TY - JOUR
AB - We consider N × N Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive eigenvalues is of order 1/ N. Under suitable assumptions on the distribution of the single matrix element, we first prove that, away from the spectral edges, the empirical density of eigenvalues concentrates around the Wigner semicircle law on energy scales η ≫ N -1. This result establishes the semicircle law on the optimal scale and it removes a logarithmic factor from our previous result [6]. We then show a Wegner estimate, i.e., that the averaged density of states is bounded. Finally, we prove that the eigenvalues of a Wigner matrix repel each other, in agreement with the universality conjecture.
AU - László Erdös
AU - Schlein, Benjamin
AU - Yau, Horng-Tzer
ID - 2701
IS - 3
JF - International Mathematics Research Notices
TI - Wegner estimate and level repulsion for Wigner random matrices
ER -
TY - CONF
AB - Efficient zero-knowledge proofs of knowledge for group homomorphisms are essential for numerous systems in applied cryptography. Especially, Σ-protocols for proving knowledge of discrete logarithms in known and hidden order groups are of prime importance. Yet, while these proofs can be performed very efficiently within groups of known order, for hidden order groups the respective proofs are far less efficient.
This paper shows strong evidence that this efficiency gap cannot be bridged. Namely, while there are efficient protocols allowing a prover to cheat only with negligibly small probability in the case of known order groups, we provide strong evidence that for hidden order groups this probability is bounded below by 1/2 for all efficient Σ-protocols not using common reference strings or the like.
We prove our results for a comprehensive class of Σ-protocols in the generic group model, and further strengthen them by investigating certain instantiations in the plain model.
AU - Bangerter, Endre
AU - Camenisch, Jan
AU - Stephan Krenn
ED - Micciancio, Daniele
ID - 2978
TI - Efficiency Limitations for Σ-Protocols for Group Homomorphisms
VL - 5978
ER -
TY - CONF
AB - Zero-knowledge proofs of knowledge (ZK-PoK) are important building blocks for numerous cryptographic applications. Although ZK-PoK have a high potential impact, their real world deployment is typically hindered by their significant complexity compared to other (non-interactive) crypto primitives. Moreover, their design and implementation are time-consuming and error-prone.
We contribute to overcoming these challenges as follows: We present a comprehensive specification language and a compiler for ZK-PoK protocols based on Σ-protocols. The compiler allows the fully automatic translation of an abstract description of a proof goal into an executable implementation. Moreover, the compiler overcomes various restrictions of previous approaches, e.g., it supports the important class of exponentiation homomorphisms with hidden-order co-domain, needed for privacy-preserving applications such as DAA. Finally, our compiler is certifying, in the sense that it automatically produces a formal proof of the soundness of the compiled protocol for a large class of protocols using the Isabelle/HOL theorem prover.
AU - Almeida, José Bacelar
AU - Bangerter, Endre
AU - Barbosa, Manuel
AU - Stephan Krenn
AU - Sadeghi, Ahmad-Reza
AU - Schneider, Thomas
ED - Gritzalis, Dimitris
ED - Preneel, Bart
ED - Theoharidou, Marianthi
ID - 2979
TI - A Certifying Compiler for Zero-Knowledge Proofs of Knowledge Based on Sigma-Protocols
VL - 6345
ER -
TY - JOUR
AB - The epitaxial growth of germanium on silicon leads to the self-assembly of SiGe nanocrystals by a process that allows the size, composition and position of the nanocrystals to be controlled. This level of control, combined with an inherent compatibility with silicon technology, could prove useful in nanoelectronic applications. Here, we report the confinement of holes in quantum-dot devices made by directly contacting individual SiGe nanocrystals with aluminium electrodes, and the production of hybrid superconductor- semiconductor devices, such as resonant supercurrent transistors, when the quantum dot is strongly coupled to the electrodes. Charge transport measurements on weakly coupled quantum dots reveal discrete energy spectra, with the confined hole states displaying anisotropic gyromagnetic factors and strong spin-orbit coupling with pronounced dependences on gate voltage and magnetic field.
AU - Georgios Katsaros
AU - Spathis, Panayotis N
AU - Stoffel, Mathieu
AU - Fournel, Frank
AU - Mongillo, Massimo
AU - Bouchiat, Vincent
AU - Lefloch, François
AU - Rastelli, Armando
AU - Schmidt, Oliver G
AU - De Franceschi, Silvano
ID - 1752
IS - 6
JF - Nature Nanotechnology
TI - Hybrid superconductor-semiconductor devices made from self-assembled SiGe nanocrystals on silicon
VL - 5
ER -
TY - JOUR
AB - We investigate electronic transport in n-i-n GaN nanowires with and without AlN double barriers. The nanowires are grown by catalyst-free, plasma-assisted molecular beam epitaxy enabling abrupt GaN/AlN interfaces as well as longitudinal n-type doping modulation. At low temperature, transport in n-i-n GaN nanowires is dominated by the Coulomb blockade effect. Carriers are confined in the undoped middle region, forming single or multiple islands with a characteristic length of ∼100 nm. The incorporation of two AlN tunnel barriers causes confinement to occur within the GaN dot in between. In the case of a 6 nm thick dot and 2 nm thick barriers, we observe characteristic signatures of Coulomb-blockaded transport in single quantum dots with discrete energy states. For thinner dots and barriers, Coulomb-blockade effects do not play a significant role while the onset of resonant tunneling via the confined quantum levels is accompanied by a negative differential resistance surviving up to ∼150 K.
AU - Songmuang, Rudeeson
AU - Georgios Katsaros
AU - Monroy, Eva
AU - Spathis, Panayotis N
AU - Bougerol, Catherine
AU - Mongillo, Massimo
AU - De Franceschi, Silvano
ID - 1753
IS - 9
JF - Nano Letters
TI - Quantum transport in GaN/AlN double-barrier heterostructure nanowires
VL - 10
ER -