[t]/(tm)Rm≔R[t]/(tm) and Q⊂RQ⊂R is surjective. This result is used to study a particular case of the following question: if AA is a subring of a ring BB and f∈A[n]f∈A[n] is a coordinate over BB does it imply that ff is a coordinate over AA? It is shown that if A=R[tm,tm+1,…]⊂R[t]=BA=R[tm,tm+1,…]⊂R[t]=B then the answer to this question is “yes”. Also, a question on the Venereau polynomial is settled, which indicates another “coordinate-like property” of this polynomial.

Rigid Rings and Makar-Limanov Techniques

A ring is rigid if it admits no nonzero locally nilpotent derivation. Although a “generic” ring should be rigid, it is not trivial to show that a ring is rigid. 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 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 rings for which the question of rigidity remains unsettled.

RFID Security: Cryptography and Physics Perspectives

In this chapter, we provide an overview of mechanisms that are cheap to implement or integrate into RFID tags and that at the same time enhance their security and privacy properties. We emphasize solutions that make use of existing (or expected) functionality on the tag or that are inherently cheap and thus enhance the privacy friendliness of the technology “almost” for free. Technologies described include the use of environmental information (presence of light, temperature, humidity, etc.) to disable or enable the RFID tag, the use of delays to reveal parts of a secret key at different moments in time (this key is used to later establish a secure communication channel), and the idea of a “sticky tag,” which can be used to re-enable a disabled (or killed) tag whenever the user considers it to be safe. We discuss the security and describe usage scenarios for all solutions. Finally, we summarize previous works that use physical principles to provide security and privacy in RFID systems and the security-related functionality in RFID standards.